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FIGURE 7 | Regime diagram for hydrostatic single-layer flow over an obstacle. U and do are the initial fluid velocity and layer thickness, with cg the wavespeed. In the region EABC the flow is partially blocked, with an upstream hydraulic jump controlled by a critical condition at the obstacle crest. DAE is the “hysteresis” region, in which the flow may be either partially blocked as in EABC, or supercritical, as above AD, as indicated by arrows. For more details see Section 2.3 of Baines (1995, 1998). One may expect similar types of behavior to occur for two-layer flow over topography. Some examples have been — Figure 7 | Regime diagram for hydrostatic single-layer flow over an obstacle. U and do are the initial fluid velocity and layer thickness, with cg the wavespeed. In the region EABC the flow is partially blocked, with an upstream hydraulic jump controlled by a critical condition at the obstacle crest. DAE is the “hysteresis” region, in which the flow may be either partially blocked as in EABC, or supercritical, as above AD, as indicated by arrows. For more details see Section 2.3 of Baines (1995, 1998). One may expect similar types of behavior to occur for two-layer flow over topography. Some examples have been

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Lenticular clouds formed by flow over mountains in Patagonia Image by Ivana Stiperski. Mountainous regions occupy a significant fraction of the Earth’s continents and are characterized by specific meteorological phenomena operating on a wide range of scales. Being a home to large human populations, the impact of mountains on weather and hydrology has significant practical consequences. Mountains modulate the climate and create micro-climates, induce different types of thermally and dynamically driven circulations, generate atmospheric waves of various scales (known as mountain waves), and affect the boundary layer characteristics and the dispersion of pollutants.

FIGURE 1 | Wind vectors averaged over 1.6 km along the lower ABL flight leg (370 m ASL) with the release positions of successful dropsondes (S1-S7) indicated. Reference wind vector is shown in the top left corner, while the orientation of the coordinate system is denoted in the bottom right corner. The local topography is shaded.

The two lower flight legs are referred to as the upper and lower ABL leg. 8 and r stand for the potential temperature and water vapor mixing ratio, while subscripts N, S and D denote the northern (44.96-45.05°N) and southern (44.90-44.96°N) part of the segment chosen for the analysis, and the data from dropsonde S83 at the heights of the two lower flight legs, respectively. TABLE 1 | Seventh November 1999 flight legs.

FIGURE 2 | (A) Raw u and v components of the wind velocity along the lower ABL flight leg (870m ASL) over the Adriatic. The segment chosen for the analysis of possible rolls (44.90-45.05°N) is shown in red. (B) The three wind components over the analyzed segment; shown are the raw and 120-m moving-average smoothed data. A 5m s~! offset has been added to w for presentation purposes.

FIGURE 3 | Spatial structure of the weighted energy spectra k*S along the entire upper (A-C) and lower (D-F) ABL flight leg for (A,D), v (B,E) and w (C, F) wind components. The two white horizontal dashed lines indicate the analyzed segment. A noticeable increase in energy at the horizontal scale of approximately 1 km is present in all plots around the latitude of 45°N. The spectra are calculated on overlapping subintervals of 512 data points (about 10km long) which slide by 103 data points (about 2km), thus obtaining 100 spectra over the 216-km long flight legs. The y-axis values correspond to the central latitudes of subintervals.

FIGURE 4 | Vertical profiles of the (A) longitudinal u and (B) transverse v wind components, (C) potential temperature 6 and (D) mixing ratio r from the dropsonde S3 released at (13.63°E, 44.96°N). Horizontal dotted lines denote the heights of the two lower flight legs (870 and 680 m).

FIGURE 5 | Potential temperature at the two lower flight legs along the analyzed segment. FIGURE 6 | Spectral coherence (top) and phase angle (bottom) between u and w (left) and v and w (right) wind components over the analyzed segment (44.90-45.05°N) at the upper ABL flight leg (680 m).

FIGURE 7 | As in Figure 6, except for the lower ABL flight leg (370 m).

FIGURE 1 | Vertical potential temperature (0) profile of a generic two-layer flow with a density interface. The wind profile U(z) is assumed tc be constant with height (not shown).

Inversions with strength AO > A@,,i, or located at height hy > crit, Cause wave trapping because they make stationary waves become evanescent in the layer aloft. Equation (7) shows that, given Nz and U, the critical wavenumber depends on the inversion strength A@ (through g’) and on the lower layer depth hy. Critical values for AO and hy can be determined inserting k = l, = N2/U into Equation (7). Solving for A@ or h, then gives:

