Climate scientists have a lot of insight into the factors driving weather systems in the mid-latitudes, where the rotation of the earth is an important influence. The tropics are less well served, and this can be a problem for global climate models which don’t capture many of the phenomena observed in the tropics that well.
What we do know about the tropics however is that despite significant contrasts in sea surface temperatures (Fig. 1) there is very little horizontal temperature variation in the atmosphere (Fig. 2) – because the Coriolis force (due to the Earth’s rotation) that enables this gradient in more temperate climates is not present. We believe that the large-scale circulation acts to minimise the effect these surface contrasts have higher up. This suggests a model for vertical wind which cools the air over warmer surfaces and warms it where the surface is cool, called the Weak Temperature Gradient (WTG) Approximation, that is frequently used in studying the climate in the tropics.
Thermodynamic ideas have been around for some 200 years. Carnot, a Frenchman worried about Britain’s industrial might underpinning its military potential(!), studied the efficiency of heat engines and showed that the maximum mechanical work generated by an engine is determined by the ratio of the temperatures at which energy enters and leaves the system. It is possible to treat climate systems as heat engines – for example Kerry Emanuel has used Carnot’s idea to estimate the pressure in the eye of a hurricane. I have been building on a recent development of these ideas by Olivier Pauluis at New York University who shows how to divide up the maximum work output of a climate heat engine into the generation of wind, the lifting of moisture and a lost component, which he calls the Gibbs penalty, which is the energetic cost of keeping the atmosphere moist. Typically, 50% of the maximum work output is gobbled up by the Gibbs penalty, 30% is the moisture lifting term and only 20% is used to generate wind.
For my PhD, I have been applying Pauluis’ ideas to a modelled system consisting of two connected tropical regions (one over a cooler surface than the other), which are connected by a circulation given by the weak temperature gradient approximation. I look at how this circulation affects the components of work done by the system. Overall there is no impact – in other words the WTG does not distort the thermodynamics of the underlying system – which is reassuring for those who use it. What is perhaps more interesting however, is that even though the WTG circulation is very weak compared to the winds that we observe in the two columns, it does as much work as is done by the cooler column – in other words its thermodynamic importance is huge. This suggests that further avenues of study may help us better express what drives the climate in the tropics.
When modelling urban areas, vegetation is often ignored in attempt to simplify an already complex problem. However, vegetation is present in all urban environments and it is not going anywhere… For reasons ranging from sustainability to improvements in human well-being, green spaces are increasingly becoming part of urban planning agendas. Incorporating vegetation is therefore a key part of modelling urban climates. Vegetation provides numerous (dis)services in the urban environment, each of which requires individual attention (Salmond et al. 2016). However, one of my research interests is how vegetation influences the aerodynamic properties of urban areas.
Two aerodynamic parameters can be used to represent the aerodynamic properties of a surface: the zero-plane displacement (zd) and aerodynamic roughness length (z0). The zero-plane displacement is the vertical displacement of the wind-speed profile due to the presence of surface roughness elements. The aerodynamic roughness length is a length scale which describes the magnitude of surface roughness. Together they help define the shape and form of the wind-speed profile which is expected above a surface (Fig. 1).
Figure 1: Representation of the wind-speed profile above a group of roughness elements. The black dots represent an idealised logarithmic wind-speed profile which is determined using the zero-plane displacement (zd) and aerodynamic roughness length (z0) (lines) of the surface.
For an urban site, zd and z0 may be determined using three categories of methods: reference-based, morphometric and anemometric. Reference-based methods require a comparison of the site to previously published pictures or look up tables (e.g. Grimmond and Oke 1999); morphometric methods describe zd and z0 as a function of roughness-element geometry; and, anemometric methods use in-situ observations. The aerodynamic parameters of a site may vary considerably depending upon which of these methods are used, but efforts are being made to understand which parameters are most appropriate to use for accurate wind-speed estimations (Kent et al. 2017a).
Within the morphometric category (i.e. using roughness-element geometry) sophisticated methods have been developed for buildings or vegetation only. However, until recently no method existed to describe the effects of both buildings and vegetation in combination. A recent development overcomes this, whereby the heights of all roughness elements are considered alongside a porosity correction for vegetation (Kent et al. 2017b). Specifically, the porosity correction is applied to the space occupied and drag exerted by vegetation.
