MOUNTAIN METEOROLOGY | Valley Winds

Valley Winds D Zardi, University of Trento, Trento, Italy Ó 2015 Elsevier Ltd. All rights reserved. This article is a revision of the previous edition article by J. Egger, volume 6, pp 2481–2490, Ó 2003, Elsevier Ltd.

Synopsis The article reviews the distinctive properties of daily periodic, thermally driven winds typically occurring in mountain valleys. The mechanisms leading to the development of the horizontal pressure gradients driving such winds are examined, emphasizing the basic processes involved, as well as their connections with key physical factors, such as solar radiation and topographic features. Interactions with other thermally driven winds, such as slope flows on valley sidewalls and mountainplain circulations, are also discussed. Implications for phenomena associated with the water cycle and moist processes, as well as with air pollution transport, are also briefly outlined.

Introduction Valley winds are daily periodic, thermally driven circulations which develop in mountain valleys under favorable synoptic conditions, i.e., clear sky and weak or absent upper ambient winds. A valley may be loosely defined as a rather elongated orographic channel, either confined between two elevated mountain ranges, or carved into a plain (such as a canyon). A valley geometry is typically marked by the processes that concurred to shape it. These may consist in earth crust modifications by tectonic movements, erosion by glacier expansion and retreat, terrain erosion and sediment deposition performed by rivers, long-term action of atmospheric factors, or various combinations of these processes. Valleys are usually open to adjacent plains, unlike closed basins – such as the Meteor Crater in Arizona, USA – which are completely surrounded by elevated walls. Typical geometrical elements of a valley include the floor and the sidewalls. Accordingly, among the various geometrical factors affecting valley winds, we will mainly refer to the valley floor width, the sidewall slope angle, and the sidewall crest height above the valley floor. Clear skies allow strong incoming shortwave radiation during daytime, as well as outgoing longwave radiation during nighttime, and thus favor both diurnal surface heating and nocturnal cooling, i.e., the required thermal forcing. In addition, weak or absent upper winds allow an unperturbed development of these flows, which will be then only controlled by the combination of surface thermal forcing and topographic features. Valley winds typically blow up-valley during daytime, and down-valley during nighttime. These flows are actually the lower, and more evident, branches of closed circulations, with the respective upper branches flowing in the opposite directions above the sidewall ridge-top level (Figure 1). However, these upper equalizing flows, sometimes called antiwinds, are more difficult to detect: being unconfined by sidewalls, unlike the valley winds below, they can occur over larger widths, and comparable depths, so they usually display smaller mean speeds. Moreover, they are more directly exposed to the perturbing influence of upper ambient winds. Basically valley winds develop as a consequence of horizontal pressure gradients between the interior of a valley and an adjacent plain. Such gradients arise because the air

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temperature cycle, associated with the daytime warming and nighttime cooling of the atmosphere, in the interior of a valley, i.e., up to a height comparable with the mean sidewall crest elevation, typically displays at any level a larger amplitude than at the same level above an adjacent plain. Accordingly, as the vertical pressure distribution is to a large extent controlled by the hydrostatic balance, these different vertical thermal profiles produce horizontal valley–plain pressure gradients, which, reversing twice per day, drive upvalley winds during daytime and down-valley winds during nighttime (Figure 1). Notice that valley winds are not the only thermally driven circulations, which may develop over complex terrain. Actually they may be viewed as one component of a whole system of interconnected diurnal winds, typically occurring, at different scales, under the same favorable synoptic situations, over major mountain ranges surrounded by plain areas. The simplest flows are slope winds, blowing up the sunlit inclines during daytime, and downward during nighttime. Up-slope flows are sometimes called anabatic winds, and down-slope flows katabatic winds (from the ancient Greek verbs ‘anabainein’, ‘going up’, and ‘katabainein’, ‘going down’). In particular the word katabatic wind is extensively used to denote drainage winds blowing on glaciers and large ice surfaces in the polar regions (see Mountain Meteorology: Katabatic Winds). Such flows also occur along the sloping sidewalls of large valleys, and contribute, as shown in the following section, to the development of valley winds. At even larger scales, an overall organized air motion can be identified, conveying air toward the mountain range in the lower layers during daytime, and promoting a reversed flow during nighttime. These low-level flows are also accompanied by corresponding return upper winds, flowing in the opposite directions. Altogether this comprehensive system forms the so-called mountain-plain circulation. Further cases of daily periodic thermally driven circulations are found in closed basins, as well as on isolated plateaus. The present article mainly focuses on valley winds. Slope flows and mountain-plain circulations will be only briefly outlined, insofar as it is convenient for understanding their connections with valley winds. The interested reader will find an extensive treatment of all the above circulations in the review by Zardi and Whiteman (2013).

Encyclopedia of Atmospheric Sciences 2nd Edition, Volume 4

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Figure 1 Idealized picture of the vertical structure associated with daytime up-valley wind (upper panel) and nighttime down-valley wind (lower panel) between a valley and an adjacent plain. The red and blue curves reproduce vertical profiles of the horizontal wind component at the valley inlet. The two columns of air – one representing of the atmosphere over the valley floor, and one above the plain – include red and blue sections, indicating layers where potential temperature is relatively warm (W) or cold (C). The free atmosphere is unperturbed by the daily cycle above the tops of the columns. Reproduced with permission from Zardi, D., Whiteman, C.D. 2013. Diurnal mountain wind systems. In: Chow, F.K., De Wekker, S.F.J., Snyder, B. (Eds.), Mountain Weather Research and Forecasting – Recent Progress and Current Challenges, Springer Atmospheric Sciences. Springer, Berlin, pp. 37–122. Adapted from Whiteman, C.D., 2000. Mountain Meteorology: Fundamentals and Applications. Oxford University Press, New York, 355pp.

Being forced by the diurnal cycle of surface radiation, all of these circulations display a similar daily periodic up-and-down reversal. Nevertheless, the cycles of the various circulations occurring in the same area may be differently phased among them. Many factors may affect these phase delays, such as the varied exposure of the underlying terrain to incoming solar radiation, the different timing and amounts of sensible heat flux allowed by unequal surface properties, and the intrinsically different reaction timescales resulting from the circulation extent (timescales are typically larger for circulations encompassing larger areas). Also, diurnal valley winds are not the only circulations that may be found in mountain valleys, where various kinds of airflows may be produced by the action of upper winds, or pressure gradients associated with synoptic scale structures, rather than from the diurnal cycle of incoming solar radiation. The former are called dynamically driven winds, as opposed to the thermally driven valley winds, which are the main subject of the present article. Indeed, as the latter are originated from the heating and cooling of the valley atmosphere via surface energy

budgets, they are not caused by upper winds blowing above the valley, which may possibly condition, but not primarily determine, their evolution and spatial structure. In fact, thermally driven diurnal wind systems are better developed when the above external forcings are weaker. This may be argued from the panels on the first row of Figure 2: here the direction of valley winds is not affected by the direction of the upper geostrophic wind, and this is the only case displaying a natural diurnal cycle. In contrast, dynamically driven valley winds are clearly marked by the action of the forcing synoptic systems. Indeed three main channelling scenarios are associated with the ambient wind above the valley, and arise either from downward transport of horizontal momentum; from channelling of ambient winds by the valley sidewalls, and the consequent alignment with the valley axis; or from pressuredriven channelling. The connection between geostrophic wind direction and the resulting channelled wind in the valley is schematically shown in Figure 2 for all the above cases. The first mechanism consists in a strong downward transport of horizontal momentum from above the valley, caused

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Figure 2 The relationship between above-valley (geostrophic) and valley wind directions for four possible forcing mechanisms: thermal forcing, downward momentum transport, forced channelling, and pressure-driven channelling. The valley is assumed to run from northeast to southwest. Reproduced with permission from Whiteman, C.D., Doran, J.C., 1993. The relationship between overlying synoptic-scale flows and winds within a valley. Journal of Applied Meteorology 32, 1669–1682.