FIGURE 2 | (A) MODIS Terra visible satellite image on 24 December 2013, showing signature of trapped lee waves downwind of the Desertas islands in the Madeira archipelago. Coastlines are shown with solid white-black contours. The location of the sounding site (Funchal) is marked with a black dot. Flow is from left to right. Satellite image from NASA Earthdata and SRTM topography data from Jarvis et al. (2008). (B-D) Funchal operational sounding at 1200 UTC 24 December 2013. Th panels show vertical profiles of (B) potential temperature, (C) wind speed projected in lee wave direction and (D) Scorer parameter Px IN/U@)]? (black), Px IN/Ul2 with U=10ms~! (gray) and observed wavenumber ke (dashed). The solid black lines in (B,C) show the approximated idealized sounding that defines the parameters listed in Table 1. Gray shaded areas in (B) indicate regions where relative humidity RH > 90%. The vertical structure of the atmosphere during this event, as measured in nearby Funchal, is shown in Figure 2B. It consists of a neutrally stratified lower layer (Nj = 0) with 6) = 291 K, a boundary-layer inversion with A@ = 8 K at h; = 1100 m and a continuously stratified free atmosphere with Ny = 0.010 s~! aloft. The flow is westerly with almost no directional shear. A representative value of U = 10 ms_! for the wind speed is determined from the wind profile in Figure 2C as the average in the layer below z = 2h. The altitude of the inversion coincides with the layer of largest relative humidity (gray shading, RH = 97% at hj = 1100 m), implying that the cloud pattern in Figure 2A likely corresponds to an interfacial wave. Further

TABLE 1 | Flow parameters determined from the sounding in Figure 2.

FIGURE 3 | Comparison of the wavelength 1 estimated from the FDR o forced interfacial waves (Equation 7, dashed) and from the Baines (1995) three-layer model (Equation 13, solid). FIW (forced interface wave) represents the observed flow configuration, IIW (interna interface wave) assumes N2 = 0 and Free IIW (free internal interface wave) assumes AO = AGerit.

FIGURE 4 | Wave perturbations w4 2 (top) and uy 2 (bottom) determined from linear model solutions (Equations A2 and A3). Model parameters are liste in Table 1 and correspond respectively to: (A-D) forced interface waves; (B-E) internal interface waves; (C-F) free interface waves. Red and blue shading denote respectively positive and negative areas. The contour interval is 0.6 ms~!.

FIGURE 5 | Dependence of the lee wavelength 1 on: (A) inversion strength, Ad; (B) inversion height, h,; (C) free-atmospheric stratification, No; and (D) wind speed, U. Solid and dashed lines correspond respectively to Agyy and Ayyy. Black dots represent the wavelength estimated from the observed flow profile (see Figure 2); gray dots indicate the corresponding wavelength when No = 0; and white dots mark the critical values A@¢,j¢ and h4¢,j¢ at the corresponding wavelength A = 2nU/No. Shaded areas indicate the propagating regime in the upper layer, i.e., where wave trapping on the interface is not possible.

FIGURE 7 | Estimation of the error due to stratification effects in the shallow-water approximation. Gray shading and contours represent the values of € = 1 — (lah) - coth(/2h4). The white dot shows the flow configuratior of the observed lee wave case.

FIGURE 6 | Estimation of the stratification impact on interfacial

FIGURE 2 | Notation sketch for hydraulic jumps, with velocities relative to a frame of reference moving with the jump. For the subscripts, layer 1 is the lower, layer 2 the upper, “u” denotes upstream, “d” downstream, and fot the pressure, “s” denotes surface, and “i” the interface. There have been essentially three previous attempts which have involved assumptions about the dynamics to give expressions for

FIGURE 1 | A representative diagram showing the nature of the flows considered in this analysis. These are hydrostatic two-layer flows with a rigid lid, forced by flow over a long obstacle. See text for notation. This section summarizes the results given in Baines (2015). An hydraulic jump in two-layer fluids is here defined to be a HYDRAULIC JUMPS IN TWO-LAYER FLOWS

FIGURE 3 | Some representative jump speeds as a function of jump amplitude, moving into fluid at rest, for a range of density ratios (02/4 = 0.1, 0.2, 0.5, 0.79, 0.99). The upstream lower layer thicknesses are given by ry = d4,4/D = 0.1 and 0.35. The dashed portions of the curves denote the regions where jump speed decreases with increasing amplitude. This makes them potentially unstable. Further, for these dashed curves, the flow is supercritical (relative to the jump) on the downstream side. This means that disturbances from downstream cannot propagate up to the jump and increase (or affect) it. In particular, jumps with amplitude greater than that of maximum speed cannot be generated from downstream, so that only the solid parts of the curves represent enduring jumps generated by flow over topography.

where piq and pj, denote the pressures at the downsteam and upstream interfaces respectively, which may be related hydrostatically to the surface pressures. This analysis obviates the necessity for the various different assumptions made or proposed by Yih and Guha (1955), Wood and Simpson (1984), Klemp et al. (1997) and Li and Cummins (1998). where S denotes the normal vector to the boundary of A, and 1 denotes the vector along it, in the anti-clockwise sense. Since the density is uniform in each layer, and if uj, = u2,, this equation reduces to

We now consider two-layer flow over a long obstacle for which the horizontal length scale L and the time scale of the motion are sufficiently large for the equation for vertical motion to be hydrostatic, apart from the possible presence of hydraulic jumps. Under these conditions the equations of motion for the two layers may be written where 1, U2, d,,d2 denote the velocities and thicknesses of layers 1 and 2, and h(x) is the height of any bottom topography on the lower surface. If the upper layer has a rigid upper surface, and we assume that the total flow of fluid through the system is constant, we have, at all locations x,

FIGURE 5 | Definition sketch for notation for flow over an obstacle witt an upstream jump. All velocities are relative to a frame of reference at rest with the obstacle. Here the velocities and thickness immediately downstream of the jump (section “a”) are the same as those immediately upstream of the obstacle.

