1. Scientific Background

Mountains affect the atmosphere over a wide range of scales and in many different ways. The most obvious one is by creating micro-climates, as temperature decreases with altitude, and cloud formation and precipitation are enhanced when the air is lifted over orography. However, many other more subtle but no less important effects exist. Flow over mountains generates internal gravity waves (generally known as mountain waves) (Smith, 1979), which if of sufficiently high amplitude are associated with flow configurations known as downslope windstorms (Klemp and Lilly, 1975). These storms may cause widespread damage on the lee slope of major mountain ranges, such the Rocky Mountains (Lilly, 1978), with costs that can rise up to several million dollars (Munoz, 2000). When trapped near the surface, mountain waves (then known as trapped lee waves) may lead to the formation of rotor circulations near the surface, where the mean flow reverses over short horizontal distances (Doyle and Durran, 2002); this is an important aviation safety hazard. Additionally, high-amplitude mountain waves often break aloft, either due to the effect of the decreasing density of air with height (McFarlane, 1987), or due to so-called critical levels, where the mean flow either stagnates (Booker and Bretherton, 1967) or rotates with height (Shutts, 1995). This wave breaking generates turbulence, which is one of the main sources for clear-air turbulence (CAT), another major aviation safety hazard (Sharman et al., 2006) that affects millions of people worldwide, with heavy costs in passenger injuries and aircraft maintenance (Abernethy, 2008).

On the other hand, through wave-mean flow interaction, mountains have a large impact on the global atmospheric circulation, which has been recognized for a long time (Palmer et al., 1986). Mountain waves exert a drag force on orography, and the corresponding reaction force acting on the atmosphere decelerates the mean large-scale circulation (Smith, 1979). This effect must be parameterized in global weather prediction models, and especially in climate models, which have a lower resolution, because the mountains that produce most of this force are not yet adequately taken into account explicitly at the resolutions currently employed (Kim et al., 2003). A correct representation of the drag is important not only for reproducing the intensity of the mid-latitude jets in numerical models, but also, via thermal-wind balance, to avoid temperature errors as large as 10 K in the stratosphere in the polar regions (Palmer et al., 1986). This is relevant to the formation of polar stratospheric clouds, which have a prominent role in ozone depletion (Solomon, 1999) and are very sensitive to these temperatures. Due to its dependence on the large-scale wind speed and static stability, gravity wave drag is likely to account for non-trivial feedbacks in climate change scenarios, where the mean values of such atmospheric parameters are expected to change. Finally, gravity wave drag is known to influence the intensity of the Brewer-Dobson circulation of the stratosphere (McLandress and Shepherd, 2009), which has an important role in the ventilation of ozone and other long-lived chemical species in the atmosphere (van Noije et al., 2004). Gravity wave drag therefore potentially has a substantial impact on the reliability of climate change forecasts.

However, existing drag parameterizations are very crude (Lott and Miller, 1997; Gregory et al., 1998), ignoring a number of dynamical effects, such as the variation of the wind and static stability with height, rotation of the Earth, non-hydrostaticity, etc. Trapped lee waves, which are intrinsically non-hydrostatic, are typically neglected in parameterizations (although a modification to include them was implemented for some time in the UK Met Office Unified Model - see Gregory et al., 1998 - but subsequently abandoned). These limitations may be responsible for part of the imbalance that has been found to occur in the global angular momentum budget as reproduced by numerical simulations (Huang et al., 1999; Egger and Hoinka, 2005).

The best way to formulate more complete, physically sound, drag parameterizations is by using mountain wave theory. Up to this point, mountain wave theory has largely fallen into two separate categories: linear theory (Smith, 1980), or fully nonlinear (e.g. hydraulic) theory (Long, 1953). Drag parameterizations are typically based on very simple linear theory, as explained above. This might have been adequate for applications when these parameterizations were developed (more than 10 years ago), but improvements since then in other aspects of weather and climate modelling mean that it is now overdue to revisit the drag parameterization problem, which in many areas is a limiting factor to the performance of weather and climate predictions (Shaw et al., 2009). Theoretical developments subsequent to the formulation of existing parameterizations, and the advent of much more realistic numerical simulations, offer prospects for rapid advances. Better predictions of the flow bifurcation into a fully nonlinear regime are needed. There is much evidence that this bifurcation is predictable from linear theory (as with hydraulic flow, e.g. Grubisic et al., 1995). Numerical simulations can help assess the validity of these predictions for the transition between linear and nonlinear flow. Recent advances in drag evaluation taking into account various physical processes currently neglected in drag parameterizations also need to be translated into the formulation of new parameterizations.