by either turbulent mixing, gravity waves, or other mechanisms. Friction determines a slight turning of the wind from the geostrophic wind direction toward the lower pressure as the ground is approached. This coupling is most likely to occur during unstable or neutrally stratified conditions in wide valleys, with low sidewalls and flat bottom, where thermally driven winds are less likely to develop, and channelling along the valley axis by the sidewalls would be rather ineffective. A second mechanism is known as forced channelling: it occurs when ambient winds, which are in geostrophic balance above the valley, are channelled by the valley sidewalls so that the wind aligns with the valley axis. In this case, the direction and speed of the valley wind depend on the sign and magnitude of the component of the ambient wind projected along the valley axis. Wind blows up or down the valley axis depending on the direction of the geostrophic wind relative to it. As a consequence, winds are predominantly aligned with the valley axis, with sudden shifts when geostrophic wind shifts across a line normal to the valley axis. A third mechanism is pressure-driven channelling, which occurs when the wind in the valley is driven by the component of the geostrophic pressure gradient in the along-valley direction. This gradient will be zero only when geostrophic wind is directed along the valley axis. Winds in the valley will shift from up to down valley (or vice versa) when the geostrophic wind

direction shifts across the valley axis. Pressure-driven channelling produces winds blowing predominantly along the valley axis, as for the previous case, but the valley wind reversal occurs for geostrophic wind directions 90 different from those of the forced channelling mechanism. Notice that winds in the valley can blow in opposition to along-valley wind direction components above the valley. The above dynamically driven winds may typically display strong intensities, depending on how strong the forcing synoptic situations are. In contrast, thermally driven valley winds generally display weak to moderate speeds. Nevertheless, some remarkable examples of strong valley winds have been observed. For instance, in the Kali Gandaki Valley in Nepal, connecting the Indian Plain to the Tibetan Plateau (Figure 3), wind speeds in the order of 5–15 m s1 are commonly met (Figure 4). Strong and gusty wind speeds may also occur when valley winds blow through elevated rims or gaps overlooking lower lands. As an example, such a situation occurs rather regularly in spring and summertime in the Alps, at the Lakes Valley exit. The latter is shaped as an elevated saddle, opening on the steep western side of the Adige Valley, north of the city of Trento. Here the local wind known as ‘Ora del Garda’ – a coupled lake and valley breeze, originating from Lake Garda shores, and then channelling along the nearby Lakes Valley – outflows through the saddle, and suddenly jumps onto

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Figure 5 The area north of the city of Trento where the ‘Ora del Garda’ wind, blowing from the Lakes Valley (A) through an elevated saddle ( ), interacts with the up-valley wind blowing in the Adige Valley from south (B). Reproduced with permission of the American Meteorological Society from de Franceschi, et al., 2002. Proceedings of the 12th Conference on Mountain Meteorology, Park City, Utah.

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Figure 3 Map of the Kali Gandaki Valley in Nepal. Dots indicate the main villages and towns. Solid lines are height contours (labeled in m AMSL). Horizontal distances are in km. Reproduced with permission from Egger, J. et al., 2000. Diurnal winds in the Himalayan Kali Gandaki Valley. Part I: Observations. Monthly Weather Review 128, 1106–1122.

the Adige Valley floor: interacting with the local up-valley wind (as suggested in Figure 5), this outflow results in a strong and gusty wind, blowing there throughout the afternoon. The typical diurnal cycle of valley winds follows the natural sequence of daytime heating and nighttime cooling at the

Earth’s surface. The basic components of the valley winds are schematized in Figure 6, along with the timing of their diurnal development. Black arrows indicate along-valley flows, whereas white arrows denote all the airflow components blowing on valley cross sections. Notice that here, for the sake of simplicity, the valley is represented by a very idealized topography, and heating is assumed to occur symmetrically on both sides of the valley. This may only occur under very particular circumstances, e.g., when the valley axis lies on the same vertical plane as the sun trajectory in the sky (such as along the equator at equinoxes), and terrain properties are symmetrically distributed on the two sides of the valley, so as to make surface energy budgets symmetrically identical as well. Also forcing from upper winds should be symmetrically acting on the two sides. These simplifying assumptions give an idea of how many factors may variously affect the spatial distribution of key variables associated with valley wind development, such as temperature, wind strength, and direction. After sunrise (Panel A) incoming solar radiation increasingly hits the ground. In a valley, direct radiation typically starts

Figure 4 Monthly mean values of the hourly mean wind speed observed in the Kali Gandaki Valley in Kagbeni (2900 m AMSL) in (a) February– March and (b) September–October 1990. Measurements were taken at a height of 9 m AGL. Notice the typical diurnal cycle, with peak wind speeds in the early afternoon. Reproduced with permission from (a) Egger, J. et al., 2002. Diurnal winds in the Himalayan Kali Gandaki Valley. Part I: Observations. Monthly Weather Review 128(4), 1106–1122 and (b) Egger, J. et al., 2000. Diurnal winds in the Himalayan Kali Gandaki Valley. Part III: piloted aircraft soundings. Monthly Weather Review 130, 2042–2058.

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Figure 6 Diurnal cycle of valley winds: see text for explanation. Reproduced with permission from Defant, F., 1949. Zur Theorie der Hangwinde, nebst Bemerkungen zur Theorie der Berg- und Talwinde [A theory of slope winds, along with remarks on the theory of mountain winds and valley winds]. Archiv für Meteorologie, Geophys. Bioclimatologie, Ser. A 1, 421–450. [Theoretical and Applied Climatology] [English translation: Whiteman, C.D., Dreiseitl, E., 1984. Alpine meteorology, Translations of classic contributions by Wagner A., Ekhart, E., Defant, F., PNL-5141/ASCOT-84-3. Pacific Northwest Laboratory, Richland, Washington, 121pp. http://www.osti.gov/bridge/servlets/purl/6665518/6665518.pdf.]

lighting the crests first, and then gradually reaches the valley floor. As a consequence of the energy partitioning resulting from the surface budget (which will be addressed in the following section), part of the energy input associated with solar radiation is converted into sensible heat flux, which is increasingly supplied to the air layers adjacent to the ground. On the sidewalls this heating progressively reduces the existing temperature deficit. This deficit was produced by nighttime energy loss from radiative ground cooling, and favored the development of nocturnal drainage flows down the slopes. On the contrary, as soon as the morning heating proceeds, air parcels adjacent to the sunlit slopes become warmer, and positively buoyant. As a result they promote organized upward motions conveying warmer air all along the sloping sidewalls, from the valley floor all the way up to the crest level. Here air parcels inertially rise

even above the crest level, where they cannot get heat from the ground any more. Then they either are buoyant enough to rise further and form thermals, possibly producing cumulus clouds, or, after eventually overshooting their neutral-buoyancy level, remain trapped into a horizontal return flow converging toward the valley center. Indeed this return flow is part of a compensating circulation bringing air parcels downward to the floor level, where air is diverted toward the sidewall feet to feed slope flows. This circulation contributes, along with heat locally supplied by energy partitioning at the valley floor, to remove the nocturnal stable layer on the floor, and thus to break up the ground-based nocturnal inversion, which was built up by the nighttime drainage of cold air down the sidewalls. Moreover, subsidence at the valley core produces an adiabatic compression of air parcels, and hence further contributes to raising air