FIGURE 4 | Comparison between jump speeds c, (scaled with co) computed using the Full Vortex Sheet model (FVS) with experimental observations with water and kerosene (p/p; = 0.79), from Baines (1984),

FIGURE 6 | The same as Figure 5, except for larger obstacle heights where the flow contains a rarefaction. Here the jump has the maximum speed, and section “b” immediately upstream of the obstacle has larger lower-layer thickness than section “a,” immediately downstream of the jump.

Equation (4.8) can then be integrated directly to give the “Riemann invariant”

FIGURE 9 | Flow properties for steady-state flow over an obstacle, depicted on the Fo—Hm diagram for r = ry = 0.1, p2/p4 = 0.99—the near-Boussinesq case. The flow is subcritical below AB, and upstream hydraulic jumps occur to the right of EAB below EC; the lower layer is completely blocked to the right of BC. Rarefactions that increase the upstream disturbance above that due to the jump of maximum speed occur in the small region immediately below EC, above the curve with ra/ru = 3.85. In the region AEFA, there are three possible flow states: supercritical flow, and two states with different upstream jump heights, given by the cross-over of the two curves passing through any given point.

FIGURE 8 | Curves for the onset of critical flow at the obstacle crest as Hm increases from zero, with no upstream jump, for a range of density ratios, for ry = 0.1. For Fo values larger (or Hm less) than those on the upper part of these curves, the steady flow is everywhere supercritical, and for Fo (or Hm) less than the lower part (where these curves effectively coincide), the steady flow is subcritical.

FIGURE 10 | As for Figure 9, but for the parameters r, = 0.1, p2/p4 = 0.1. The properties are essentially the same, except for the region DEGF, within which the flow has two possible flow states: supercritical flow, or critical flow at the obstacle crest with an upstream jump.

The functions aj, b; in Equation (3.8) take the following general forms. The variable 7 is relative to layer thicknesses dj, do, for the lower and upper layers respectively, where dy + dz + h = D. With dj; and dp as reference values, for aj (n, v) we have

FIGURE 1 | Schematic of the three-dimensional valley-plain system indicating the four control volumes and the mean along-valley circulation during the up-valley wind phase. The arrows indicate the net mass flux across the interfaces between adjacent control volumes. See Figure 3 for a top view of the valley-plain system. where H, is the turbulent sensible heat flux normal to the land surface A,;, R is the radiation flux, and H is the turbulent sensible heat flux normal to the surface Aj. The surface Ag is the atmospheric component of the surface of the control volume V. For a conventional control volume the last term simplifies to the integral of the vertical turbulent sensible heat flux across the top surface of the control volume. Equation (1) is derived by integration of the potential-temperature equation and by using Gauss’ theorem to convert the resulting volume integral of the turbulent heat flux divergence into a surface integral and by decomposing the resulting surface integral into a land surface part A; and an atmospheric part Ag (as in Schmidli and Rotunno, 2010). In other words, the net change of heat content in an arbitrary volume V' (m/6') is equal to the sum

We first derive an expression for the net heat exchange of the valley with its surroundings due to advection. The bulk heat budget for an arbitrary control volume V can be expressed as

FIGURE 2 | Dependence of the parameters 1, Bgp and the different approximations of the advective ratio fg (see main text) on the height of the upper control surface (depth of the control volume), for the topography to be introduced in Section 3 and illustrated in Figure 3.

The abbreviations refer to valley length (L), valley width (W), valley depth (H), potential temperature lapse rate (LR), surface sensible heat flux (SH), and momentum roughness length (Zo). TABLE 1 | Summary of the numerical experiments. 4. RESULTS

FIGURE 3 | Computational domain adopted in this paper. The lines denote the height contours of the topography (contour interval = 250 m)

FIGURE 4 | Evolution of the valley wind system for the reference case. Along-valley and cross-valley sections after 3, 6, and 9h of integration showing the along-valley flow (thick contours; contour interval = 0.5ms~!: negative values are dashed), potential temperature [contour interval = 1 K (left panels) and 0.5 K (right panels)], eddy diffusivity (shading; 10 m2 s~'), and the cross-valley circulation (wind vectors). The axis units are kilometers.

FIGURE 5 | Time evolution of the mean up-valley wind at the valley entrance (left panel) and the heat budget tendencies for the valley control volun (right panel). uj, denotes the average of the along-valley wind over the inflow layer, that is up to he. The dashed line indicates the a-priori estimate, fa(hc), of the steady-state advective heating rate.

FIGURE 6 | Scaling the advective heat flux: comparison of different approximations of fg with the diagnosed value from the numerical simulations. (A) basic approximation: fa = fa(hc), (B) improved estimate with fg = gg (he), (C) improved estimate with fa = fa (he).

FIGURE 7 | Diagnosed depth of the inflow layer, he.

FIGURE 8 | Scaling the along-valley mass flux M: comparison of different a-priori estimates of M with the corresponding diagnosed value from the numerical simulations. (A) Basic approximation M = M(hc), (B) improved estimate with M = M(he, fg), (C) improved estimate with M = M(he, fa). The former estimate is compared to the simulated along-valley flux up to ridge height, the latter two estimates are compared to the total simulated up-valley flux, that is to the height he.

