A summary of gap flow results within MAP is given including conceptual models, dynamical understanding, observational and modeling tools, and open issues

Georg J. Mayr

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GAP FLOWS – OUR STATE OF KNOWLEDGE AT THE END OF MAPGeorg J. MayrInstitute for Meteorology and Geophysics, University of Innsbruck, Innrain 52, 6020 Innsbruck, AustriaE-mail: georg.mayr@uibk.ac.atAbstract: A summary of gap flow results within MAP is given including conceptual models, dynamical understanding,observational and modeling tools, and open issues.Keywords – MAP, gap flow, foehn, hydraulics, gravity wave1 INTRODUCTIONMountain ranges are rarely smooth ridges. They are criss-crossed by indentations of various depths. Someof these gaps allow air to flow from one side to the other without having to detour over or around the mountainrange. The constriction of the cross-sectional area that air encounters on its way through the gap can lead toan asymmetric flow configuration with a relatively slowly moving but deeper layer on the upstream side and afaster and thinner layer on the downstream side of the gap. Such gap flows often show the characteristics offoehn as defined by WMO (1992) as a strong, gusty wind warmed and dried by descent, in general on the leeside of a mountain. And indeed, most of the famous foehn and downslope wind locations are downstream ofa gap, e.g. the Wipp Valley and Innsbruck (Austria), Rhine and Reuss Valleys (Switzerland), Senj (Croatia;bora), Independence (Owens Valley; site of Sierra Wave Project and currently T-REX), and Boulder. MAP wasthe first international field program with an explicit goal of studying gap flows, selecting the central AlpineWipp Valley as target area (Mayr et al., 2004). Pan and Smith (1999) summarize the gap flow studies prior toMAP.2 PURE AND HYBRID GAP FLOWS IN THE WIPP VALLEYDepending on the synoptic conditions on a scale larger than the gap-scale, air from one side of the mountainrange may flow to the other either only through the lower terrain provided by the gaps (”pure” gap flow) or alsoacross the higher surrounding ridges (”hybrid” gap flow). Fig.1 depicts two examples from the MAP SOP. The100 80 60 40 20 0 20 40 60 80 100500100015002000250030003500400045005000distance from Brenner Pass along the Alpine crest (km)elevation (m MSL)W20Oct21OctEpuregapflowhybrid gap flowFigure 1: Main Alpine Crest along the Austrian-Italian border looked at from the south (Italy). The deepest of the pro-nounced indentations is the double gap of the Wipp Valley at the Brenner Pass. The altitude of the top of the layer flowingfrom south to north indicates a pure gap flow on 20 October 1999 and a hybrid gap flow on the following day. (Adaptedfrom Armi and Mayr, 2005).shallow depth of a pure gap flow (like the one of 20 October 1999 studied in more detail in Maric´ and Durran(2005)) allows to apply the reduced-gravity shallow water approximation (”hydraulics”) as a conceptual model(e. g. Pan and Smith, 1999; Flamant et al., 2002; Gohm and Mayr, 2004). The advantage of this concept, whichSchweitzer (1953) first applied for the explanation of foehn flow, is the retention of nonlinear terms in markedcontrast to the linearized gravity wave concept that has proved so useful for deeper flows over mountains.A relatively deep upstream layer accelerates before it reaches the narrowest part, where it changes from a6subcritical to a supercritical state, becoming thinner and faster. The change back to a subcritical state and thusthe adjustment of the flow to the larger-than-gap scale environment downstream mostly takes place at the exitof the Wipp Valley near Innsbruck. (Reduced) surface pressure is an integral measure for this acceleration ofthe flow, which is evident even on average over the whole MAP SOP (Fig. 2a). Since the Wipp Valley isnot a smooth and homogeneous channel modulations of this overall acceleration occur. In particular, ridgesprotruding sideways into the main valley (cf. Fig. 2b) cause some local transitions between supercritical flowdown their lee slopes and subcritical flow upstream of the next ridge. Given appropriate moisture conditionsthese abrupt transitions back to a thicker, slower flow are visible from cumuliform clouds. Surface pressureeither increases again or slows its decrease (e.g.immediately after Brenner Pass (Bre) in Fig. 2a). Hydraulicsimulations (Gohm and Mayr, 2004) in Fig. 2b give an overall impression of the connection between small-scale topography and transitions of flow state.When the depth of the flowing layer increases to also spill over the surrounding ridges, the interaction between30 20 10 0 1010010203040x in kmy in km25252525 2525252525252525252525 25252522525252525252525252525252525252525252525252525252525 252525252525252525252525252525505050505050 5050505050 50505050505050505050550550505050 5050505050505050505050075 75757575757575757577757575757575757575757575757575(b)Inn ValleyWipp ValleyIB-3-2-101234 (a)∆p in hPaBreIbkFigure 2: (a) Average and standard deviation (bars) of reduced pressure along the Wipp Valley from automatic weatherstations over the MAP SOP (from Gohm and Mayr (2004)). (b) Relative frequency of supercritical flow in hydraulicsimulations with a wide variety of initial conditions. Locations that were supercritical in at least 50% of the simulations arestipled. Frequency isolines of 25, 50, and 75% are drawn. Topography is shaded grey and the locations of Brenner Pass (B)and Innsbruck (I) are marked. (Adpated from Gohm and Mayr, 2004).gap and ridge flows and in particular the launch of three-dimensional gravity waves modifies the gap flow(Gabersˇek and Durran, 2004; Za¨ngl, 2002c, 2003) yet does not drastically alter it. Overall, the flow descendsfurther in the case of hybrid gap flow, accelerates more, and produces a stronger pressure decrease along thelee slope.Several scenarios may lead to flow that accelerates through a gap.The obvious one is a larger-scale flowthat has a component in the gap flow direction. The second one has different air masses on either side of thegap. The typical situation for the Wipp Valley is that a passing cold front has left cold air on the northern andsouthern side of the Alps. With the approach of a synoptical scale ridge, warm air is advected with westerlyto southwesterly flow along the western flank of the