Mountain Meteorology j Valley Winds temperature within the valley atmosphere. As a consequence, the overall temperature drop, and the associated density excess, produced by nocturnal cooling, are gradually overcome during the morning, as heat is increasingly supplied to the valley atmosphere. Similar processes are produced by incoming radiation over the adjacent plain, where daytime heating removes the ground-based nocturnal inversion and raises surface temperatures high enough to eventually trigger the development of atmospheric convection. However, the heating processes in the valley are quite different from those occurring on the plain. In particular, the organized circulation activated by sidewall slopes on each valley cross section is more effective in promoting a vertical heat transfer than random convective motions developing over the adjacent plain. As a consequence, at any height air temperatures throughout the valley volume are generally higher than over the plain. This contrast, increasing during the course of the day, produces a progressive reversal of the along-valley pressure gradient, and hence a reversal of the winds from down- to up-valley (Panel B). Indeed, the higher the sun over the horizon, the larger the sunlit portions of the sidewalls, and the stronger the incoming radiation per unit surface area. Accordingly, the intensity of along-valley winds typically reaches a maximum by mid-afternoon (Panel C). The strength of up-valley winds may even overwhelm slope winds, which may get increasingly embedded in them (Panel D). As soon as solar radiation starts declining, slope winds progressively weaken as well: indeed the energy input from declining solar radiation can no longer compensate the longwave net radiative loss. As a consequence, the sensible heat flux to the air layers adjacent to the slopes becomes negative, and a cooling phase begins, resulting in a progressive reversal of slope winds (Panel E). The slope winds then act as drainage flows, bringing colder air along the sidewalls to the valley floor, and thus contributing to an overall cooling of the valley atmosphere. The up-valley wind inertially continues blowing for some time after sunset, and thus maintains a residual mechanical turbulence production in the surface layer, which favors turbulent mixing and thus sustains sensible heat fluxes. Such a circulation promotes a rather efficient overall cooling of the valley atmosphere, whose lower layers rapidly become colder than the layers at equal heights above the adjacent plain. This contrast leads to a gradual reversal of the daytime plain–valley horizontal pressure gradient, and accordingly to a weakening of the up-valley wind (Panel F), and then, finally, to the onset of a down-valley wind (Panel G). This wind typically blows stronger and stronger, and in increasingly deeper layers, during the course of the night (Panel H). The resulting nocturnal circulation is maintained by the combination of cooling processes, favored by outgoing radiation and advection of colder air, which keep operating till dawn, when the cycle starts again from the beginning (Panel A). As a result of these alternating slope and valley winds, at any point on a valley sidewall the surface wind vector displays a typical rotation during the day, as shown in Figure 7. As implied in the above description, as far as a valley shape and layout are similar to the idealized topography reproduced in Figure 6, the main stream of the valley wind will ideally follow the along-valley axis. However, a variety of modifications in space and time – such as accelerations and decelerations, deviations, secondary circulations, bifurcations, and

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confluences – may occur in connection with changes in topographic factors – such as valley cross-section area, or shape, or valley curvatures. Further modifications may derive from varied surface properties, or from interactions with concurring winds flowing along tributary valleys, as well as from changes in the external forcings, such as the varying intensity of solar radiation at the ground in space and time, or the changing action of upper winds. A full account of these effects cannot be provided here: the interested reader will find further details and literature references to various case studies in the mentioned chapter by Zardi and Whiteman (2013). It is interesting to observe that the development of valley winds displays many analogies with the development of coastal breezes (see Mountain Meteorology: Land and Sea Breezes). The latter are daily periodic wind systems blowing normal to the shorelines of seas or large lakes, under the same weather situations that favor the development of valley winds. Coastal flows are produced by horizontal pressure gradients associated with the different vertical thermal structures developing over the land and over the water surface. As these contrasts occur, with opposite results, both under the daytime heating, and under the nocturnal cooling phase, they produces coastal breezes in much the same way as valley winds are produced by valley–plain contrasts, reversing twice per day. In particular, the overall structure of both wind systems may be viewed as an organized, large-scale solenoidal vortex, rotating in such a way that its lower branch blows from the plain to the valley interior – or, respectively, from above the sea toward the onshore region – after sunrise, and gradually reverses after sunset. Indeed such circulation, as well as the associated flow vorticity, is produced by baroclinic effects, i.e., from the misalignment of pressure and density gradients associated with the above mentioned thermal contrasts (see Air Sea Interactions: Freshwater Flux; Momentum, Heat, and Vapor Fluxes; Sea Surface Temperature; Surface Waves. Dynamical Meteorology: Vorticity).

Physical Processes Controlling Valley Winds In the previous section, we outlined the basic features of a typical diurnal valley wind system, providing an intuitive insight in the combination of the physical factors concurring in its development. In the present section, we will explore in more detail some of the above processes, and the mechanisms involving them, along with the factors controlling their occurrence, intensity, and duration.

Radiation and Energy Budgets In general, thermally forced flows are driven by buoyancy effects and pressure gradients arising from air density variations associated with heating or cooling of air parcels. On the other hand, local changes in air temperature result from a combination of factors, as clearly summarized in the tendency equation for potential temperature at any point in the atmosphere:

v q _ cp rq ¼ V$A  V$H  V$R þ Q vt T

[1]

Here cp is the air specific heat at constant pressure, while r, T, and q are the average values (with respect to turbulent

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Figure 7 Diurnal rotation of the wind velocity vector resulting from the combination of slope and valley winds. Green arrows denote the velocity vector at the indicated hours, whereas red circle arrows represent the wind rotation. Reproduced with permission from Whiteman, C.D., 2000. Mountain Meteorology: Fundamentals and Applications. Oxford University Press, New York, 355pp.

fluctuations) of air density, temperature, and potential temperature, respectively. The term A ¼ cp r u q is the sensible heat flux associated with advection by the mean wind velocity u, H ¼ cp ru0 q0 is the turbulent sensible heat flux (produced by the coupling between turbulent fluctuations of wind velocity u0 and potential temperature q0 ). (Following Reynolds decomposition for turbulent flows, primed variables indicate turbulent fluctuations with respect to the mean values, indicated by an overbar.) R is the radiative heat flux, including both the shortwave and the longwave component. _ includes the rates of heating (or cooling) associated Finally, Q with conversion of water vapor into or from liquid water or ice. Notice that both advective and turbulent heat fluxes imply some air motions, i.e., respectively, a mean wind velocity u and turbulent velocity fluctuations u0 . However, in the ideal situations for thermally driven flows, i.e., dry atmosphere under clear sky and calm synoptic winds, little or no advection is produced by any large scale flows, and little turbulence can be produced mechanically, i.e., through the typical energy cascade from large to small eddies, via the coupling between mean wind shear and turbulent momentum fluxes. Rather, advection and turbulence are mainly associated with air motions originated by the combination of gravity with unbalanced density gradients, produced by heating or cooling. However, these heating and cooling are not primarily induced by the absorption or emission of radiation (the term V$R in eqn [1]), which is usually negligible within the layers involved in valley winds systems. Rather they come from processes controlling energy partitioning at the surface. Typically, the surface energy budget may be expressed in terms of the components normal to the surface (labeled with ‘s’) of the above mentioned fluxes, i.e., radiation flux Rs, and sensible heat flux Hs, along with latent heat flux Ls, and heat flux exchanged with subsurface layers, i.e., the ground heat flux Gs, as RS þ HS þ LS þ GS ¼ 0

[2]

In eqn [2] all fluxes toward the surface (both from the atmosphere and from ground) are positive, and all fluxes away from the surface are negative. The turbulent latent heat flux Ls is associated with evaporation (sublimation) from, or condensation (deposition) onto, the surface. It is produced by the coupling between turbulent fluctuations of the wind velocity component normal to the surface w0 and specific humidity q0 , i.e., Ls ¼ ð‘i rw0 q0 Þs , ‘i being the appropriate latent heat (i.e., the latent heat of vaporization ‘v or the latent heat of sublimation ‘s depending on the situation) (see Dynamical Meteorology: Acoustic Waves). Ground heat flux depends on heat conduction in the subsurface ground (soil, rock, etc.). The (net all-wave) surface radiation flux Rs may be decomposed into four components, namely RS ¼ K[ þ KY þ L[ þ LY