FIGURE 1 | Structure of the lower atmosphere over a mountain. The solid line indicates the boundary between the free atmosphere and the atmosphere influenced by the mountain. The dashed line indicates the top of the slope atmosphere, while the hatched pattern indicates the valley atmosphere (after Ekhart, 1948).

FIGURE 2 | Idealized vertical structure of the lower troposphere under daytime convective conditions over flat and homogeneous terrain, subdivided into the surface layer (SL), the mixed layer (ML), the entrainment zone (EZ), and the free troposphere (FT). The vertical profiles represent wind velocity u(2), specific humidity q(z), potential temperature 6(2), air pollutant concentration c(z), vertical turbulent sensible heat flux H(z), standard deviation of turbulent vertical velocity fluctuations ow/(z), and backscatter signal intensities Bg(z) from a sodar and By_(z) from a lidar. Zs is the terrain height while z; and Z, are the depth and the height of the CBL, respectively. We are making a distinction between CBL depth and CBL height. In applications where the volume of air in which e.g., pollutants are mixed is considered, or for scaling arguments, it is important to use CBL depth z; (or thickness) which is the height of the CBL top above ground level (AGL). On the other hand, for Conventionally, CBL heights have been determined most frequently from vertical temperature profiles. In recent years, the development and availability of remote sensors such as sodars (sound detection and ranging) and lidars (light detection and ranging) have provided alternatives to this conventional method and have enabled the documentation of the daily variation of the CBL height at large temporal and spatial resolution. Sodars detect temperature fluctuations (turbulence), winds, and wind shear, while lidars detect vertical aerosol distribution. Particularly, downward looking airborne lidars have proven useful for the investigation of the spatial variability of CBL heights (e.g., Melfi et al., 1985; Kiemle et al., 1995; Hayden et al., 1997; Hageli

FIGURE o | Diurnal boundary layer structure over a siope. Upper panel: time-height section of airflow regimes over a slope during fair weather conditions. hr and hg are the height of surrounding ridges and the base height of the free troposphere, respectively. Ticks on the time axis indicate midnight (MN), sunrise (SR), noon (NN), and sunset (SS). Lower panel: vertical profiles of potential temperature 6(z) over the slope at selectec times ty to tg marked in the upper panel by small arrows.

FIGURE 4 | Conceptual models of slope wind circulation and CBL structure over a slope on a fair weather day. The green box in (G) on the lower left shows the location of the depicted cross section over a slope facing a valley or a plain. Thin solid and dashed lines represent isentropes and the top of the turbulent CBL, respectively. Solid and dashed arrows indicate the airflow and the compensating subsidence over the valley center or over the plain. (A) Slope wind circulation with homogeneously stratified atmosphere over the valley center or plain. (B) Two staggered slope wind circulations separated by a strongly stratified layer. (C) Slope wind circulation limited to lower slope due to strongly stratified layer aloft. (D) Slope wind venting into neutrally stratified layer aloft. (E) Recirculation of slope winds within the turbulent CBL. (F) Jump in CBL depth due to erosion of the inversion above the upslope wind layer and a deep neutrally stratified layer aloft.

FIGURE 5 | Conceptual models of CBL development in the center of a valley. The location of the idealized vertical profiles of potential temperature 6(z) at times tg-tg is shown by the green dot in (A). (B-D) in the top row show three basic types of CBL development, while (E-H) in the bottom row show four combinations (mixed types) of the three basic types. The main direction of heat supply and erosion of the valley inversion for the three basic types are illustrated by numbered arrows in (A): arrow 1: turbulent heat flux from the valley floor (type 1); arrow 2: subsiding valley inversion (type 2); and arrow 3: heating from valley side walls by slope wind recirculation (type 3). The dashed line at tg indicates that a well-mixed potential temperature profile throughout the entire valley atmosphere does not necessarily occur. CBL evolution can be notably different from valley to valley depending on the relative importance of surface heating, subsidence, and other processes in valley atmospheres. A schematic illustration of vertical potential temperature profiles at four consecutive times (t0-t3) observed over valley floors under a variety of conditions is shown in Figure 5. Note that these profiles night (Figure 4D). This means that slope flow detachment in this conceptual model occurs at elevations above the (subsiding) valley inversion. Reuten et al. (2005) provide observational evidence that scenarios where the return circulation penetrates into the inversion capping the upslope wind layer, might be typical only for cases with shallow CBLs in the valley or over the adjacent plain. Later in the day, when the CBL in the valley or over the plain exceeds a critical height (about half the height of the nearby ridges), the return circulation occurs within the turbulent valley/slope CBL (Figure 4E). In these situations, turbulent vertical momentum transfer within the CBL mixes the upslope wind layer with the return circulation aloft, possibly weakening or destroying the organized slope wind circulation. An upslope flow re-circulation contained within the CBL has also been found in numerical model simulations (e.g., Demko and Geerts, 2010). Another type of CBL behavior observed over a slope is described by Kossmann et al. (1998) for cases with a terrain following CBL top or residual layer top (Figure 4F). In such situations with near- neutral stratification above the slope flow layer, any weakening of the along-slope cold air advection due to disturbances in the upslope flow can lead to turbulent erosion of the inversion above the slope wind layer. This results in a sudden increase of CBL height from the top of the slope wind layer to the top of the near-neutral layer. Re-intensification of the upslope winds might then re-establish an inversion above the slope wind layer due to undercutting. During the course of the day, these mechanisms can lead to significant oscillations in CBL