The development is assessed across several areas typical of a European city, ranging from a densely-built city centre to an urban park. The results demonstrate that where buildings are the dominant roughness elements (i.e. taller and occupying more space), vegetation does not obviously influence the calculated geometry of the surface, nor the aerodynamic parameters and the estimated wind speed. However, as vegetation begins to occupy a greater amount of space and becomes as tall as (or larger) than buildings, the influence of vegetation is obvious. Expectedly, the implications are greatest in an urban park, where overlooking vegetation means that wind speeds may be slowed by up to a factor of three.
Up to now, experiments such as those in the wind tunnel focus upon buildings or trees in isolation. Certainly, future experiments which consider both buildings and vegetation will be valuable to continue to understand the interaction within and between these roughness elements, in addition to assessing the parameterisation.
Grimmond CSB, Oke TR (1999) Aerodynamic properties of urban areas derived from analysis of surface form. J Appl Meteorol and Clim 38:1262-1292.
Kent CW, Grimmond CSB, Barlow J, Gatey D, Kotthaus S, Lindberg F, Halios CH (2017a) Evaluation of Urban Local-Scale Aerodynamic Parameters: Implications for the Vertical Profile of Wind Speed and for Source Areas. Boundary-Layer Meteorology 164: 183-213.
Kent CW, Grimmond CSB, Gatey D (2017b) Aerodynamic roughness parameters in cities: Inclusion of vegetation. Journal of Wind Engineering and Industrial Aerodynamics 169: 168-176.
Salmond JA, Tadaki M, Vardoulakis S, Arbuthnott K, Coutts A, Demuzere M, Dirks KN, Heaviside C, Lim S, Macintyre H (2016) Health and climate related ecosystem services provided by street trees in the urban environment. Environ Health 15:95.
For a small city, Delft punches above its weight. It is famous for many things, including its celebrated Delftware (Figure 1). It was also the birthplace of one of the Dutch masters, Johannes Vermeer, who coincidentally painted some fine cityscapes with cumulus clouds in them (Figure 2). There is a university of technology with some impressive architecture (Figure 3). It holds the dubious honour of being the location of the first assassination using a pistol (or so we were told by our tour guide), when William of Orange was shot in 1584. To this list, it can now add hosting a one-week conference on the future of cumulus parametrization, and hopefully bringing about more of these conferences in the future.
Figure 1: Delftware.
Figure 2: Delft with canopy of cumulus clouds. By Johannes Vermeer, 1661.
Figure 3: AULA conference centre at Delft University of Technology – where we were based for the duration of the conference.
So what is a cumulus parametrization scheme? The key idea is as follows. Numerical weather and climate models work by splitting the atmosphere into a grid, with a corresponding grid length representing the length of each of the grid cells. By solving equations that govern how the wind, pressure and heating interact, models can then be used to predict what the weather will be like days in advance in the case of weather modelling. Or a model can predict how the climate will react to any forcings over longer timescales. However, any phenomena that are substantially smaller than this grid scale will not be “seen” by the models. For example, a large cumulonimbus cloud may have a horizontal extent of around 2km, whereas individual grid cells could be 50km in the case of a climate model. A cumulonimbus cloud will therefore not be explicitly modelled, but it will still have an effect on the grid cell in which it is located – in terms of how much heating and moistening it produces at different levels. To capture this effect, the clouds are parametrized, that is, the vertical profile of the heating and moistening due to the clouds are calculated based on the conditions in the grid cell, and this then affects the grid-scale values of these variables. A similar idea applies for shallow cumulus clouds, such as the cumulus humilis in Vermeer’s painting (Figure 2), or present-day Delft (Figure 3).
These cumulus parametrization schemes are a large source of uncertainty in current weather and climate models. The conference was aimed at bringing together the community of modellers working on these schemes, and working out which might be the best directions to go in to improve these schemes, and consequently weather and climate models.
Each day was a mixture of listening to presentations, looking at posters and breakout discussion groups in the afternoon, as well as plenty of time for coffee and meeting new people. The presentations covered a lot of ground: from presenting work on state-of-the-art parametrization schemes, to looking at how the schemes perform in operational models, to focusing on one small aspect of a scheme and modelling how that behaves in a high resolution model (50m resolution) that can explicitly model individual clouds. The posters were a great chance to see the in-depth work that had been done, and to talk to and exchange ideas with other scientists.