[3]

with KY being the incoming shortwave radiation, including both direct and diffuse solar radiation, K[ the outgoing shortwave radiation (i.e., the fraction of incoming shortwave radiation reflected by the surface), L[ the outgoing longwave radiation emitted by the surface, and LY the incoming longwave radiation emitted downward by the atmosphere (air gases, water vapor, and clouds). Such a budget occurs at any point of the ground surface. However, over complex terrain it typically displays a higher variability in space and time, following topographic effects on incoming solar radiation. A remarkable example of a typical diurnal cycle of incoming shortwave radiation in a valley is shown in Figure 8, where mean diurnal cycles are shown from measurements performed at different points in the Riviera Valley in the Swiss Alps (Figure 9). Therefore the surface energy budget is the main factor controlling thermally driven circulations, promoting both the turbulent heat fluxes and the advective motions required to develop the whole system of valley winds. Accordingly, factors controlling this budget also affect the development of valley winds. For instance, clear skies and clean air favor

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Figure 8 Diurnal cycles of incoming short-wave radiation at different measurements sites in the Riviera Valley, Switzerland (see Figure 9 for location), namely CVF (filled dots), ESM (dashed line), ESF2 (full line), and ESR (triangles). Panels (a) and (b) represent average values during valley wind days on slope-parallel and horizontal surfaces, respectively, while panel (c) refers to overcast days. The bold curve in (b) denotes the mean diurnal cycle of extraterrestrial irradiance on a horizontal surface at site CVF. Note the different vertical axes. CVF, Centered in valley floor; ESM, Eastern slope meadow; ESF2, Eastern slope forest; ESR, Eastern slope ridge. Reproduced with permission from Matzinger, N., et al., 2003. Surface radiation budget in an Alpine valley. Quarterly Journal of the Royal Meteorological Society 129, 877–895.

stronger energy exchanges, allowing elevated values of incoming solar radiation at surface level during daytime, as well as outgoing radiation emitted from the ground during nighttime. Hence such conditions favor both daytime heating and nighttime cooling of air layers at the earth surface. However, this heating or cooling depends on the energy budgets (eqns [2] and [3]), whose terms are controlled by soil properties – such as heat capacity, thermal conductivity, and moisture content – as well as by surface properties, such as reflectivity, emissivity, and topographic features. As a consequence, the strongest diurnal wind systems are typically found in elevated and dry environments: elevation provides a better exposure to solar radiation during the day, and strong longwave radiative loss at night, whereas dryness typically reduces shortwave attenuation from air turbidity and cloud cover, as well as the latent heat flux involved in water evaporation or condensation, thus allowing more energy excess (or deficit) to be available for more intense heating (or cooling) of the atmosphere.

The picture of the diurnal cycle provided in Section Introduction suggests that slope flows along the valley sidewalls play a key role in the development of valley winds, as they are the earliest drivers of the whole valley wind system. Indeed, by reacting quickly to changes in the surface energy budget, following the radiation cycle at the ground, slope flows effectively promote heat and mass advection along the slopes, thus producing exchanges both in the vertical and in the cross-valley directions. As these exchanges are determined by the topographic features of the valley cross section, they occur in a much more organized way than the analogue vertical exchange processes over flat terrain: here during daytime thermal convection feeds stochastically generated thermals, resulting in an increasingly deep convective boundary layer (CBL), whereas nocturnal cooling leads to a largely uniform, increasingly stable boundary layer. To understand the basic dynamics implied in slope flows, it is worth recalling here a prototypal model proposed by Prandtl (1942). (Strictly speaking, the original Prandtl theory accounts for a momentum flux dominated by molecular viscosity and a heat flux determined by heat conduction, i.e., for a laminar atmospheric flow. Here we propose a straightforward extension of the theory to the turbulent case, which is more likely to occur in a real atmosphere. The mathematical expression of the solution remain in fact the same, if molecular viscosity and heat diffusivity are replaced by their respective turbulent analogs, provided that they may be assumed to be constant.) Indeed let us consider an infinite plane surface tilted by an angle a over the horizontal (Figure 10), and an overlying stably stratified atmosphere, initially at rest and displaying a constant vertical potential temperature lapse rate g. Then imagine perturbing this static equilibrium situation by imposing a prescribed constant value DTs for the temperature anomaly at any point of the surface (or, equivalently, a prescribed value Hs of the sensible heat flux). Let us adopt for convenience a frame of reference, where s is the coordinate along the slope (positive up-slope) and n is the coordinate normal to the slope (positive from the surface toward the atmosphere). As the surface temperature anomaly DTs is invariant with s, let us seek for a solution that does not depend on the along-slope coordinate, but only depends on n. Mass continuity then implies that the motion be perfectly parallel to the slope, i.e., there will be only one velocity component along s (positive up-slope). Moreover, let us seek for a steady-state solution. Accordingly the equations for conservation of momentum and energy at leading order reduce to: 0 ¼ bg sin a q  g sin a u ¼ 

v 0 0 u w vn

v 0 0 w q vn

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[5]

Equation [4] represents the local balance between two forces (per unit mass). The first term represents the buoyancy force, resulting from the combination of gravity (g), topography (a), and the relative density anomaly, represented by bq, where b is the coefficient of thermal expansion and q is the potential temperature anomaly with respect to the

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Figure 9 Cross section through the Riviera Valley, Switzerland. Labels indicate sites where radiation measurements were made under the MAP Riviera project in 1999. Characteristics of each site are listed in the table. Reproduced with permission from Matzinger, N., et al. 2003. Surface radiation budget in an Alpine valley. Quarterly Journal of the Royal Meteorological Society 129, 877–895.

Figure 10 Profiles of velocity (u) and potential temperature anomaly for up-slope flow (q) according to Prandtl’s (1942) model (see text for explanation). Adapted with permission from Schumann, 1990. Largeeddy simulation of the up-slope boundary layer. Quarterly Journal of the Royal Meteorological Society 116, 637–670.

unperturbed situation. This term produces a positive (upslope) buoyancy force on lighter parcels (i.e., parcels displaying a larger potential temperature than at the same level in the unperturbed atmosphere) and vice versa. The second term represents friction effects, produced by turbulent momentum flux in the direction normal to the slope. Friction always counteracts air motions, either up-slope or down-slope, and a steady motion requires that buoyancy and friction permanently balance each other. Equation [5] represents a local energy balance between along-slope heat advection and sensible heat flux normal to the slope. For positive u the first term reproduces an upslope advection of potentially colder air from lower layers, thus contributing to local cooling. The second term is positive when heat flows from the surface to the atmosphere, which occurs when the surface displays a higher temperature than the overlying atmosphere layers. A similar reasoning applies, simply reversing the signs, for downslope flows associated with surface cooling. The balance between the two requires that the wind blows up-slope on a surface which is heating the atmosphere, and down-slope when it is cooling.

Mountain Meteorology j Valley Winds To make progress toward a solution of eqns [4] and [5] we need to specify the structure of turbulent fluxes, or at least to stipulate a relationship between them and the unknown variables u and q. One way is to postulate that turbulent transport processes behave in a similar way to their molecular analogs, such as viscous friction or heat conduction, where fluxes of momentum or heat are proportional to velocity and temperature gradients, respectively. So let us set: vu u0 w0 ¼ Km vn

[6]

vq vn

[7]

w0 q0 ¼ Kh

where Km and Kh are the eddy viscosity and eddy heat diffusivity, respectively. Assuming further that these are constant values throughout the slope flow layer, substituting in eqns [4] and [5] one gets two coupled linear equations that admit the solution found by Prandtl (1942): u ¼ U expðn=‘Þsinðn=‘Þ

[8]

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[9]

(a)