The broad problems outlined above will be addressed, focusing on the more specific aspects described next (from the local to the global scale).

Triggering mechanisms for downslope windstorms

Downslope windstorms are known to be intrinsically nonlinear, being induced by high amplitude mountain waves (Peltier and Clark, 1979). However, the transition from the low-amplitude flow regime (described by linear theory, e.g. Wang and Lin, 1999a) to the nonlinear regime is not well understood. Models aiming to explain these flows have taken distinct approaches: some of them are based on linear resonance in a multi-layered atmosphere (Klemp and Lilly, 1975), but the most successful model relies on a hydraulic analogy (Smith, 1985). Downslope windstorms are also associated with high-drag states, where mountain wave drag is much higher than estimated by linear theory (Wang and Lin, 1999b). These high-drag states have been investigated using numerical simulations with environmental critical levels (Clark and Peltier, 1984), where multiple drag maxima are produced as the critical level is lifted. Teixeira et al. (2005) showed that a linear two-layer model qualitatively reproduces the drag maxima in flow over a 3D mountain (Miranda and Valente, 1997), and that these maxima may be attributed, not to the effect of critical levels, but to the wind profile curvature maxima that accompany them. However, in flow over 2D mountains, some intermediate drag maxima predicted by linear theory are suppressed as the flow becomes more nonlinear (Bacmeister and Pierrehumbert, 1988), and the critical level appears to become the controlling feature. This suppression of intermediate drag maxima (and of the associated severe wind states) has decisive implications for the prediction of downslope windstorms. Here we intend to quantify the triggering mechanisms for downslope windstorms and high-drag states, which must be related to the transition between the linear and nonlinear flow regimes.

Diagnostics of lee-wave rotors

Lee-wave rotors, which are closed circulations with horizontal axes of rotation occurring on the lee of mountains, and associated with trapped lee waves, are also intrinsically nonlinear phenomena, characterized by flow reversal, and require consideration of friction to be accurately represented in numerical models (Doyle and Durran, 2002). These flow structures have great practical relevance for aviation safety (Darby and Poulos, 2006). Previous studies by Teixeira et al.(2013a, 2013b) have used linear theory to calculate the drag produced by trapped lee waves for simple piecewise-constant atmospheric profiles (something that, surprisingly, had not been done before). In one of these recent investigations (Teixeira et al., 2013b), it was noticed that linear trapped lee wave drag correlates well with the occurrence of rotors in numerical simulations including nonlinearity and friction (Vosper, 2004). Here we intend to discover what linear processes determine the formation of these nonlinear lee-wave rotors, by evaluating the drag for more general and realistic flows with continuous wind and stability profiles, and assessing the relationship between linear drag and rotor occurrence. This will enable the development of simple diagnostics for rotor formation based on key parameters of the incoming flow.

Methods for predicting clear-air turbulence

The importance of good CAT predictions for aviation safety has long been recognized (Dutton, 1971), and in recent years various methods have been developed for that purpose. The most widely-used method, known as Graphical Turbulence Guidance (GTG), uses a combination of diagnostics (based on the Richardson number, turbulent kinetic energy (TKE), eddy dissipation rate, frontogenesis function, etc.) to produce forecasts for the location and intensity of CAT (Sharman et al., 2006). Other methods use the mean flow deformation rate as the main diagnostic (Ellrod and Knapp, 1992). However, the physical basis of these methods is relatively weak. Recently, they have been criticized, and a new method was proposed (Knox et al., 2008), based on the Lighthill-Ford theory of spontaneous imbalance, which showed some improvement in forecast skill. This approach essentially assumes that CAT is generated by the radiation (and subsequent breaking) of gravity waves. More recently still, encouraging results were found using a method based on the Taylor-Goldstein equation without rotation (Kopec et al., 2011), which is the basis for linear mountain wave modelling. Gravity wave breaking is decisive for CAT generation, since it is an important source of turbulence (Jiang and Doyle, 2004), and directional wind shear, which is ubiquitous in the atmosphere, is one of the factors leading to wave breaking. Previously, Teixeira and Miranda (2005) had derived a wave breaking condition for resonant flow over a 2D ridge, but the topology of flows with directional shear over 3D orography is much more complex. Here we intend to evaluate the critical mountain height and other quantitative criteria for gravity wave breaking in flows with directional shear using high-resolution numerical simulations. From the ensuing physical insights, a new, physically-based, wave overturning condition for CAT forecast methods based on the Taylor-Goldstein equation will be formulated.

