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.

Is missing orographic gravity wave drag near 60°S the cause of the stratospheric zonal wind biases in chemistry–climate models?

Nearly all chemistry–climate models (CCMs) have a systematic bias of a delayed springtime breakdown of the Southern Hemisphere (SH) stratospheric polar vortex, implying insufficient stratospheric wave drag. In this study the Canadian Middle Atmosphere Model (CMAM) and the CMAM Data Assimilation System (CMAM-DAS) are used to investigate the cause of this bias. Zonal wind analysis increments from CMAMDAS reveal systematic negative values in the stratosphere near 608S in winter and early spring. These are interpreted as indicating a bias in the model physics, namely, missing gravity wave drag (GWD). The negative analysis increments remain at a nearly constant height during winter and descend as the vortex weakens, much like orographic GWD. This region is also where current orographic GWD parameterizations have a gap in wave drag, which is suggested to be unrealistic because of missing effects in those parameterizations. These findings motivate a pair of free-runningCMAMsimulations to assess the impact of extra orographicGWDat 608S. The control simulation exhibits the cold-pole bias and delayed vortex breakdown seen in the CCMs. In the simulation with extra GWD, the cold-pole bias is significantly reduced and the vortex breaks down earlier. Changes in resolved wave drag in the stratosphere also occur in response to the extra GWD, which reduce stratospheric SH polar-cap temperature biases in late spring and early summer. Reducing the dynamical biases, however, results in degraded Antarctic column ozone. This suggests that CCMs that obtain realistic column ozone in the presence of an overly strong and persistent vortex may be doing so through compensating errors.

Large-scale dynamics of the mesosphere and lower thermosphere: an analysis using the extended Canadian Middle Atmosphere Model

The extended Canadian Middle Atmosphere Model is used to investigate the large-scale dynamics of the mesosphere and lower thermosphere (MLT). It is shown that the 4-day wave is substantially amplified in southern polar winter in the presence of instabilities arising from strong vertical shears in the MLT zonal mean zonal winds brought about by parameterized nonorographic gravity wave drag. A weaker 4-day wave in northern polar winter is attributed to the weaker wind shears that result from weaker parameterized wave drag. The 2-day wave also exhibits a strong dependence on zonal wind shears, in agreement with previous modeling studies. In the equatorial upper mesosphere, the migrating diurnal tide provides most of the resolved westward wave forcing, which varies semiannually in conjunction with the tide itself; resolved forcing by eastward traveling disturbances is dominated by smaller scales. Nonmigrating tides and other planetary-scale waves play only a minor role in the zonal mean zonal momentum budget in the tropics at these heights. Resolved waves are shown to play a significant role in the zonal mean meridional momentum budget in the MLT, impacting significantly on gradient wind balance. Balance fails at low latitudes as a result of a strong Reynolds stress associated with the migrating diurnal tide, an effect which is most pronounced at equinox when the tide is strongest. Resolved and parameterized waves account for most of the imbalance at higher latitudes in summer. This results in the gradient wind underestimating the actual eastward wind reversal by up to 40%.

Climatology and predictability of the late summer stratospheric zonal wind turnaround over Vanscoy, Saskatchewan

A climatology of the late summer stratospheric zonal wind turnaround phenomenon is presented, with a particular focus on the behaviour over the Meteorological Service of Canada’s balloon-launching site at Vanscoy, Saskatchewan (52°N, 107°W). Turnaround refers to the change in sign of the zonal wind velocity and occurs twice each year at stratospheric mid-latitudes, in early spring and in late summer. The late summer turnaround is of particular interest to the high-altitude ballooning community because it offers the ideal conditions for launch, but it is also an interesting dynamical phenomenon in its own right. It is studied here using both the National Centers for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR) reanalysis and the United Kingdom Meteorological Office (MetO) analysis products as well as climate simulation data from the Canadian Middle Atmosphere Model (CMAM). The phenomenon and its interannual variability are documented. The predictability of the late summer turnaround over Vanscoy is investigated using both statistical averages and autocorrelation analysis. From the statistical averages, it is found that during every year since 1993, the period from 26 August to 5 September has contained appropriate launch dates. From the autocorrelation analysis, it is found that stratospheric zonal wind anomalies can persist for a month or more during most of the summer, but there is a predictability horizon at the end of the summer — just before turnaround

Extended Canadian middle atmosphere model: zonal-mean climatology and physical parameterizations