FIGURE 6 | Vertical cross sections of thermal wind circulation and CBL structure in a valley for (A) a cross valley section during the morning transition and (B) an along valley section around noon or mid-afternoon. The solid black line indicates CBL depth z;. Thin solid vectors indicate airflow components in the cross section direction. Red solid lines indicate vertical profiles of potential temperature 6(z). The dashed line in (A) indicates a sun ray which separates the sunny and shaded parts of the valley. Green lines in (B) indicate vertical profiles of the horizontal along-valley wind component with the horizontal black vectors depicting the direction of the flow. Curved black vectors and vertically pointing white arrows indicate subsidence or lifting at the CBL top caused by horizontal divergence or convergence of the along-valley airflow. Along-valley CBL height structure is affected by areas of horizontal flow divergence or convergence and resulting compensating vertical motions along the valley. Freytag (1987) concluded from valley air mass budgets that compensating lifting and subsidence are strongest at the valley head and the valley mouth, respectively. Bianco et al. (2011) indeed found deeper valley CBLs near the valley head associated with deceleration of the thermally driven up-valley winds (Figure 6B). They hypothesized that these deeper CBLs were caused by lifting due to the convergence in the horizontal wind field in the valley, as was already observed by Freytag (1987). Similarly, compensating subsidence as a result of divergence at the valley mouth represents a mechanism for shallower CBLs at the valley mouth than at the valley show that in the val head. Model simulations by Rampanelli et al. (2004) CBLs can be significantly deeper over the plain than ey where along-valley cold air advection counteracts CBL growth (Figure 6B). Spatial variability in cold air advection and varying heating rates along the valley as a result of the complex along the flow pattern also cause irregularities in CBL heights valley (De Wekker, 2002; Weigel et al., 2006). In other situations however, observed afternoon CBL heights are horizonta ly homogeneous along and across the valley despite the presence of complex and asymmetric flow patterns (Kuwagata and Kimura, 1995, 1997; De Wekker et al., 2005).

FIGURE 7 | CBL evolution in the afternoon over a mountain basin (A,B) and over a plateau (C,D). Airflow and vertical profiles of potential temperature 6 are shown by arrows and red lines, respectively. The intrusion of cold air in the late afternoon leads to shallower CBLs over both basins and plateaus.

FIGURE 8 | Conceptual model of the CBL development over mountainous terrain on a fair weather day (A) before sunrise, (B) in the early morning, (C) at noon, and (D) in the late afternoon. Dark blue shading indicates strongly stable stratification in nocturnal cold air pools. Arrows indicate thermal circulation and turbulent mixing. The dashed lines indicate the top of the turbulent CBL. Vertical profiles of potential temperature 6 are shown in red at several locations along the cross section (after Fiedler et al., 1987).

FIGURE 9 | Schematic illustration of advective effects on CBL structure over mountainous terrain. (A) Lifted CBL top over a ridge due to convergence of upslope winds, (B) depressed CBL at a mountain base due to subsiding return circulation of a slope wind system, (C) lowered CBL top over a ridge due to Bernoulli effect, (D) depressed CBL over a ridge due to horizontal advection of a tilted CBL top, and (E) formation of an elevated mixed layer (EML) over a valley due to horizontal advection of a CBL formed over high windward terrain. The solid and dashed black lines indicate the top of the CBL before and after considering the advective effect. Arrows illustrate the airflow. Closely related to the question of terrain-following vs. level CBL heights is how the CBL evolves over individual mountain tops and ridges and their direct surroundings. Various advective effects illustrated in Figure 9 are known to influence CBL heights in these terrain locations. As was pointed out in the conceptual model (Figure 8), a relatively deep CBL can exist over the mountain top early in the day because cold air forming during nighttime drains to lower terrain which results in shallower and weaker surface-based temperature inversions at sunrise over mountain ridges and peaks than over surrounding valleys or plains. Such “bulging” CBLs over mountain tops and ridges have been observed in several field studies that were mostly performed to investigate dry convection over mountain tops and ridges preceding moist convection later in the day (e.g., Braham and Draginis, 1960; Fosberg, 1967, 1969; Raymond and Wilkening, 1980, 1982; Demko and Geerts, 2010). Many of these studies do not explicitly address variability of CBL heights but from their published data, some information about CBL heights can be derived. In general, the studies show that the bulging of the CBL over the highest elevations is caused by heating of the slopes and ridgetops and a resulting “convection core”. Lifting generated by upslope winds can enhance this bulging CBL height behavior (Figure 9A), while background winds forcing the convective core to move downwind of isolated mountain tops can