New drag parameterization formulations

Moving towards larger-scale processes, existing orographic drag parameterizations are very crude. In the UK Met Office and European Centre for Medium Range Weather Forecasts (ECMWF) parameterizations, the wave drag is calculated using a linear hydrostatic expression (Phillips, 1984), which does not take into account the variation of the wind or static stability with height. Over the last 10 years, analytical corrections to the drag due to vertical wind shear have been derived using linear theory. This was done for flow over an axisymmetric mountain (Teixeira et. al., 2004), over a 2D ridge (Teixeira and Miranda, 2004) and over a mountain with an elliptical horizontal cross-section (Teixeira and Miranda, 2006) (which is the kind of orography used in the ECMWF model to represent the world's mountain ranges in each grid box). More recently, Teixeira and Miranda (2009) evaluated the wave momentum fluxes (which have a direct impact in decelerating the mean atmospheric circulation) for directionally sheared flows over an axisymmetric mountain. The extension of these results to elliptical mountains is straightforward and will be carried out soon. Preliminary results from offline tests suggest that wind profile variations tend to increase the surface drag at the global scale (especially in Antarctica, where they may affect the strength of the polar vortex, see Miranda et al., 2009), but more systematic tests, using actual global model runs, are still lacking. We intend to implement and test these modifications to the drag parameterizations of the UK Met Office and ECMWF global models, through partnerships with these institutions. The inclusion of trapped lee-wave drag in these parameterizations will also be pursued.

2. Methodology and Work Plan

The problems outlined above will be tackled using a combination of theory (analytical and semi-analytical models) and numerical simulations (with a high-resolution version of the UK Met Office Unified Model). Problems involving waves (such as described above) lend themselves particularly well to semi-analytical methods, especially when asymptotic techniques allow one to achieve a certain degree of departure from idealized limits (e.g. Broutman et al., 2006). Numerical simulations, on the other hand, circumvent the problem of inadequate data sampling in field measurements, which may be especially acute for localized processes, such as downslope windstorms or rotors. Although there have been measurement campaigns addressing these processes (Mobbs et al., 2005; Sheridan and Vosper, 2012), such campaigns are, by nature, very expensive. Additionally, CAT can almost only be measured directly via chance encounters with aircraft, being inaccessible to most other means of detection apart from costly remote sensing techniques (Trier et al., 2012). Numerical simulations allow a much greater freedom and control over the flow conditions, and a better sampling of phenomena, at a considerably cheaper cost (Sheridan and Vosper, 2012; Smith and Skyllingstad, 2011), although their limitations as imperfect representations of reality must be borne in mind. Additionally, they may be used to perform idealized experiments, where simplified conditions are considered, and physical processes may be turned on or off, allowing a better identification of key mechanisms at work in each problem (Vosper, 2004; Grubisic and Stiperski, 2009). They are also useful for testing analytical and semi-analytical models outside their strict regimes of validity. Finally, this kind of approach encourages collaborations between theoreticians and numerical modellers.