Certain ideas for improving the parametrization schemes resurfaced repeatedly. The need for scale-awareness, where the response of the parametrization scheme takes into account the model resolution, was discussed. One idea for doing this was the use of stochastic schemes to represent the uncertainty of the number of clouds in a given grid cell. The concept of memory also cropped up – where the scheme remembers if it had been active at a given grid cell in a previous point in time. This also ties into the idea of transitions between cloud regimes, e.g. when a stratocumulus layer splits up into individual cumulus clouds. Many other, sometimes esoteric, concepts were discussed, such as the role of cold pools, how much tuning of climate models is desirable and acceptable, how we should test our schemes, and what the process of developing the schemes should look like.
In the breakout groups, everyone was encouraged to contribute, which made for an inclusive atmosphere in which all points of view were taken on board. Some of the key points of agreement from these were that it was a good idea to have these conferences, and we should do it more often! Hopefully, in two years’ time, another PhD student will write a post on how the next meeting has gone. We also agreed that it would be beneficial to be able to share data from our different high resolution runs, as well as to be able to compare code for the different schemes.
The conference provided a picture of what the current thinking on cumulus parametrization is, as well as which directions people think are promising for the future. It also provided a means for the community to come together and discuss ideas for how to improve these schemes, and how to collaborate more closely with future projects such as ParaCon and HD(CP)2.
It was the morning of 16th October when South East England got battered by the Great Storm of 1987. Extreme winds occurred, with gusts of 70 knots or more recorded continually for three or four consecutive hours and maximum gusts up to 100 knots. The damage was huge across the country with 15 million trees blown down and 18 fatalities.
The forecast issued on the evening of 15th October failed to identify the incoming hazard but forecasters were not to blame as the strongest winds were actually due to a phenomenon that had yet to be discovered at the time: the Sting Jet. A new topic of weather-related research had started: what was the cause of the exceptionally strong winds in the Great Storm?
It was in Reading at the beginning of 21st century that scientists came up with the first formal description of those winds, using observations and model simulations. Following the intuitions of Norwegian forecasters they used the term Sting Jet, the ‘sting at the end of the tail’. Using some imagination we can see the resemblance of the bent-back cloud head with a scorpion’s tail: strong winds coming out from its tip and descending towards the surface can then be seen as the poisonous sting at the end of the tail.
In the last decade sting-jet research progressed steadily with observational, modelling and climatological studies confirming that the strong winds can occur relatively often, that they form in intense extratropical cyclones with a particular shape and are caused by an additional airstream that is neither related to the Cold nor to the Warm Conveyor Belt. The key questions are currently focused on the dynamics of Sting Jets: how do they form and accelerate?
Works recently published (and others about to come out, stay tuned!) claim that although the Sting Jet occurs in an area in which fairly strong winds would already be expected given the morphology of the storm, a further mechanism of acceleration is needed to take into account its full strength. In fact, it is the onset of mesoscale instabilities and the occurrence of evaporative cooling on the airstream that enhances its descent and acceleration, generating a focused intense jet (see references for more details). It is thus necessary a synergy between the general dynamics of the storm and the local processes in the cloud head in order to produce what we call the Sting Jet .
Browning, K. A. (2004), The sting at the end of the tail: Damaging winds associated with extratropical cyclones. Q.J.R. Meteorol. Soc., 130: 375–399. doi:10.1256/qj.02.143
Clark, P. A., K. A. Browning, and C. Wang (2005), The sting at the end of the tail: Model diagnostics of fine-scale three-dimensional structure of the cloud head. Q.J.R. Meteorol. Soc., 131: 2263–2292. doi:10.1256/qj.04.36
Martínez-Alvarado, O., L.H. Baker, S.L. Gray, J. Methven, and R.S. Plant (2014), Distinguishing the Cold Conveyor Belt and Sting Jet Airstreams in an Intense Extratropical Cyclone. Mon. Wea. Rev., 142, 2571–2595, doi: 10.1175/MWR-D-13-00348.1.
Hart, N.G., S.L. Gray, and P.A. Clark, 0: Sting-jet windstorms over the North Atlantic: Climatology and contribution to extreme wind risk. J. Climate, 0, doi: 10.1175/JCLI-D-16-0791.1.