FIGURE 11 | Schematic illustration of mountain induced exchange processes between the convective boundary layer and the overlying atmosphere. E, entrainment; AV, advective venting; MV, mountain venting; and MCV, mountain-cloud venting. Vectors indicate airflow while c(z) and 6(z) indicate vertical profiles of pollutant concentration and potential temperature, respectively. The dotted and dashed line indicate the top of the aerosol layer (AL) and the CBL, respectively (after Kossmann et al., 1999; De Wekker, 2002; De Wekker et al., 2004). Some of the hypothesized mechanisms that transport air pollutants between the CBL and the FT in mountainous terrain are summarized in a conceptual diagram in Figure 11. Rotach et al. (2015) also discusses some of these mechanisms in some more detail. Figure 11 highlights the generation of multi-layer temperature and air pollution profiles and also the close connection of spatial CBL and AL structure with vertical transport and mixing mechanisms. The dotted line depicts the AL height which can be considered the maximum vertical extent of aerosol transport while the dashed line depicts the CBL height, defined as the base of a capping inversion that limits the depth of penetrative convection. While AL and CBL heights are approximately equal over flat terrain, mountainous terrain exerts a profound influence on aerosol distribution in the atmosphere: mixing and transport processes are often enhanced compared to those over flat and horizontally homogeneous terrain and the equality of AL and CBL heights breaks down. CBL heights are considerably lower than AL heights, show more spatial variability, and tend to follow the terrain more than AL heights, although the extent to which the CBL height follows the terrain decreases during the day (De Wekker et al., 2004). De Wekker et al. (2004) pointed out that simultaneous measurements of The diurnal boundary layer cycle over flat terrain has two ways of vertically transporting air pollutants in the atmosphere— pollutants are mixed upward by convection through a deepening CBL during daytime, while pollutants in the residual layer (the elevated remnant of the previous day's CBL) are entrained downward into the growing CBL. It is frequently assumed that constituents within the CBL are well-mixed and capped by an inversion. The inversion acts as a lid and limits the transport of constituents to the atmosphere above. As pointed out in Section “Definition and Determination of CBL Heights,” these characteristics are often used to define the top of the CBL. There

FIGURE 1 | Conceptual sketch of thermally driven flows In mountainous terrain. “z;” denotes the Mixed layer height (red dash-dotted line) over the adjacent plain. Blue arrows, plain-to- mountain circulation and valley wind circulation; black arrows, slope-flow and mountain venting. Situation during daytime.

FIGURE 2 | Backscatter ratio as measured with airborne lidar over a transect across the Alps on July 30 1997, 16.20 LST (reproduced with permissio from Nyeki et al., 2000). The highest visible peak (at horizontal distance 0) is Jungfraujoch. The Rhone Valley at approximately —20 km. Exchange of aerosols is a readily observable example for the exchange of mass in mountainous terrain. Nyeki et al. (2000) have documented elevated aerosol layers—reaching over the tops of the Alps, i.e., up to some 4200 m a.s.l. (above sea level, see Figure 2)—and attributed this to the growth of the convective boundary layer up to this level. More recently, simulations of De Wekker et al. (2004) have shown that the height of the “aerosol ayer” does not correspond to the “mixed layer” (or convective boundary layer) height (see discussion in Section Thermally Forced Exchange Processes Over Mountainous Terrain). Similar conclusions had already been drawn by De Wekker (2002), based on simulations of the Riviera Valley (Rotach et al., 2004) with the meteorological part of the simulations validated using observations (De Wekker et al., 2005), but the aerosols (particles) artificially being introduced into the domain. However, the elevated aerosol concentrations as in Figure 2 can be taken as experimental evidence for (i) the efficiency of mass exchange over truly complex topography and (ii) the fact that different processes, i.e., turbulent exchange within the mountain boundary layer and meso-scale processes (mountain venting), are co- responsible for the total EAE over mountainous terrain. The relative importance of these (and geometrical, i.e., terrain related) COz is another potential tracer for mass exchange, but the low resolution of global CO2 inversion models is insufficient to resolve the impact of meso-scale (thermal) circulations on CO2 exchange processes (Pérez-Landa et al., 2007). A combination of high-resolution numerical modeling and experimental data from a 2-week campaign in the coastal region of Valencia (E) influenced by profound topography, was used by Pérez-Landa et al. (2007) to assess the impact of non-resolved meso-scale circulations. While encountering a number of difficulties—e.g., the “correct” attribution of source (sink) strength, timing and localization to the “tracer” (CO2)—as usual in a study with pioneering character such as this one, the authors could clearly demonstrate the importance of thermal circulations (dominantly sea breeze in their case, but in combination with topographic forcing) on the regional budget of CO2. Similarly concerned with the quality of CO2 budget modeling using coarse-grid inversion technique, Pillai et al. (2011) present evidence for the impact of thermally driven circulations on the flux-tower site “Ochsenkopf” situated in the “Fichtelgebirge,” a moderately high—some 500m elevation with respect to surroundings— pre-alpine region in southern Germany. By demonstrating that “the effects of meso-scale transport such as mountain-valley circulations and mountain-wave activities on atmospheric CO distributions are reproduced remarkably well in the high- resolution models” they indirectly confirm the importance of these exchange processes in mountains terrain. Sun et al. (2010), in a multi-scale and multi-disciplinary study using a wealth of different observational and modeling techniques, investigated

FIGURE 3 | Effect of height-to-width ratio on the thermally forced cross-valley circulation. Potential temperature (thin contour lines), cross-valley wind speed (color shading), and three different boundary layer heights are shown for a 1000 m (A) and 2000 m (B) deep valley with identical forcing and after 6h of simulation. See Wagner et al. (2015a) for the definition of the boundary layer heights and the simulations. The bold black line denotes the valley-mean potential temperature profile.