Work plan

Concerning the triggering of downslope windstorms, the transition between linear and nonlinear mountain wave flow regimes will be modelled using a weakly-nonlinear approximation to solve Long's equation (Long, 1953). A similar approach, but considering an incoming flow with constant wind and static stability, was adopted previously by Miles and Huppert (1969) to obtain a leading-order correction to mountain wave drag due to nonlinearity. Since the resonant processes that lead to downslope windstorms and high-drag states are believed to rely on wind or stability profile effects (Smith, 1985; Scinocca and Peltier, 1991), here a sheared mean wind will be assumed. The solution to Long's equation is then considerably more complicated because that equation becomes nonlinear. However, previous numerical simulations suggest that this approach is likely to account for essential features of nonlinear flow. Firstly, Teixeira et al. (2008) showed that the drag for flow with a critical level at high Richardson number over low amplitude mountains displayed a large enhancement, which means that substantial mountain wave amplification can occur even in weakly nonlinear flow. Secondly, Teixeira et al. (2005) demonstrated that the suppression of intermediate drag maxima in high-drag states also starts to occur for relatively weak nonlinearity. Therefore, a weakly-nonlinear model should be appropriate. Results from this model will be compared to those of numerical simulations, to delimit their range of applicability and extend the results beyond that range.

Concerning lee-wave rotor diagnostics, our theoretical knowledge is still at an earlier stage, so essentially linear theory and numerical simulations will be carried out. The numerical simulations of Vosper (2004) that were compared with the linear trapped lee-wave calculations of Teixeira et al. (2013b), showing an apparent correlation between this quantity and the occurrence of rotors, considered lee waves trapped at an inversion capping a neutral atmospheric layer near the surface. The link between drag and lee-wave rotors will be further quantified by carrying out numerical simulations over a wider parameter range for this situation, and also for the two-layer atmosphere originally proposed by Scorer (1949) (where the lee waves are trapped within the lower, most stable layer near the surface), comparing them with the linear trapped lee-wave drag calculated by Teixeira et al., (2013a). After these exploratory calculations, both analytical theory and numerical simulations will be used to tackle more realistic situations where the wind velocity and static stability vary continuously. A good example of this is the linearly increasing velocity profile of Wurtele et al. (1987). This will allow the formulation of diagnostics for rotor formation with a more general applicability. The linear calculations adopted in this latter case will be performed using the Wentzel-Kramers-Brillouin (WKB) approximation including the effect of turning points (Broutman et al., 2006).

Concerning CAT prediction, numerical simulations will be carried out of mountain waves in flows with directional shear. While it is well established that wave breaking will always occur some distance below critical levels (where the flow stagnates) in flows with unidirectional shear (Booker and Bretherton, 1967), the situation is more complex in flows with directional shear over 3D orography. For this situation, which is much more realistic and in fact ubiquitous in nature, critical levels have a continuous distribution with height, so the wave amplification they induce is weakened, and it is not yet clear whether wave breaking will always occur. Calculations using linear theory by Broad (1995) suggest that breaking always occurs, but some of the underlying assumptions, such as the formulation of a breaking criterion in Fourier space (when wave breaking is a localized process in physical space) seem questionable. Here, numerical simulations will be performed to understand wave breaking in directionally sheared flows at a fundamental level. A good idealized case to begin with is that of waves forced by an axisymmetric mountain for a wind of constant magnitude that turns with height, such as assumed by Teixeira et al. (2004) and Teixeira and Miranda (2009). The critical mountain height for wave breaking will be determined for different values of the Richardson number, and mountain width (which controls non-hydrostatic effects). Using linear theory, and taking the results of the numerical simulations as guidance, a wave overturning condition for use in CAT forecast methods based on the Taylor-Goldstein equation (e.g. Kopec et al., 2011) will be formulated. This wave overturning condition will be assessed against high-resolution numerical simulations with realistic orography and wind profiles.

Finally, concerning the formulation of orographic drag parameterization schemes, the wave drag expressions that are currently employed in the UK Met Office and ECMWF parameterizations will be reformulated to take into account wind profile effects, and subsequently tested. This will be based on the modifications to the drag due to wind shear previously derived, which broadly fall into two categories: corrections to the surface drag (Teixeira and Miranda, 2004, 2006; Teixeira et al., 2004), or corrections to the divergence of the wave momentum flux at critical levels (Teixeira and Miranda, 2009). An assessment of the modified surface drag, using reanalysis data and orography representative of the Earth's mountain ranges was carried out by Miranda et al. (2009), suggesting that the drag tends to increase due to wind profile effects, especially in Antarctica. Analogous sensitivity tests still need to be made for the variation of the wave momentum flux with height. High-resolution numerical simulations using real orography will be used for that purpose. When both components of the revised drag parameterization have been implemented in the UK Met Office and ECMWF global models, these models will be run in order to check whether the forecast skill is improved. This will nake use of existing collaborations with Dr Simon Vosper, at the UK Met Office, and Dr Anton Beljaars, at ECMWF. Another aspect of drag parameterization which requires revision is the representation of trapped lee wave drag. Recent work on this subject by Teixeira et al. (2013a, 2013b), as well as future work on rotors, included in the present project, will help to develop a new parameterization of this effect.