This paper describes the energetics and zonal-mean state of the upward extension of the Canadian Middle Atmosphere Model, which extends from the ground to ~210 km. The model includes realistic parameterizations of the major physical processes from the ground up to the lower thermosphere and exhibits a broad spectrum of geophysical variability. The rationale for the extended model is to examine the nature of the physical and dynamical processes in the mesosphere/lower thermosphere (MLT) region without the artificial effects of an imposed sponge layer which can modify the circulation in an unrealistic manner. The zonal-mean distributions of temperature and zonal wind are found to be in reasonable agreement with observations in most parts of the model domain below ~150 km. Analysis of the global-average energy and momentum budgets reveals a balance between solar extreme ultraviolet heating and molecular diffusion and a thermally direct viscous meridional circulation above 130 km, with the viscosity coming from molecular diffusion and ion drag. Below 70 km, radiative equilibrium prevails in the global mean. In the MLT region between ~70 and 120 km, many processes contribute to the global energy budget. At solstice, there is a thermally indirect meridional circulation driven mainly by parameterized nonorographic gravity-wave drag. This circulation provides a net global cooling of up to 25 K d^-1.

Southern annular mode dynamics in observations and models, Part I: The influence of climatological zonal wind biases in a comprehensive GCM

A common bias among global climate models (GCMs) is that they exhibit tropospheric southern annular mode (SAM) variability that is much too persistent in the Southern Hemisphere (SH) summertime. This is of concern for the ability to accurately predict future SH circulation changes, so it is important that it be understood and alleviated. In this two-part study, specifically targeted experiments with the Canadian Middle Atmosphere Model (CMAM) are used to improve understanding of the enhanced summertime SAM persistence. Given the ubiquity of this bias among comprehensive GCMs, it is likely that the results will be relevant for other climate models. Here, in Part I, the influence of climatological circulation biases on SAM variability is assessed, with a particular focus on two common biases that could enhance summertime SAM persistence: the too-late breakdown of the Antarctic stratospheric vortex and the equatorward bias in the SH tropospheric midlatitude jet. Four simulations are used to investigate the role of each of these biases in CMAM. Nudging and bias correcting procedures are used to systematically remove zonal-mean stratospheric variability and/or remove climatological zonal wind biases. The SAM time-scale bias is not alleviated by improving either the timing of the stratospheric vortex breakdown or the climatological jet structure. Even in the absence of stratospheric variability and with an improved climatological circulation, the model time scales are biased long. This points toward a bias in internal tropospheric dynamics that is not caused by the tropospheric jet structure bias. The underlying cause of this is examined in more detail in Part II of this study.

The dependence of southern ocean meridional overturning on wind stress

An eddy-resolving numerical model of a zonal flow, meant to resemble the Antarctic Circumpolar Current, is described and analyzed using the framework of J. Marshall and T. Radko. In addition to wind and buoyancy forcing at the surface, the model contains a sponge layer at the northern boundary that permits a residual meridional overturning circulation (MOC) to exist at depth. The strength of the residual MOC is diagnosed for different strengths of surface wind stress. It is found that the eddy circulation largely compensates for the changes in Ekman circulation. The extent of the compensation and thus the sensitivity of the MOC to the winds depend on the surface boundary condition. A fixed-heat-flux surface boundary severely limits the ability of the MOC to change. An interactive heat flux leads to greater sensitivity. To explain the MOC sensitivity to the wind strength under the interactive heat flux, transformed Eulerian-mean theory is applied, in which the eddy diffusivity plays a central role in determining the eddy response. A scaling theory for the eddy diffusivity, based on the mechanical energy balance, is developed and tested; the average magnitude of the diffusivity is found to be proportional to the square root of the wind stress. The MOC sensitivity to the winds based on this scaling is compared with the true sensitivity diagnosed from the experiments.

Balance model for equatorial long waves

Geophysical fluid models often support both fast and slow motions. As the dynamics are often dominated by the slow motions, it is desirable to filter out the fast motions by constructing balance models. An example is the quasi geostrophic (QG) model, which is used widely in meteorology and oceanography for theoretical studies, in addition to practical applications such as model initialization and data assimilation. Although the QG model works quite well in the mid-latitudes, its usefulness diminishes as one approaches the equator. Thus far, attempts to derive similar balance models for the tropics have not been entirely successful as the models generally filter out Kelvin waves, which contribute significantly to tropical low-frequency variability. There is much theoretical interest in the dynamics of planetary-scale Kelvin waves, especially for atmospheric and oceanic data assimilation where observations are generally only of the mass field and thus do not constrain the wind field without some kind of diagnostic balance relation. As a result, estimates of Kelvin wave amplitudes can be poor. Our goal is to find a balance model that includes Kelvin waves for planetary-scale motions. Using asymptotic methods, we derive a balance model for the weakly nonlinear equatorial shallow-water equations. Specifically we adopt the ‘slaving’ method proposed by Warn et al. (Q. J. R. Meteorol. Soc., vol. 121, 1995, pp. 723–739), which avoids secular terms in the expansion and thus can in principle be carried out to any order. Different from previous approaches, our expansion is based on a long-wave scaling and the slow dynamics is described using the height field instead of potential vorticity. The leading-order model is equivalent to the truncated long-wave model considered previously (e.g. Heckley & Gill, Q. J. R. Meteorol. Soc., vol. 110, 1984, pp. 203–217), which retains Kelvin waves in addition to equatorial Rossby waves. Our method allows for the derivation of higher-order models which significantly improve the representation of Rossby waves in the isotropic limit. In addition, the ‘slaving’ method is applicable even when the weakly nonlinear assumption is relaxed, and the resulting nonlinear model encompasses the weakly nonlinear model. We also demonstrate that the method can be applied to more realistic stratified models, such as the Boussinesq model.