FIGURE 4 | Flow and temperature fields, (A) and (C) and tracer concentration, (B) and (D) from high-resolution numerical simulations of a deep embedded valley (upper row) and a shallower embedded valley (lower row) in a mountain range. Thin solid lines: potential, temperature, arrows x-z wind vector, color shading vertical velocity, (A) and (C), and tracer mixing ratio, (B) and (D). The black bold solid line corresponds to the Convective Boundary Layer height (diagnosed from first height where the gradient of potential temperature exceeds 0.001 km~! when searching from the below), green line: “aerosol layer height” (diagnosed from maximum gradient in mixing ratio). The tracer is released across the entire mountain range at the lowest eight grid points (about 110m from ground) at constant rate. Figure reassembled from different figures in Lang et al. (2015). See this paper for details of the simulations.

FIGURE 5 | Flow and temperature fields from high-resolution simulation of a 1.5km deep symmetric valley, (A) at the equator, east-west orientation; (B) at 44°N, east-west orientation; and (C) at 44°N, north-south orientation. Solid lines are isentropes, arrows xz-wind vectors, the color code for the x-component of the wind [ms~"]. The panels show the situation on the second day of the simulation, 2 pm local time. The solar forcing in all three panels corresponds to the case of 550 Wm~2 amplitude (roughly 240 Wm-2 amplitude in surface heat flux) of Leukauf et al. (2015). For details of the simulations see Leukauf et al. (2015) or Wagner et al. (2015a,b).

FIGURE 1 | Schematic figure of the different wind systems combining to Alpine pumping with an idealized line of surface air pressure reduced to the altitude of the foreland.

* Averaged over the evaluation domain. * Wind speeds at 850 hPa for 00, 12, 23 UTC over Munich/Oberschleissheim. TABLE 1 | Identification criteria combinations with threshold values and average yearly number of days identified from the COSMO-CLM simulation results for the period 1989-2008.

FIGURE 3 | Model domains for EUROPE (left) and for MUNICH (right) nested into the Europe domain (location of the nest is shown by the black frame) The domain for the analysis of model results is shown by the red frame.

FIGURE 4 | Daily score of the four criteria combinations defined in Table 1.

TABLE 2 | Average times of inflow (red), outflow (blue), and transition (brown) phases of Alpine pumping derived from the mean hourly wind fields for the different criteria combinations.

FIGURE 5 | Averaged surface wind maps of the horizontal wind vector at 10 m agl for SR criterion (left) and PR_UW criteria combination (right) at 1 UTC (top) and 00 UTC (bottom). Bold black lines show the urban area of Munich (indicated by the letter M) and the German-Austrian border, while thin black contour lines represent the terrain height. 8 x 8 model grid points within the black rectangular frame (south of Munich) are used to calculate the wind oscillation criterion. The triangles at the top of the panels indicate the geographical longitude of the meridional cross sections shown in Figure 7.

FIGURE 6 | Latitude-time sections of the southerly surface wind component at the longitude of Munich, averaged over 5 grid cells in zonal direction for the SR criterion (left) and the PR_LUW combination (right). The vertical structure of the Alpine pumping layer is strongly related to the distance to the Alps and the time of the day (Figure 7). Analysis of meridional vertical cross sections of the simulated wind field through Munich show higher wind velocities close to the Alps (discussed in the previous Section “Temporal and Spatial Characteristics Near the Surface”) also extend to higher levels. Furthermore, the vertical cross sections confirm that wind reversals between the daytime and nighttime phases of Alpine pumping occur earlier in this region compared to the foreland. With greater distance from the Alps, the increasing time lag in wind reversal is evident in the entire inflow and outflow layer. The depth of the surface bound inflow and outflow layers are found to increase from north to south. Averaged winds above 2500 m reflect weak synoptic scale winds blowing mostly from northerly directions during days selected by the SR criterion and the PR_UW combination (Figure 7). Hourly and daily data from a reanalysis-driven regional climate simulation with COSMO-CLM model for the period of 1989- 2008 were analyzed to identify days with Alpine pumping and to determine the mean diurnal variation of the direction, intensity,

FIGURE 7 | Averaged v and w wind components along a meridional vertical cross section through Munich at 12:00 UTC (top) and 00:00 UTC (bottom) for the SR criterion (left) and PR_UW combination (right), with potential temperature shown by color shading in the background. The two black dots mark the northern and southern border of Munich.

FIGURE 1 | (A) Particulate Matter pollution during wintertime inversions over Grenoble (Photography: courtesy of Eric Chaxel). (B) View of the mountain ranges and Grenoble valleys discussed in the paper. (C) Locations of the ground-based Automatic Weather Stations (yellow) and air-quality stations (red, not used in the present study); the acronyms are defined in Table 1. Extracted and adapted from Largeron and Staquet (2016) with background maps taken from Google Earth.

The low-elevation stations are located at the valley bottom. TABLE 1 | Description of the ground-based Automatic Weather Stations in the Grenoble valleys.

FIGURE 2 | Time series of 2-m air temperature in December 2006 at (A) the low-elevation station of LV (black) and the high-elevation station of CR (red). The gray-shaded zones refer to temperature inversions (the temperature in CR is higher than in LV); persistent inversions defined by criterion (1) are indicated by a yellow veil; (B) two low-elevation stations, LV (black) and POC (gray); (C) two high-elevation stations, CR (black) and LG (gray).