Volonté, A., P.A. Clark, S.L. Gray. The role of Mesoscale Instabilities in the Sting-Jet dynamics in Windstorm Tini. Poster presented at European Geosciences Union – General Assembly 2017, Dynamical Meteorology (General session)
Mountains come in many shapes and sizes and as a result their dynamic impact on the atmospheric circulation spans a continuous range of physical and temporal scales. For example, large-scale orographic features, such as the Himalayas and the Rockies, deflect the atmospheric flow and, as a result of the Earth’s rotation, generate waves downstream that can remain fixed in space for long periods of time. These are known as stationary waves (see Nigam and DeWeaver (2002) for overview). They have an impact not only on the regional hydro-climate but also on the location and strength of the mid-latitude westerlies. On smaller physical scales, orography can generate gravity waves that act to transport momentum from the surface to the upper parts of the atmosphere (see Teixeira 2014), playing a role in the mixing of chemical species within the stratosphere.
Figure 1 shows an example of the resolved orography at different horizontal resolutions over the Himalayas. The representation of orography within models is complicated by the fact that, unlike other parameterized processes, such as clouds and convection, that are typically totally unresolved by the model, its effects are partly resolved by the dynamics of the model and the rest is accounted for by parameterization schemes.However, many parameters within these schemes are not well constrained by observations, if at all. The World Meteorological Organisation (WMO) Working Group on Numerical Experimentation (WGNE) performed an inter-model comparison focusing on the treatment of unresolved drag processes within models (Zadra et al. 2013). They found that while modelling groups generally had the same total amount of drag from various different processes, their partitioning was vastly different, as a result of the uncertainty in their formulation.
Climate models with typically low horizontal resolutions, resolve less of the Earth’s orography and are therefore more dependent on parameterization schemes. They also have large model biases in their climatological circulations when compared with observations, as well as exhibiting a similarly large spread about these biases. What is more, their projected circulation response to climate change is highly uncertain. It is therefore worth investigating the processes that contribute towards the spread in their climatological circulations and circulation response to climate change. The representation of orographic processes seem vital for the accurate simulation of the atmospheric circulation and yet, as discussed above, we find that there is a lot of uncertainty in their treatment within models that may be contributing to model uncertainty. These uncertainties in the orographic treatment come from two main sources:
Model Resolution: Models with different horizontal resolutions will have different resolved orography.
Parameterization Formulation: Orographic drag parameterization formulation varies between models.
The issue of model resolution was investigated in our recent study, van Niekerk et al. (2016). We showed that, in the Met Office Unified Model (MetUM) at climate model resolutions, the decrease in parameterized orographic drag that occurs with increasing horizontal resolution was not balanced by an increase in resolved orographic drag. The inability of the model to maintain an equivalent total (resolved plus parameterized) orographic drag across resolutions resulted in an increase in systematic model biases at lower resolutions identifiable over short timescales. This shows not only that the modelled circulation is non-robust to changes in resolution but also that the parameterization scheme is not performing in the same way as the resolved orography. We have highlighted the impact of parameterized and resolved orographic drag on model fidelity and demonstrated that there is still a lot of uncertainty in the way we treat unresolved orography within models. This further motivates the need to constrain the theory and parameters within orographic drag parameterization schemes.
Nigam, S., and E. DeWeaver, 2002: Stationary Waves (Orographic and Thermally Forced). Academic Press, Elsevier Science, London, 2121–2137 pp., doi:10.1016/B978-0-12-382225-3. 00381-9.
Priestley, M. D. K., J. G. Pinto, H. F. Dacre, and L. C. Shaffrey (2016), Rossby wave breaking, the upper level jet, and serial clustering of extratropical cyclones in western Europe, Geophys. Res. Lett., 43, doi:10.1002/2016GL071277.
Extratropical cyclones are the number one natural hazard that affects western Europe (Della-Marta, 2010). These cyclones can cause widespread socio-economic damage through extreme wind gusts that can damage property, and also through intense precipitation, which may result in prolonged flood events. For example the intensely stormy winter of 2013/2014 saw 456mm of rain fall in under 90 days across the UK; this broke records nationwide as 175% of the seasonal average fell (Kendon & McCarthy, 2015). One particular storm in this season was cyclone Tini (figure 1), this was a very deep cyclone (minimum pressure – 952 hPa) which brought peak gusts of over 100 mph to the UK. These gusts caused widespread structural damage that resulted in 20,000 homes losing power. These extremes can be considerably worse when multiple extratropical cyclones affect one specific geographical region in a very short space of time. This is known as cyclone clustering. Some of the most damaging clustering events can result in huge insured losses, for example the storms in the winter of 1999/2000 resulted in €16 billion of losses (Swiss Re, 2016); this being more than 10 times the annual average.