Observations of wind speed profiles over Greater London, UK, using a Doppler lidar

To calculate the potential wind loading on a tall building in an urban area, an accurate representation of the wind speed profile is required. However, due to a lack of observations, wind engineers typically estimate the characteristics of the urban boundary layer by translating the measurements from a nearby reference rural site. This study presents wind speed profile data obtained from a Doppler lidar in central London, UK, during an 8 month observation period. Used in conjunction with wind speed data measured at a nearby airport, the data have been used to assess the accuracy of the predictions made by the wind engineering tools currently available. When applied to multiple changes in surface roughness identified from morphological parameters, the non-equilibrium wind speed profile model developed by Deaves (1981) provides a good representation of the urban wind speed profile. For heights below 500 m, the predicted wind speed remains within the 95% confidence interval of the measured data. However, when the surface roughness is estimated using land use as a proxy, the model tends to overestimate the wind speed, particularly for very high wind speed periods. These results highlight the importance of a detailed assessment of the nature of the surface when estimating the wind speed above an urban surface.

Response of tropical cyclones to idealized climate change experiments in a global high resolution coupled general circulation model

We present an assessment of how tropical cyclone activity might change due to the influence of increased atmospheric carbon dioxide concentrations, using the UK’s High Resolution Global Environment Model (HiGEM) with N144 resolution (~90 km in the atmosphere and ~40 km in the ocean). Tropical cyclones are identified using a feature tracking algorithm applied to model output. Tropical cyclones from idealized 30-year 2×CO2 (2CO2) and 4×CO2 (4CO2) simulations are compared to those identified in a 150-year present-day simulation, which is separated into a 5-member ensemble of 30-year integrations. Tropical cyclones are shown to decrease in frequency globally by 9% in the 2CO2 and 26% in the 4CO2. Tropical cyclones only become more intese in the 4CO2, however uncoupled time slice experiments reveal an increase in intensity in the 2CO2. An investigation into the large-scale environmental conditions, known to influence tropical cyclone activity in the main development regions, is used to determine the response of tropical cyclone activity to increased atmospheric CO2. A weaker Walker circulation and a reduction in zonally averaged regions of updrafts lead to a shift in the location of tropical cyclones in the northern hemisphere. A decrease in mean ascent at 500 hPa contributes to the reduction of tropical cyclones in the 2CO2 in most basins. The larger reduction of tropical cyclones in the 4CO2 arises from further reduction of mean ascent at 500 hPa and a large enhancement of vertical wind shear, especially in the southern hemisphere, North Atlantic and North East Pacific.

Proactive R&D management and firm growth: a punctuated equilibrium model

The external environment is characterized by periods of relative stability interspersed with periods of extreme change, implying that high performing firms must practice exploration and exploitation in order to survive and thrive. In this paper, we posit that R&D expenditure volatility indicates the presence of proactive R&D management, and is evidence of a firm moving from exploitation to exploration over time. This is consistent with a punctuated equilibrium model of R&D investment where shocks are induced by reactions to external turbulence. Using an unbalanced panel of almost 11,000 firm-years from 1997 to 2006, we show that greater fluctuations in the firm's R&D expenditure over time are associated with higher firm growth. Developing a contextual view of the relationship between R&D expenditure volatility and firm growth, we find that this relationship is weaker among firms with higher levels of corporate diversification and negative among smaller firms and those in slow clockspeed industries.

Estimating the potential yield of small wind turbines in urban areas: a case study for Greater London, UK