Alps to the north resulting in relatively warmer air tothe north of the Wipp Valley. The ensuing hydrostatic pressure difference then drives the gap flow and alsoleads to southerly flow upstream of the gap below the crest (Za¨ngl, 2003). The hydrostatic pressure differencedriving bora through the gaps of the Dinaric Alps is frequently due to the difference between a cold continentalair mass and a warmer maritime one over the Adriatic Sea. Numerical simulations in highly idealized flowand topographical settings (Sprenger and Scha¨er, 2001; Za¨ngl, 2002a) examined the possibility of gap flowsforming with a geostrophic flow parallel to the mountain ridge, i.e. perpendicular to the gap. The results showa strong sensitivity to the shape of the mountain range due to the resulting mesocale modifications of the flowand pressure field. Also identified was the crucial role of surface friction. Its inclusion might lead to a reversalof the gap flow direction.If (turbulent) friction influences important flow characteristics even for such highly idealized and smoothorography, its influence will increase with the increased roughness of real gap orography (Za¨ngl, 2003). Flowseparation (Gohm and Mayr, 2005) and the establishment of potential vorticity banners (Ross and Vosper,2003) are strongly shaped by turbulence; not only in the atmosphere but also the ocean (e. g. Armi and Farmer,2003; Farmer and Armi, 1999, 2001).3 TOOLS7hydraulics, which adequately describes pure gap flows, radiosoundings up- and downstream of the gap areneeded for the vertical profile. At least for the central Alps, the mesoscale and synoptic scale environmentchange rapidly enough to need soundings every three hours. Despite the relatively short distance of about 30km, in-situ stacked measurements by a research airplane may take too long for the flow to remain stationary.Better are dropsonde curtains. Targeting, however, may be difficult because of wind shear.Remote sensors can also map gap flow quickly. Airborne aerosol lidars (e. g. Flamant et al., 2002; Gohm et al.,2004; Gohm and Mayr, 2004) are ideal for identifying the top of the gap flow layer and thus observe depthchanges and consequently changes of the flow state. A caveat: reflectivity of saturated aerosols is higher sothat clouds complicate the interpretation. An airborne Doppler lidar was only in the test phase during MAP buthas since become operational and is better suited for wider gaps due to the required spatial oversampling. ADoppler lidar on the ground suffers little of its usual limitation by only measuring the wind component alongits beam: channeling within the valley makes that a good approximation of the actual wind (Durran et al., 2003)and the Doppler lidar a very useful tool for the observation of gap flow (e. g. Weissmann et al., 2004; Gohmet al., 2004; Gohm and Mayr, 2004). Unfortunately, there seems to be no remote sensor capable of measuringtemperature and thus the mass field of a large part of the gap flow. Integral information about the flow state (viapressure) and the descent of isentropes is provided by fixed and mobile (Mayr et al., 2002) platforms along theground. Calibration of the automatic weather stations is imperative.An essential tool are numerical models. Computing power had just become sufficient at the time of MAPto perform simulations with the required mesh sizes of a few hundred meters. A detailed field experimentdata set can be used to tune the numerical model setup. The model in turn fills the spatial and temporaldata gaps that even an international pooling of observational resources leaves, makes it possible to study therelative importance of the various terms in the dynamic and thermodynamic equations, and to isolate crucialmechanisms with sensitivity studies.4 OPEN ISSUESOne of the explicit goals of MAP was the improvement of (numerical) weather forecasting. A direct result isthe development of an objective forecasting method (Drechsel and Mayr, 2005). Research models, precursorsof operational models’ future capabilities, passed the test against the high-density gap flow data set (Gohmet al., 2004; Za¨ngl et al., 2004). A problem, however, is the steep and narrow topography of a gap in tworespects: the already patched one (Za¨ngl, 2002b) is that ”horizontal” numerical diffusion has to be computedtruly horizontally instead of along the terrain-following model levels. Ultimately models with horizontal levelsmight be required and are under development. The unsolved aspect is ”surface friction”, i.e. the turbulentfluxes, which are only parameterized to come from the bottom of a grid cell, but not from the side as is thecase for a deep gap. The underestimation of surface friction leads to an underestimation of the descent ofthe isentropic surfaces downstream of the gap (Gohm et al., 2004). The second problem for the numericalmodels is the very stable but thin layer (often an inversion) that caps the gap flow layer on the upstreamand downstream side (where it is widened). Usually there is only a hint of this cap in the initial conditionsprovided by operational NWP analyses and the finer-scale simulations themselves produce it too weakly andgenerally not at the correct altitudes, which significantly deteriorates the resulting gap flow field. For gaps inother locations capping inversions are even stronger (e.g. Falklands: Mobbs et al., 2005) than for the WippValley. For space reasons, only one of the open dynamical issues can be mentioned here (more in the talk): theinteraction of gap flow with and its determination by downstream conditions.Acknowledgments: I thank the GAP community (see the references for all the names) for their great contribu-tions. This work was partly supported by the Austrian Science Foundation through FWF15070.References83 TOOLSThe small-scale nature and the fixed location of gap flow make it possible to obtain a comprehensive pictureof the flow with a limited set of instrumentation. Since up- and downstream conditions play a crucial role inReferencesArmi, L., and D. Farmer, 2003: Stratified flow over topography: bifurcation fronts and transition to theuncontrolled state. Proc. Roy. Soc., 458, 513–538.Armi, L., and G. J. 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GAP FLOWS – OUR STATE OF KNOWLEDGE AT THE END OF MAP

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