Up until recently cyclone clustering had been given little attention in terms of scientific research, despite it being a widely accepted phenomenon in the scientific community. With these events being such high risk events it is important to understand the atmospheric dynamics that are associated with these events; and this is exactly what we have been doing recently. In our new study we attempt to characterise cyclone clustering in several different locations and associate each different set of clusters with a different dynamical setup in the upper troposphere. The different locations we focus on are defined by three areas, one encompassing the UK and centred at 55°N. Our other two areas are 10° to the north and south of this (centred at 65°N and 45°N.) The previous study of Pinto et al. (2014) examined several winter seasons and found links between the upper-level jet, Rossby wave breaking (RWB) and the occurrence of clustering. RWB is the meridional overturning of air in the upper troposphere. It is identified using the potential temperature (θ) field on the dynamical tropopause, with a reversal of the normal equator-pole θ gradient representing RWB. This identification method is explained in full in Masato et al. (2013) and also illustrated in figure 2. We have greatly expanded on this analysis to look at all winter clustering events from 1979/1980 to 2014/2015 and their connection with these dynamical features.
We find that when we get clustering it is accompanied with a much stronger jet at 250 hPa than in the climatology, with average speeds peaking at over 50 ms-1 (figures 3a-c). In all cases there is also a much greater presence of RWB in regions not seen from the climatology (Figure 3d). In figure 3a there is more RWB to the south of the jet, in figure 3b there is an increased presence on both the northern and southern flanks, and finally in figure 3c there is much more RWB to the north. The presence of this anomalous RWB transfers momentum into the jet, which acts to strengthen and extend it toward western Europe.
The location of the RWB controls the jet tilt; more RWB to the south of the jet acts to angle it more northwards (figure 3a), there is a southward deflection when there is more RWB to the north of the jet (figure 3c). The presence of RWB on both sides extends it along a more central axis (figure 3b). Therefore the occurrence of RWB in a particular location and the resultant angle of the jet acts to direct cyclones to various parts of western Europe in quick succession.
In our recently published study we go into much more detail regarding the variability associated with these dynamics and also how the jet and RWB interact in time. This can be found at http://dx.doi.org/10.1002/2016GL071277.
This work is funded by NERC via the SCENARIO DTP and is also co-sponsored by Aon Benfield.
Della-Marta, P. M., Liniger, M. A., Appenzeller, C., Bresch, D. N., Köllner-Heck, P., & Muccione, V. (2010). Improved estimates of the European winter windstorm climate and the risk of reinsurance loss using climate model data. Journal of Applied Meteorolo
Kendon, M., & McCarthy, M. (2015). The UK’s wet and stormy winter of 2013/2014. Weather, 70(2), 40-47.
Masato, G., Hoskins, B. J., & Woollings, T. (2013). Wave-breaking characteristics of Northern Hemisphere winter blocking: A two-dimensional approach. Journal of Climate, 26(13), 4535-4549.
Pinto, J. G., Gómara, I., Masato, G., Dacre, H. F., Woollings, T., & Caballero, R. (2014). Large‐scale dynamics associated with clustering of extratropical cyclones affecting Western Europe. Journal of Geophysical Research: Atmospheres, 119(24).
Priestley, M. D. K., J. G. Pinto, H. F. Dacre, and L. C. Shaffrey (2017). The role of cyclone clustering during the stormy winter of 2013/2014. Manuscript in preparation.
The interaction between atmospheric flow and topography is at the origin of various important weather phenomena, as we have already seen in Carly Wright’s blog post. When a mountain range is particularly high and extended it can even block or deflect weather systems, as it happens with the Alps. For example, in Figure 1 we can see the main Alpine range with its over-4000m-high peaks blocking a cold front coming from the north. The main ridge acts as a wall, enhancing condensation and precipitation processes on the upstream side (stau condition) and leaving clear skies on the downstream lee side, where dry and mild katabatic foehn winds flow. The contrast is striking between sunny weather on Lake Maggiore and snowy conditions over Monte Rosa, just a few miles apart. The same phenomenon is shown in Figure 2 with a satellite image that highlights how a cold front coming from northwest gets blocked by the Alpine barrier. A person enjoying the sunny day in the southern side of the Alps, if unaware of this mechanism, would be very surprised to know that the current weather is so different on the other side of the range.