1=2

where U ¼ Ng1 Pr T DTs , with N ¼ (bgg)1/2 being the Brunt–Vaisala frequency of the unperturbed atmosphere and PrT ¼ Km/Kh the turbulent Prandtl number. The length scale ‘ is provided by:   4Kh Km 1=4 ‘ ¼ [10] 2 N 2 sin a An example of the slope-normal profiles provided by this solution is shown in Figure 10. The potential temperature anomaly is maximum at the surface, and then its magnitude decreases exponentially with distance from the surface, reversing sign at the nodes of the cosine function. This means that some upper counterflow accompanies the development of the main flow adjacent to the surface. Indeed, as a result of friction, due to the thermal upward thrust, layers which have not themselves been heated are set in motion, so after they have risen to a new position they are colder than the particles which were there, when the stratification of the air was undisturbed. The wind strength scale U is proportional to the surface temperature anomaly DTs: therefore a large, positive DTs produces a strong up-slope flow, and vice versa. Figure 10 also shows how potential-isothermal lines are modified by the

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Figure 11 Velocity profiles from observations (curves B) performed with pilot balloons on the Nordkette (near Innsbruck, Austria) and theoretical predictions (curves T) based on Prandtl’s (1942) model for up-slope (a) and down-slope (b) winds. Dashed lines indicate the difference between observed and theoretically calculated wind speed above the maximum. Reproduced with permission from Barry, R.G., 2008. Mountain Weather and Climate, third ed. Cambridge University Press, 506pp; Adapted from Defant, F., 1949. Zur Theorie der Hangwinde, nebst Bemerkungen zur Theorie der Berg- und Talwinde [A theory of slope winds, along with remarks on the theory of mountain winds and valley winds]. Archiv für Meteorologie, Geophys. Bioclimatologie, Ser. A 1, 421–450. [Theoretical and Applied Climatology] [English translation: Whiteman, C.D., Dreiseitl, E., 1984. Alpine meteorology, Translations of classic contributions by Wagner A., Ekhart, E., Defant, F., PNL-5141/ASCOT-84-3. Pacific Northwest Laboratory, Richland, Washington, 121pp.] http://www.osti.gov/bridge/servlets/purl/6665518/6665518.pdf.

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slope flow: far from the surface the isolines are perfectly horizontal and equally spaced, reflecting the constant vertical lapse rate of potential temperature in the unperturbed atmosphere. Closer to the surface, isolines bend downward for a heated surface, associated with up-slope flow, and upward for a cooling surface, associated with down-slope flows. The above theoretical model explains many aspects involved in the development of slope flows, and despite many idealizing assumptions (infinite plane slope, s-invariance) and approximations (linearization, simplified representation of turbulence), it captures the essentials of real slope winds, as shown by measurements taken on real slopes reported in Figure 11. The main discrepancies appear in up-slope flows, where measurements suggest a deeper layer characterized by upward velocity than estimated by the model profile. This has probably to do with the stronger upward convective motions associated with thermally generated turbulence. This idea is also supported by high-resolution numerical simulations. Figure 12 shows slope-normal profiles of along-slope wind speed and potential temperature anomaly from large eddy simulations of steady turbulent up-slope flow over an infinite slope for various slope angles (a ¼ 2, 4, 7, 10, and 30 ). Both velocity and temperature profiles display some similarities with Prandtl’s solutions. However, for angles a  10 a well-mixed layer develops, which makes potential temperature uniform for a significant depth above the surface layer, and also makes the velocity profiles rather flat. Further results for realistic cases of down-slope flows are not reported here, as they are the subject of the article Mountain Meteorology: Katabatic Winds in this Encyclopedia.

Turbulence As envisaged in the previous section, turbulent motions play a key role in enhancing momentum and energy exchanges in thermally driven flows. As discussed before, the main forcing for valley winds comes from energy and momentum exchanges at the surface, where flows are inherently turbulent, and this implies that these exchanges are stronger where turbulence is more intense. A measure of the turbulence intensity is provided by the turbulent kinetic energy (TKE). TKE is defined as the kinetic energy per unit mass associated with the turbulent velocity fluctuations, namely TKE ¼ u02 þ v02 þ w02 , where u, v, and w are the velocity components with respect to some Cartesian coordinate system and an overbar denotes the average with respect to turbulence. The two main mechanisms controlling the production of TKE are the so-called mechanical production, arising from the coupling of momentum flux with the gradient of the mean flow, and buoyancy production, originated by the coupling of buoyancy flux with background stratification. While the former is always positive, i.e., always contributes to increasing TKE, the latter is positive under unstable conditions, whereas it acts to suppress turbulence under stable situations. Figure 13 shows the spatial distribution of (subgrid) TKE obtained with large eddy simulations on a valley cross section of two idealized valleys – a wider and a narrower one – at two different times, i.e., at 13 p.m. (upper panels) and at 17 p.m. (lower panels). During daytime surface heating continuously feeds buoyancy production of TKE, which is then redistributed either by larger thermals,

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Figure 12 Profiles of mean velocity (left) and temperature (right) from Large-Eddy Simulations of turbulent up-slope flows for inclination angles a ¼ 2, 4, 7, 10, and 30 . Mean wind speed , temperature , and height above the slope n are normalized by the following scales: v* ¼ (bgHs/N)1/2, H ¼ v*/N, and q* ¼ Hs/v* With the setting adopted for the simulations (g ¼ 0.003 K m1, b ¼ 1/300 K1, g ¼ 10 m s2, and Hs ¼ 0.1 K m s1) the scale values result in v* ¼ 0.58 m s1, H ¼ 58 m, and q* ¼ 0.17 K. The error bars signify standard deviations. The thin line in the panel on the right corresponds to the well-mixed situation. Reproduced with permission from Schumann, 1990. Large-eddy simulation of the up-slope boundary layer. Quarterly Journal of the Royal Meteorological Society 116, 637–670.

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Figure 13 Consecutive mid-domain cross sections of q (isolines every 0.2 K, thick every 1 K; q ¼ 312 K at top) and subgrid-scale TKE (shading) in the (left) narrow and (right) wide valley runs. Subgrid-scale TKE, approximately one order of magnitude smaller than the explicitly resolved fraction, is used merely to suggest the position of the dominant turbulent eddies. TKE, Turbulent kinetic energy. Reproduced with permission from Serafin, S., Zardi, D., 2010. Daytime Heat Transfer Processes Related to Slope Flows and Turbulent Convection in an Idealized Mountain Valley. Journal of the Atmospheric Sciences 67, 3739–3756.

especially above the valley floor of a wide valley, or by the combined effect of slope flows and the resulting cross-valley circulation. These two processes realize a sort of competition between a more organized flow, marked by orographic features of the terrain, and randomly generated thermals on the valley floor, more similar to those typically forming on openly flat terrain. As a consequence, in a narrow valley slope

Figure 14 An idealized sketch of the cross-valley circulation induced by up-slope flows (1) ending in thermal plumes (2) at the crest tops, and in horizontal motions (3) at mountaintop level. Adiabatic subsidence (4) stabilizes the valley core, and suppresses the development of a convective boundary layer (5) on the valley floor. Arrows and whirls suggest the main features of the flow field. Reproduced with permission from Serafin, S., Zardi, D., 2010. Daytime Heat Transfer Processes Related to Slope Flows and Turbulent Convection in an Idealized Mountain Valley. Journal of the Atmospheric Sciences 67, 3739–3756.

Figure 15 Comparison of potential temperature profiles over a plain (dashed black line, about 8 h after sunrise), wide valley (gray line, 7 h after sunrise), and narrow valley (continuous black line, 7 h after sunrise). The cross sections of the two valleys are the same as in Figure 13. The different times correspond to an equal energy input for all cases. The horizontal gray line indicates the level of the top of the valley sidewall. Reproduced with permission from Serafin, S., Zardi, D., 2011. Daytime development of the boundary layer over a plain and in a valley under fair weather conditions: a comparison by means of idealized numerical simulations. Journal of Atmospheric Science 68, 2128–2141.

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flows are expected to be stronger, and thermal plumes on the sidewall crests more developed, than in a wider one.