3. Impact and Dissemination

The results obtained in this project concerning downslope windstorms, lee-wave rotors and CAT will be exploited to improve our understanding of the triggering processes and modelling capability of these phenomena, and develop innovative operational methods to predict them. The reformulation of the drag parameterization schemes taking into account the vertical variation of the wind will be exploited ultimately for improving the skill of weather forecasts in an operational context, and also the skill of climate forecasts, including those of future climate scenarios. This will be achieved through collaborations with the UK Met Office and ECMWF, where seminars and talks will be presented on these subjects. Over the duration of the project, collaborations with other operational centres and opportunities to give seminars and talks will be sought.

Relevant scientific contributions resulting from the planned research will be published in leading international journals, such as the Journal of the Atmospheric Sciences and Quarterly Journal of the Royal Meteorological Society, whose scope includes studies focused on the fundamental physics and dynamics of the atmosphere. A review on gravity wave drag will be prepared for a higher-impact journal. Results will also be presented at international conferences, particularly those specifically targeting Mountain Meteorology. A workshop about the effects of orography on the atmosphere will be organized, to bring together experts in this research area, and share results. Participation in other workshops with relevant themes will also be sought.

Publications and other research outputs from this project will be publicized in Centaur, the University of Reading repository of publications authored by members of staff, in the professional web page of the PI at the Department of Meteorology and also in the web page of the Mountain Meteorology group (when it exists). These web pages will be developed gradually, as the project's planned research activities unravel. Additionally, a web page specifically dedicated to the project will be created and maintained, where information on the research progress will be disseminated. This information will be of differing technical levels, including results aimed at a more specialized audience, but also some content directed at the general public. In this page, the progress of the work plan will be monitored, namely, by publicizing the associated deliverables (published journal articles, presentations in conferences, participation in workshops, seminars and invited talks, etc.).

Outreach

During the project, the PI will respond to any media requests for comments in his area of expertise. He will also build, improve and update regularly his personal and group web pages hosted by the Department of Meteorology, so as to reflect his research interests and ongoing projects, in a form understandable by the general public.

Seminars will be given at the UK Met Office and at ECMWF, in order to present to a wider community the main findings of the activities planned in this project. The operational impact of this research, reflected in the new gravity wave drag parameterizations incorporated into the UK Met Office and ECMWF weather prediction and climate models, counts as outreach, in the sense that it will have an impact on the skill of weather and climate forecasts, which concern society as a whole.

The project will lead to the organization of workshops and/or summer schools aimed at students at various levels, taking place at the Department of Meteorology or elsewhere, during the last 2 years of the project. The PI will be available for getting involved in visits to universities and community organizations, to promote the research developed in the project. The project's findings, or related aspects, will also be showcased in the Open Day of the Department of Meteorology, where students and the general public visit this research institution and receive first-hand experience of our activities. the PI will be available to give public talks and write articles in newspapers about the results of this research and how they are practically relevant to the general public. Finally, the project may lead to the preparation of e-Newsletters and Fact Sheets to be released on the internet to the attention of the public at large. Some of these activities are likely to be organized and promoted by the Walker Institute for Climate System Research, which is part of the Department of Meteorology and helps in organizing dissemination and stakeholder events, including outreach activities directed at the general public. It will be ensured that the research produced by this project is well represented at these events.

These events are expected to have societal impact by attracting students to a scientific career. Since specific output from the present project is expected to be used to substantiate these outreach activities, it is preferable that they take place towards the end of the project. All of these events will be publicized on the web.

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