A comparison with Figure 3 helps to notice that in Figure 2 the shape of the cloud band closely mirrors the mountain range. As an additional remark, this comparison shows that foehn bring clear skies even in the Po Valley, having blown away the typical mist/fog occurring in the region in Autumn and Winter months in high pressure regimes. The stau/foehn dynamics is actually very fascinating, and you can read more about it in Elvidge and Renfrew (2015 ) and in Miltenberger et al. (2016), among others. Unfortunately, the interaction of weather systems with the Alps can often trigger very damaging phenomena, like heavy and long-lasting precipitation on one side of the slope, and this is what the rest of this post will be focused on. In fact, the most recent event of this kind just happened at the end of November, with intense and long-lasting rain affecting the southern slope of the Alps and causing floods particularly in the Piedmont region, in northwestern Italy ( Figure 4).
Figure 5 shows that the accumulated rainfall in the event goes over 300 mm in a large band that follows the shape of the southern Alpine slope in the region (see map of Piedmont, from Google Maps), reaching even 600 mm in a few places. This situation is the result of moist southerly flow being blocked by the Alps and thus causing ascent and consequent precipitation to persist on the same areas for up to five days. It is quite common to see quasi-stationary troughs enter the Mediterranean region during Autumn months causing strong and long-lasting moist flows to move towards the Alps. Hence, it is crucial to understand where the heaviest precipitation will occur. In other words, will it rain the most on top of the ridge or on the upstream plain? What processes are controlling the location of heavy precipitation with respect to the slope?
The study published by Davolio et al. (2016), available here and originated from my master degree’s thesis, tackles this issue focusing on northeastern Italy. In fact, the analysis includes three case studies in which heavy and long-lasting rain affected the eastern Alps and other three case studies in which intense rainfall was mainly located on the upstream plain. Although all the events showed common large-scale patterns and similar mesoscale settings, characterised by moist southerly low-level flow interacting with the Alps, the rainfall distribution turned out to be very dissimilar. The study highlights that the two precipitation regimes strongly differ in terms of interaction of the flow with the mountain barrier. When the flow is able to go over the Alps the heaviest rain occurs on top of the ridge. When the flow is instead blocked and deflected by the ridge (flow around), creating a so-called barrier wind,intense convection is triggered on the upstream plain (Figure 6) .
The key mechanism that explains this different evolution is connected to the thermodynamic state of the impinging flow. In fact, when the southerly moist and warm air gets close to the Alpine barrier it is lifted above the colder air already present at the base of the orography. It can be said that the colder air behaves as a first effective mountain for the incoming flow. If this lifting process triggers convection, then the persistence of a blocked-flow condition is highly favoured (see Figure 7). On the contrary, if this initial lifting process does not trigger convection the intense moist flow will eventually be able to go over the ridge, where a more substantial ascent will take place, causing heavy rain on the ridge top. This study also looks at numerical parameters used in more idealised analyses (like in Miglietta and Rotunno (2009)), finding a good agreement with the theory.
To summarise, we can say that the Alpine range is able to significantly modify weather systems when interacting with them. Thus, an in-depth understanding of the processes taking place during the interaction, along with a coherent model is necessary to capture correctly the effects on the local weather, being either a rainfall enhancement, the occurrence of foehn winds or various other phenomena.
Davolio, S., Volonté A., Manzato A., Pucillo A., Cicogna A. and Ferrario M.E. (2016), Mechanisms producing different precipitation patterns over north-eastern Italy: insights from HyMeX-SOP1 and previous events. Q.J.R. Meteorol. Soc., 142 (Suppl 1): 188-205. doi:10.1002/qj.2731
Elvidge A. D., Renfrew, I. A. (2015). The causes of foehn warming in the lee of mountains. Bull. Am. Meteorol. Soc.97: 455–466, doi:10.1175/BAMS-D-14-00194.1.
Miglietta M. and Rotunno R., (2009)Numerical Simulations of Conditionally Unstable Flows over a Mountain Ridge.J. Atmos. Sci.,66, 1865–1885, doi: 10.1175/2009JAS2902.1.
Miltenberger, A. K., Reynolds, S. and Sprenger, M. (2016), Revisiting the latent heating contribution to foehn warming: Lagrangian analysis of two foehn events over the Swiss Alps. Q.J.R. Meteorol. Soc., 142: 2194–2204. doi:10.1002/qj.2816