Vertical Thermal Structure and Horizontal Pressure Gradients The main mechanism driving valley winds originates from pressure unbalances arising at various levels between neighboring regions – namely within a valley and above an adjacent plain – as a consequence of different processes producing air heating or cooling at different levels in the two regions. The processes leading to these contrasts can be better understood by considering again an ideal valley–plain system, consisting of a simple valley with an along-valley invariant, symmetric cross section, and a horizontal floor, facing an open plain. Vertical accelerations associated with either upward or downward motions characterizing valley winds are usually small. Therefore, the vertical pressure distribution is essentially governed by hydrostatic balance. Hence horizontal pressure gradients, driving along valley flows, arise just from changes in the vertical temperature distribution occurring during the diurnal cycle in the valley atmosphere and in the adjacent plains.

To point out the relationship between the vertical thermal structure and the along-valley pressure gradient, consider a valley with a perfectly horizontal floor at the same level as the adjacent plain. Let us concentrate on the along-valley pressure distribution considering the values that pressure assumes over a vertical plane based on the along-valley axis at the valley floor. Also, let us focus on the daytime phase, as similar reasoning may be easily extended by analogy to the nighttime phase. The mechanisms leading to the heating of the valley atmosphere over a vertical cross section are schematized in Figure 14. Up-slope flows along the sidewalls convey heated air up to the crest level, where it either produces vertically ascending thermal plumes, or gets involved in the upper return flow converging toward the valley center and feeding the subsidence motion that compensates the removal of heated air operated by up-slope flows at lower levels. These mechanisms result in a vertical thermal structure, which is remarkably different from the classical CBL profile occurring under the same weather situation and solar radiation over a plain. Figures 15 and 16 offer a comparison between the two situations, and some hints about the influence of the valley width. The vertical structure of the CBL in

Figure 16 Daytime development of the vertical profiles of temperature and pressure differences, taken at the same heights, between the interior of an idealized valley and an adjacent plain region. Two cases are considered, representative of a narrow and a large valley (the two valley cross sections are the same as in Figure 13). Upper panels refer to the narrow valley and lower panels to the larger one. In all frames, profiles evolve in time from an unperturbed state (representative of sunrise time), where the atmosphere has the same vertical structure both in the valley and in the plain (light gray), to a final condition (12 h later) where the contrasts between the valleys and the plains are largest (black). Reproduced with permission from Serafin, S., Zardi, D., 2011. Daytime development of the boundary layer over a plain and in a valley under fair weather conditions: a comparison by means of idealized numerical simulations. Journal of Atmospheric Science 68, 2128–2141.

Mountain Meteorology j Valley Winds a valley displays a shallower mixed layer, topped by a deeper stable layer. The valley atmosphere is potentially warmer than over the plain throughout the depth of the boundary layer. Also, under the same forcing, the narrow valley produces a warmer atmosphere than the wider one. There are two main reasons: slope flows at the valley sidewalls promote the intake of air at the sidewall feet, and thus remove newly heated air from above the valley floor, subtracting it from getting involved in the development of the CBL. However, the wider the valley, the smaller the mean air intake per unit valley width, so this process is more effective on a narrow valley floor. As a consequence the mixed layer that develops over the valley floor is generally shallower than over a plain, and this aspect is more evident in the narrow valley. The reason consists in the fact that slope flows along the sidewalls develop almost identically in both valleys, but their effect on the core of the valley atmosphere depends on the valley cross-section aspect ratio: the larger the valley, the weaker the impact. Indeed the diversion of air from the valley toward the slope feet has less effect on a wider valley, so surface sensible heat flux can develop a CBL, which is more similar to that over a flat plain. On the other hand, the same air masses set in motion by slope flows feed the compensating subsidence at the valley top. However, mass conservation requires that the downward velocity of this sinking motion be inversely proportional to the valley width, so a weaker subsidence occurs in a wider valley. All of these processes result in valley–plain contrasts in the vertical profiles of temperature and pressure, which are well summarized for an idealized valley case in Figure 16 (see caption for explanation). Similar contrasts are also observed in real cases: Figure 17 shows such a situation observed in temperature profiles from radiosoundings taken respectively at Innsbruck, in the upper Inn Valley in the Alps, and at Munich, in the adjacent Bavarian Plain. The effect of such contrasting vertical structures on the winds is also clearly exemplified by the diurnal cycle observed in the Adige Valley, on the southern side of the Alps, facing the adjacent Po Plain (Figure 18). This valley displays a gradually sloping floor along the 150 km path connecting the surroundings of the city of Verona (91 m above mean sea level, AMSL) in

Figure 17 Vertical profiles of potential temperature from radiosoundings at Munich in the Bavarian plain (dotted line) at 519 m AMSL, and Innsbruck in the Inn Valley (solid line) at 574 m MSL, at 1200 UTC 19 July 2002. From Weissmann, et al., 2005. The Alpine mountain-plain circulation: airborne Doppler lidar measurements and numerical simulations. Monthly Weather Review 133, 3095–3109.

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Figure 18 Map of the Adige valley in the southern Alps. Courtesy L. Giovannini.

the plain to the upper valley at Merano (330 m AMSL). Results reproduced in Figures 19–21 report averaged values for all the days in which favorable weather conditions allowed a full development of valley winds in the years 2004–11. In particular, Figure 19 shows diurnal mean cycles of along-valley wind speed at various stations along the valley. Amplitude and phase of local wind strength are strongly affected by local topography and land cover. Nevertheless the typical cycle of daytime upvalley wind, peaking in the afternoon, and down-valley nocturnal winds, weaker but persisting throughout the night, is clearly reproduced at all the stations. As already pointed out, this diurnal wind cycle occurs in connection with the corresponding cycle of horizontal pressure distribution. This connection is shown by the mean diurnal oscillation of surface pressure at various stations along the valley, from the plain (Verona) to the upper valley (Merano), reproduced in Figure 20. Notice that the amplitude of the diurnal surface pressure cycle displays an increasing trend up-valley, with the smallest value in Verona and the largest in Merano. As a consequence the along-valley pressure distribution displays the layout shown in Figure 21. The pressure change with alongvalley distance from the plain is almost linear at any time. However, the higher amplitudes occurring further up-valley cause a daily periodic reversal of the pressure gradient.

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Figure 19 Average diurnal cycle of the along-valley wind strength along the Adige Valley. Courtesy L. Giovannini.

Figure 22 Vertical velocity profiles of down-valley winds normalized with the wind speed at the jet maximum um for the days 18, 20, 26, and 30 September 1984 in the Brush Creek Valley (Colorado). The solid line is a least-square fit of the expression u(z)/um ¼ Aexp(Bz) sin(pz/D), resulting in A ¼ 3.2 and B ¼ 3.3 m. Reproduced with permission from Clements, et al., 1989. Mean structure of the nocturnal drainage flow in a deep valley. Journal of Applied Meteorology 28, 457–462.

Figure 20 Average diurnal cycle of surface pressure at the stations indicated in Figure 18. Courtesy L. Giovannini.

topographic features (curvatures, valley width changes, etc.), as well as on the strength and timing of the various forcing terms. As a consequence a generally valid shape for valley wind profiles, as schematized in Figure 1, cannot be easily provided. However, in some cases vertical profiles inspired by Prandtl’s (1942) solution for slope flows successfully reproduced observations, as shown in Figure 22 for along-valley wind measurements in the Brush Creek Valley.

Interactions with Mountain-Plain Circulations

Figure 21 Average diurnal development of the surface pressure deviation (time LST in the chart). The slope of the curves gives an idea of the local horizontal pressure gradient along the valley. Courtesy L. Giovannini.