The duration of each episode is indicated in columns 2 and 3 and a measure of the intensity of the episode, (AT /AZ) episode, IS given in column 4, TABLE 2 | Persistent inversions detected using criterion (1).

FIGURE 3 | Temporal evolution of the 24-h-running average of the bulk temperature gradient AT/Az (red) and heat deficit H (black) during the 2006-2007 winter. The 9 inversions |, 1<k<9, detected by criterion (1) are circled in black. The persistence threshold (AT/AZ)winter is indicated with a gray line Extracted and adapted from Largeron and Staquet (2016).

1 the third column, only changes relative to the second column are indicated; otherwise the line is left empty. The simulated periods are indicated at the beginning of the table TABLE 3 | Main parameters of the numerical simulations.

FIGURE 4 | Maps of the wind at a given altitude during episode Ig at 06:00 UTC on December 28. (A) z = 450 m ASL; (B) z = 650 m ASL; (C) z= 850 m ASL; (D) z = 1500 m ASL.

(1993), are very unlikely and would have another signature. Indeed, a downward transport of horizontal momentum from above the valley, which would rather occur under unstable or neutrally stable conditions, would result in a linear dependency between the valley-wind direction and synoptic-wind direction (as indicated by the dashed dotted line in Figure 6). The channeling of the synoptic wind into the valleys (for a strong enough wind for instance) would lead to a step function (dashed line in Figure 6). It follows that, during a wintertime persistent inversion, a unique organization of the valley-scale circulation within the Grenoble valleys sets in in the ABL, which does not depend upon the episode, because it is decoupled from the synoptic wind. This circulation is controlled by the local topography and the radiative cooling of the ground. Hence, a single episode may be considered as being representative of any persistent inversion of the winter when the circulation in the valley is considered.

FIGURE 6 | Direction of the valley-wind vs. that of the synoptic wind. The valley-wind direction is plotted every hour of the C1 configuration, each hour having a different color, and each episode is represented by a symbol: 0: ly, *: 15, 0 : Ig, o: I7, At lg. The horizontal black line is the direction of the valley close to the Grenoble basin. (A) Grésivaudan valley; (B) Voreppe valley. The valley-wind direction is averaged over the horizontal grid points displayed in Figure 7A, from the ground up to 400 m for the Grésivaudant valley and up to 600 m for the Voreppe valley. See text for details.

FIGURE 7 | (A) The hatched zones are those over which the average for the Voreppe valley, the Grésivaudan valley and the Drac valley are performed. The point Gi referred to in Section 5, is indicated with a red + symbol. (B) Vertical profile of temperature averaged over the Grésivaudan valley. (C) Vertical profile of wind speed ( and wind direction (0c) averaged over the Voreppe valley. (D) Same as (C) in the Grésivaudan valley. The averages are performed over the horizontal grid points displayed in frame (A). Profiles are shown at 06:00 UTC on December 28.

FIGURE 8 | (A) Stagnation index S (in km) averaged over the first 50 m above the ground and over the 2 days of configuration C2. Stagnation areas appear in red and black. (B) Recirulation index R averaged as S. Recirculation areas appear in dark red. Ventilated areas (S > 250 km, R < 0.2) correspond to areas where S appears in white and R in blue.

FIGURE 9 | (A) Temporal evolution of the surface fluxes Rry, H, LE, G = Ryy - H — LE from 27 December, 18:00 UTC to 29 December, 20:00 UTC in the Grésivaudar valley at point Gr displayed in Figure 7A. The vertical dashed lines are the astronomical sunset and sunrise times for Grenoble. (B) Temporal evolution of the surface temperature (Ts) and the 2-m air temperature (To).

FIGURE 10 | (A) Vertical profile of 98 9 above point Gr (see Figure 7A) from 27 December, 18:00 UTC to 29 December, 20:00 UTC. Black : oe < 0. Orange : O< oe < |Yadiab|. Yellow : oe > uel (B) Inversion strength A@ over the same time period. (C) Inversion strength vs. inversion height for 20 case studies of wintertime persistent inversions in the Rocky mountains (extracted and adapted from Whiteman et al., 1999b). Red symbols: parameters of the thermal inversion Ig or 28 December 2006 (A) and 29 December (B).

FIGURE 1 | Vertical profiles of potential temperature 6 and wind speed u in the linear solution of the Prandtl model for the katabatic flow (A), corresponding kinetic energy KE, potential energy PE and total energy TE (B), and diffusion DIF, dissipation DIS and storage terms dTE/at (C). The height of the low-level jet hj (D), height of the stability change (E) and height at which KE becomes larger than PE (F) as function of Prandtl number Pr (x axis) and slope angle a (different color). Heights in (D-F) are relative to the reference heights harr from the solutions when Pr = 2 and a = —0.1 rad.

FIGURE 2 | (A-C) Differences between nonlinear and linear (Figure 1) solutions of the (extended) Prandtl model (cf. Grisogono et al., 2015). (D-F) are equivalent to (D-F) in Figure 1. Also, sensitivity to the nonlinearity parameter « (with increasing line thickness as « is increased) is included in (D-F), while (C) includes the vertical profile of the interaction term /NT that is equal to zero in the linear case. The reference heights Maer are based on the solutions when Pr = 2, a = —0.1 rad and e = 0.005.

Figure 28 – uploaded by Haraldur Ólafsson

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