To optimise the placement of small wind turbines in urban areas a detailed understanding of the spatial variability of the wind resource is required. At present, due to a lack of observations, the NOABL wind speed database is frequently used to estimate the wind resource at a potential site. However, recent work has shown that this tends to overestimate the wind speed in urban areas. This paper suggests a method for adjusting the predictions of the NOABL in urban areas by considering the impact of the underlying surface on a neighbourhood scale. In which, the nature of the surface is characterised on a 1 km2 resolution using an urban morphology database. The model was then used to estimate the variability of the annual mean wind speed across Greater London at a height typical of current small wind turbine installations. Initial validation of the results suggests that the predicted wind speeds are considerably more accurate than the NOABL values. The derived wind map therefore currently provides the best opportunity to identify the neighbourhoods in Greater London at which small wind turbines yield their highest energy production. The model does not consider street scale processes, however previously derived scaling factors can be applied to relate the neighbourhood wind speed to a value at a specific rooftop site. The results showed that the wind speed predicted across London is relatively low, exceeding 4 ms-1 at only 27% of the neighbourhoods in the city. Of these sites less than 10% are within 10 km of the city centre, with the majority over 20 km from the city centre. Consequently, it is predicted that small wind turbines tend to perform better towards the outskirts of the city, therefore for cities which fit the Burgess concentric ring model, such as Greater London, ‘distance from city centre’ is a useful parameter for siting small wind turbines. However, there are a number of neighbourhoods close to the city centre at which the wind speed is relatively high and these sites can only been identified with a detailed representation of the urban surface, such as that developed in this study.

Representation of model error in a convective-scale ensemble prediction system

In this paper ensembles of forecasts (of up to six hours) are studied from a convection-permitting model with a representation of model error due to unresolved processes. The ensemble prediction system (EPS) used is an experimental convection-permitting version of the UK Met Office’s 24- member Global and Regional Ensemble Prediction System (MOGREPS). The method of representing model error variability, which perturbs parameters within the model’s parameterisation schemes, has been modified and we investigate the impact of applying this scheme in different ways. These are: a control ensemble where all ensemble members have the same parameter values; an ensemble where the parameters are different between members, but fixed in time; and ensembles where the parameters are updated randomly every 30 or 60 min. The choice of parameters and their ranges of variability have been determined from expert opinion and parameter sensitivity tests. A case of frontal rain over the southern UK has been chosen, which has a multi-banded rainfall structure. The consequences of including model error variability in the case studied are mixed and are summarised as follows. The multiple banding, evident in the radar, is not captured for any single member. However, the single band is positioned in some members where a secondary band is present in the radar. This is found for all ensembles studied. Adding model error variability with fixed parameters in time does increase the ensemble spread for near-surface variables like wind and temperature, but can actually decrease the spread of the rainfall. Perturbing the parameters periodically throughout the forecast does not further increase the spread and exhibits “jumpiness” in the spread at times when the parameters are perturbed. Adding model error variability gives an improvement in forecast skill after the first 2–3 h of the forecast for near-surface temperature and relative humidity. For precipitation skill scores, adding model error variability has the effect of improving the skill in the first 1–2 h of the forecast, but then of reducing the skill after that. Complementary experiments were performed where the only difference between members was the set of parameter values (i.e. no initial condition variability). The resulting spread was found to be significantly less than the spread from initial condition variability alone.

Unsteady flow simulation of a vertical axis augmented wind turbine: a two-dimensional study

As the integration of vertical axis wind turbines in the built environment is a promising alternative to horizontal axis wind turbines, a 2D computational investigation of an augmented wind turbine is proposed and analysed. In the initial CFD analysis, three parameters are carefully investigated: mesh resolution; turbulence model; and time step size. It appears that the mesh resolution and the turbulence model affect result accuracy; while the time step size examined, for the unsteady nature of the flow, has small impact on the numerical results. In the CFD validation of the open rotor with secondary data, the numerical results are in good agreement in terms of shape. It is, however, observed a discrepancy factor of 2 between numerical and experimental data. Successively, the introduction of an omnidirectional stator around the wind turbine increases the power and torque coefficients by around 30–35% when compared to the open case; but attention needs to be given to the orientation of the stator blades for optimum performance. It is found that the power and torque coefficients of the augmented wind turbine are independent of the incident wind speed considered.

An aggregated wind power generation model based on MERRA reanalysis data: MATLAB model and example data for the April 2014 wind farm distribution of Great Britain.

The MATLAB model is contained within the compressed folders (versions are available as .zip and .tgz). This model uses MERRA reanalysis data (>34 years available) to estimate the hourly aggregated wind power generation for a predefined (fixed) distribution of wind farms. A ready made example is included for the wind farm distribution of Great Britain, April 2014 ("CF.dat"). This consists of an hourly time series of GB-total capacity factor spanning the period 1980-2013 inclusive. Given the global nature of reanalysis data, the model can be applied to any specified distribution of wind farms in any region of the world. Users are, however, strongly advised to bear in mind the limitations of reanalysis data when using this model/data. This is discussed in our paper: Cannon, Brayshaw, Methven, Coker, Lenaghan. "Using reanalysis data to quantify extreme wind power generation statistics: a 33 year case study in Great Britain". Submitted to Renewable Energy in March, 2014. Additional information about the model is contained in the model code itself, in the accompanying ReadMe file, and on our website: http://www.met.reading.ac.uk/~energymet/data/Cannon2014/