Similar pressure cycles occur at all levels within the layer affected by valley winds, and are the main drivers of the daily alternating wind strength and direction at any level. The vertical structure of these winds is strongly dependent on local

Daily periodic winds occurring along valleys lying in the major mountain ranges (such as the Alps, the Rocky Mountains, the Himalayan Chain, and Tibetan Plateau) are often embedded within the associated larger scale mountain-plain circulations, embracing the whole extent of the mountain range. Mountainplain circulations are also driven by a diurnal pressure oscillation between the mountainous region and the adjacent plains. For the largest mountains, these oscillations have been observed to affect one or more modes of the atmospheric tides at global scale. The daily periodic reversal of this wind system is somewhat delayed relative to slope and valley winds because of the larger air mass involved. Based on extensive numerical model simulations on a targeted area East of the Rocky Mountains, Wolyn and McKee (1994) identified a conceptual model of the daytime evolution of the mountain-plain circulation, which includes a sunrise state and three phases (Figure 23). The main features of the sunrise state are the bulging isentropes, the jet down the east side of the barrier and the stable core (Panel A). Divergence created by the nocturnal flows helps create the downward bulging isentropes. Phase 1 (Panel B) results from the weakening nocturnal flows interacting with surface heating, and lasts until 3–4 h after sunrise. Warming is associated with the weakening nocturnal jets, and occurs up to 20 km east of the

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Figure 23 Conceptual daytime mountain-plain circulation model: (a) sunrise state, in which there is an interaction between nocturnal thermal and ambient flows; (b) phase 1, during which the weakening nocturnal flow interacts with surface heating; (c–d) phase 2, consisting of the developing solenoid; and (e) phase 3, the migrating solenoid. Further details are discussed in the text. Reproduced with permission from Zhang, Koch, 2000. Numerical simulations of a gravity wave event over CCOPE. Part II: Waves generated by an orographic density current. Monthly Weather Review 128, 2777–2796.

barrier base. Panel C shows the first stage of phase 2, characterized by a developing solenoidal circulation. The CBL on the eastern plains is suppressed due to horizontal cold-air advection in the CBL and the warming above the CBL. In stage 2 (Panel D) sinking and horizontal warm-air advection immediately east of the solenoid center warms the air sufficiently to create a negative pressure gradient (lower to the west) in the stable core above the CBL. This region of negative pressure

gradient expands eastward, and the reversal from negative to positive of the horizontal pressure gradient is marked by a pressure ridge: when this pressure ridge passes over a site, easterly flows appear above the CBL, strong vertical wind shear develops in the region between the strengthening up-slope and the westerly return flows, and the westward mass flux in the upslope flow increases at a faster rate. Phase 3 (Panel E) is characterized by a migrating solenoid, whose center is located in

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a pressure trough beneath the eastward-moving leading edge of the cold core. The migrating solenoid is only a transient disturbance: the main daytime circulation remains nearly stationary during this phase. Generally when the solenoid passes a location, the CBL grows explosively and the depth of the up-slope flow increases.

Atmospheric Processes Affected by Daily Periodic Mountain and Valley Winds A variety of atmospheric processes may be affected by the diurnal cycle of valley winds. Here we concentrate on two aspects, namely processes involving water and those affecting air quality.

Water Cycle and Moist Processes The dynamics of valley winds involve essentially dry processes. Nonetheless many valleys lie near, or contain, water bodies or humid and vegetated areas. Whenever an appreciable water content is available, moist processes may significantly affect the energy and mass budgets associated with valley flows. For instance, higher contents of soil moisture affect the partitioning of surface fluxes, and tend to increase latent heat fluxes at the expense of reduced sensible heat fluxes, thus hampering the heating of surface layers. This is the reason why thermally driven circulations are best developed in arid environments. Rising motions of moist air may eventually lead to condensation and to the formation of clouds in the upper part

Figure 24 Map (top) and 3-D perspective (bottom) of the Elqui Valley in the Andes. The dashed line in the valley is oriented along the valley axis. ‘LS’ and ‘Vi’ indicate the positions of La Serena (145 m AMSL) and Vicuña (650 m AMSL), respectively. AMSL, above mean sea level. Reproduced with permission from Bischoff-Gauß, et al., 2008. Model Simulations of the Boundary-Layer Evolution over an Arid Andes Valley. Boundary-Layer Meteorology 128, 357–379.

Mountain Meteorology j Valley Winds of valley sidewalls or above the crests. The resulting clouds may cover the sky and thus reduce the radiative energy input, and produce showers and thunderstorms, especially in the afternoon. Nocturnal cooling by drainage winds, especially at the valley floor, may lead to condensation. The formation of dew may be beneficial as water supply to vegetation and cultures, especially in arid areas. On the other hand, frost may produce serious damage to crops, and surface icing, as well as fog, may lead to serious risks for transportation safety. Examples of the first case are found in some valleys on the western side of the Andes range, facing the Pacific Ocean, such

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as the Elqui Valley in Chile (Figure 24). Daily sums of nocturnal dew deposition by condensation of moist air, advected from the coast by daytime up-valley winds are shown in Figure 25. The annual nocturnal sum of dew deposition amounts to 5–10 mm year1, which is about 5–10% of the mean annual precipitation, but almost of the same order of magnitude as precipitation amounts in dry years. So, as in many other arid areas, dew deposition is an important additional source of water for the natural vegetation, especially in dry years. Also, organized thermally driven vertical motions of moist air associated with valley winds, may contribute, like other

Figure 25 Daily sum of nocturnal dew deposition (D) at Pelicana and daily sum of precipitation at La Vicuña in 2000 (upper panel) and accumulated annual dew formation for 2000–02 (lower panel). Reproduced with permission from Kalthoff, et al., 2006. The energy balance, evapotranspiration and nocturnal dew deposition of an arid valley in the Andes. Journal of Arid Environments 65, 420–443.

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Figure 26 Vertical profiles East of the Tibetan plateau: the vertical motion deviations (unit: cm s1, colored), the perturbation vertical circulation vectors (zonal wind and 100 times of vertical velocity), and the perturbation meridional winds (0.2 m s1; solid blue, positive; dashed, negative) latitudinally averaged between 278 and 358N diagnosed with GFS analyses at (a) 0600, (b) 1200, (c) 1800, and (d) 0000 UTC during the pre-mei-yu period (15 May–15 June). The pink solid curves show the averaged normalized diurnal precipitation deviations with the pink dashed straight line as the zero value. The black solid curves show the averaged terrain elevations. The green solid lines show that the zonal wind is equal to the mean diurnal propagation speed of 15 m s1. The S0, S1, S2, and S3 show the approximate solenoid centers. Reproduced with permission from Bao, et al., 2011. Diurnal variations of warm-season precipitation east of the Tibetan Plateau over China. Monthly Weather Review 139, 2790–2810.

combinations of thermally driven flows over complex terrain, to promote convective and orographically induced clouds, as well as the associated precipitation phenomena. Mountainplain circulations also play a key role in moisture transport, and in the initiation of moist convection. Typically convergence of the daytime flows over the mountains produces afternoon clouds and air mass thunderstorms, and the divergent nighttime sinking motions produce late afternoon and evening clearing. A remarkable example, as to intensity and extension, is offered by the mountain-plain circulation effects on warm-season precipitation east of the Tibetan Plateau, which are strongly affected by the differential heating between the plateau, the highlands, the plains, and the ocean. Figure 26 shows latitude-averaged vertical cross sections of typical circulation patterns associated with the diurnal cycle. In the early afternoon (Figure 26(a)), there are three distinct west–east solenoidal circulations in the lower- to midtroposphere. These circulations are driven by the differential diabatic heating, with the upward branches on the highland– plateau slopes and the downward branches over the low

basins, plains, and oceans. The westernmost and strongest solenoid (S1) has the westward-tilted rising branch over the eastern slope of the Tibetan Plateau and the sinking branch over the Sichuan basin. The second solenoid in the middle (S2) has a rather shallower rising branch over the highlands along the Qinling and Wushan mountain ranges, and a more extended and broader sinking branch over the east China plains. The third solenoid (S3) has the rising branch along the coastal lands and the weak sinking branch over the nearby oceans. Each of the upward branches of the solenoids corresponds to a diurnal precipitation peak. On a larger scale there also exists a broader domain-wide vertical solenoid circulation (S0) across all three solenoids with the upward branch on the eastern Tibetan Plateau and the downward branch over the plains. In the early evening (Figure 26(b)), the S0 becomes the dominant mode in the cross section, with the upward motion strengthened at the eastern slope of the Tibetan Plateau and the downward motion over most of the areas eastward except for the weak upward branch of the S2 in the lower troposphere on the eastern slope of the Qinling and Wushan mountain ranges.

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Figure 27 Selected pictures from the wintertime field measurements of pollutant dispersion in the Inn Valley (Austria). (a) Map of the target area: color scale represents elevations in km AMSL, yellow and red markers indicate the locations of measurement sites and towns. (b) Vertical transects of aerosol backscatter intensity at 1400 UTC 24 January 2006 (A1–A2 as in panel a). (c) Schematic of pollution transport processes by up-slope winds. Arrows indicate mean flow and turbulent eddies. A white solid (dashed) line indicates a closed (broken) snow cover. AMSL, above mean sea level. Reproduced with permission from Gohm, et al., 2009. Air Pollution Transport in an Alpine Valley: results from airborne and ground-based observations. Boundary-Layer Meteorology 131, 441–463.

Both the upward branches of S1 and S2 continue to be associated with local diurnal precipitation maxima at this hour, while the broader and stronger sinking branch over the east China plains corresponds to a broad local precipitation minimum phase in these regions at this hour. The coastal solenoid S3 is mostly absent in this early evening hour, though the sinking branch over the ocean is considerably stronger than over the coastal land. In the early morning (Figure 26(c)), the nighttime vertical circulation is nearly a complete reversal of the daytime circulation (Figure 26(a)) with the downward branches over the highland–plateau slopes and the upward branches over the low-lying plains–basins. Consequently, strong diurnal precipitation peaks (nocturnal rainfall maxima)

are observed over the Sichuan basin (part of S1) and over the east China plains (part of S2). However, the nocturnal circulation pattern may be further strengthened to peaked maximum at 2100 UTC: the nocturnal precipitation peak phase over the plains is also coincidental with a developing low-level southerly jet that transports more warm moist air to this area and contributes to the enhancement of nighttime precipitation. Boundary layer processes associated with the reduced turbulence diffusion due to ceased daytime heating are believed to be responsible for the development of the low-level nocturnal jet. A few hours after sunrise (Figure 26(d)), the vertical circulation evolves from the nocturnal pattern in Figure 26(c) to the daytime pattern in Figure 26(a), and is again dominated

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by the domain-scale broad solenoid (S0) as a reversal of that in Figure 26(b) with the downward motion maximized at the eastern slope of the Tibetan Plateau and the upward motion in a broad area to its east maximized at the mid-troposphere.

Air Pollution Airflows and thermal structures associated with valley winds may affect the fate of atmospheric pollutants in many ways. Typical sources of air pollution are settlements, infrastructures, and industrial activities mainly based at the valley floor or, even more frequently, on the adjacent plains. So up-valley winds may convey highly polluted air into the valleys, whereas downvalley winds may have a cleansing effect of polluted air at the valley exit over the plain during nighttime. On the other hand, up-slope flows may transport to upper levels either already formed primary pollutants, or precursors of secondary pollutants released at the valley floor. There the exposure to radiation may enhance the formation of photochemical species, which eventually get drained to lower levels by nocturnal down-slope winds. Also the thermal structures associated with valley winds, through their effects on stability, may affect the fate of atmospheric pollutants. For example, the depressed CBL over the valley floor may reduce the mixing height, leading to higher concentrations. This may be particularly critical during wintertime, when on one hand the reduced radiative input leads to shallower mixed layers, and on the other hand, more pollutants are emitted from house heating and traffic. In a similar way the frequent occurrence of nighttime inversions, especially during wintertime, also reduces the mixing height. Figure 27 provides an example of nontrivial features characterizing wintertime pollutant dispersion patterns in the Inn Valley in the Alps.

Acknowledgments Data from surface weather stations used for the graphics presented in Figures 19–21 were kindly provided by the Hydrographic Office of the Autonomous Province of Bolzano (for Merano, Bolzano, Bronzolo, and Salorno stations), the Meteorological Office of the Autonomous Province of Trento – Meteotrentino (Rovereto station), the Edmund Mach Foundation (San Michele, Trento, and Ala stations), and the Environmental Agency of the Veneto Region (Verona station). Lorenzo Giovannini kindly performed the climatological analysis of time series from the above data, and prepared Figures 18–21. The Author is greatly indebted to Massimiliano de Franceschi, Lorenzo Giovannini, Lavinia Laiti, Stefano Serafin, Elena Tomasi, and Felicity Hope for carefully reviewing the manuscript, and suggesting many valuable improvements.

See also: Agricultural Meteorology and Climatology. Air Sea Interactions: Freshwater Flux; Momentum, Heat, and Vapor Fluxes; Sea Surface Temperature; Surface Waves. Aviation Meteorology: Aircraft Emissions. Boundary Layer (Atmospheric) and Air Pollution: Complex Terrain; Convective Boundary Layer; Diurnal Cycle; Microclimate; Stably Stratified Boundary Layer; Surface Layer. Clouds and Fog: Fog. Hydrology, Floods and Droughts: Soil Moisture. Land-Atmosphere Interactions: Canopy Processes; Overview; Trace Gas Exchange. Mesoscale Meteorology: Mesoscale Convective Systems. Mountain Meteorology: Katabatic Winds; Land and Sea Breezes; Overview. Numerical Models: Parameterization of Physical Processes: Clouds; Parameterization of Physical Processes: Turbulence and Mixing. Oceanographic Topics: Surface/Wind Driven Circulation. Ozone Depletion and Related Topics: Surface Ozone Effects on Vegetation. Satellites and Satellite Remote Sensing: Earth’s Radiation Budget; Surface Wind and Stress; Water Vapor. Stratosphere/Troposphere Exchange and Structure: Local Processes. Synoptic Meteorology: Anticyclones. Thermodynamics: Moist (Unsaturated) Air.

Further Reading Barry, R.G., 2008. Mountain Weather and Climate, third ed. Cambridge University Press. 506pp. Defant, F., 1949. Zur Theorie der Hangwinde, nebst Bemerkungen zur Theorie der Berg- und Talwinde [A theory of slope winds, along with remarks on the theory of mountain winds and valley winds]. Archiv für Meteorologie, Geophys. Bioclimatologie, Ser. A 1, 421–450 [Theoretical and Applied Climatology]. [English translation: Whiteman, C.D., Dreiseitl, E., 1984. Alpine meteorology, Translations of classic contributions by Wagner A., Ekhart, E., Defant, F., PNL-5141/ASCOT84-3. Pacific Northwest Laboratory, Richland, Washington, 121pp.] http:// www.osti.gov/bridge/servlets/purl/6665518/6665518.pdf. Egger, J., 1990. Thermally forced flows: theory. In: Blumen, W. (Ed.), Atmospheric Processes over Complex Terrain. American Meteorological Society, Boston, pp. 43–57. Geiger, R., Aron, R.H., Todhunter, P., 2009. The Climate Near the Ground, seventh ed. Roman and Littlefield Publishers, Maryland, 523pp. Whiteman, C.D., 1990. Observations of thermally developed wind systems in mountainous terrain. In: Blumen, W. (Ed.), Atmospheric Processes over Complex Terrain, American Meteorological Society Meteorological Monographs, vol. 45 (23), pp. 5–42. Whiteman, C.D., 2000. Mountain Meteorology: Fundamentals and Applications. Oxford University Press, New York, 355pp. Wolyn, P.G., McKee, T.B., 1994. The mountain–plains circulation east of a 2-km-high north–south barrier. Monthly Weather Review 122, 1490–1508. Zardi, D., Whiteman, C.D., 2013. Diurnal mountain wind systems. In: Chow, F.K., De Wekker, S.F.J., Snyder, B. (Eds.), Mountain Weather Research and Forecasting – Recent Progress and Current Challenges, Springer Atmospheric Sciences. Springer, Berlin, pp. 37–122.