a multi-scale simulation of an extreme downslope windstorm ... · the mountain wave becomes trapped...

1 Naval Research Laboratory, Monterey, CA, USA2 National Center for Atmospheric Research/NOAA/ERL Environmental Technology Laboratory, Boulder, CO, USA

A multi-scale simulation of an extreme downslopewindstorm over complex topography

J. D. Doyle1 and M. A. Shapiro2

With 16 Figures

Received September 29, 1999Revised December 30, 1999

Summary

A severe localized windstorm, with near-surface winds> 60 msÿ1, occurred in an isolated valley within the Alpinemountains (> 1800 m) of central Norway on 31 January1995. A multi-scale numerical simulation of the event wasperformed with the Naval Research Laboratory (NRL)'sCoupled Ocean/Atmosphere Mesoscale Prediction System(COAMPS), con®gured with four nested grids telescopingdown to 1-km horizontal resolution. The windstormoccurred in response to topographic blocking and deforma-tion of a lower-tropospheric warm front and attendant jet(> 35 msÿ1 at 2 km). The key ®ndings are: i) mountain waveresonance and ampli®cation arising from the interaction ofthe surface-based front and jet with complex orography, ii)sensitivity of the wave response to differential diabaticheating (vertical) gradients above the front, and iii) trappedresponse within the layer of large frontal strati®cation in thelower troposphere and subsequent ampli®cation consistentwith the theoretically-established two-layer windstormanalogue of Durran (1986).

1. Introduction

The unique topography of Norway, with itsnumerous deep fjords ¯anked by steep mountains,dramatically impacts local mesoscale weatherevents such as the windstorms that frequentlyoccur in the vicinity of the complex topographysurrounding the Norwegian Oppdal Valley. Thevalley, and its winter sports village of Oppdal, islocated � 80 km from the west coast of Norway,

southwest of Trondheim, and north of the high-lands of Jotunheimen and Dovre (Fig. 1). Theoccurrence of high wind events near Oppdal isquite common; a total of ®ve destructive wind-storms occurred during 1995 alone. This naturallyraises questions regarding the origin of this localtopographic forcing. On 31 January 1995, a high-wind event with gusts estimated > 60 msÿ1,caused substantial damage throughout the valley(Harstveit et al., 1995). This study examines thesynergy between a topographically deformed frontand a subsequent downslope windstorm using theNaval Research Laboratory's (NRL) high-resolu-tion nonhydrostatic mesoscale modelling system.The evolution and dynamics of severe downslopewindstorms associated with orographically-deformed fronts over three-dimensional complextopography remain somewhat of an enigma.

Numerical simulations of the 31 January 1995windstorm were initially pursued to assess theability of a sophisticated nonhydrostatic numer-ical model to capture the evolution of a severewindstorm amidst complex three-dimensionaltopography. On closer examination of thesimulated event, a number of important issuesbecame apparent regarding orographically forcedwindstorms in three dimensions in the presenceof a complex environmental state. A furthermotivating factor is that this case, which features

Meteorol. Atmos. Phys. 74, 83±101 (2000)

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shallow mountain wave ampli®cation over three-dimensionally complex topography, represents asigni®cant departure from the classical wind-storm situation in the vicinity of the Front Rangeof the U.S. Colorado Rocky Mountains (e.g.,Lilly and Zipser, 1972; Lilly, 1978), which isoften typi®ed by deep (tropospheric/lower strato-spheric) quasi-two-dimensional wave ampli®ca-tion. The speci®c objectives of the study are to

i) evaluate the ability of a nonhydrostaticmodel to simulate the mesoscale character-istics of a downslope windstorm in threedimensions,

ii) examine the structure and dynamics of afrontal zone as it impinges upon steep topo-graphy, and

iii) explore the implications of frontal condensa-tion and latent heat release on the windstormdynamics.

Section 2 presents a theoretical overview of theproblem. Section 3 contains the model descrip-tion. The synoptic-scale and frontal-scale situa-tion is discussed in Sect. 4. Section 5 describes

the ®ne-scale structure of the windstorm fol-lowed by the concluding remarks in Sect. 6.

2. Theoretical and observational overview

It is generally accepted that downslope wind-storms are a manifestation of internal gravitywave ampli®cation induced by air ¯ow over anobstacle. The characteristics of downslope wind-storms have been studied primarily along theeastern slope of the Colorado Front Range of theRocky Mountains, coincident with the largepopulation density of atmospheric scientists.Similar high-wind events occur along mountainlees such as in the Alps (Hoinka, 1985), Andes(Sarker and Calheiros, 1974), Cascades (Colleand Mass, 1998a), Dinaric Alps (Smith, 1987),Pyrenees (Campins et al., 1995), Rockies (Lillyand Zipser, 1972), and Sierra Nevada (Alka,1960). The strongest events along the Rockiesare characterized by peak gusts > 50 msÿ1 thatinclude distinct periodic wind-speed pulsations(Neiman et al., 1988; Scinocca and Peltier, 1989;Clark and Farley, 1984) and produce signi®cant

Fig. 1. Numerical model computationaldomain, coarse-mesh terrain ®eld (200-m interval), and geographical locationsof interest. The grid increments for thefour nested meshes are 27 km, 9 km,3 km, and 1 km, respectively

84 J. D. Doyle and M. A. Shapiro

structural damage (Lilly and Zipser, 1972). Oneparticularly extreme example is the 11 January1972 Front Range windstorm for which researchaircraft observations suggested that the mesos-cale structure was dominated by a large-ampli-tude quasi-hydrostatic wave (Lilly, 1978). Nearlythe entire upstream ¯ow was found to besubsiding into a � 2 km tropospheric layer.However, the Adriatic bora (Smith, 1987) andthe Alpine foehn (Hoinka, 1985) have generalsimilarities with the Colorado Front Rangewindstorms including internal hydraulic beha-vior. It is not generally known whether the quasi-two-dimensional characteristics are representa-tive of downslope windstorms in the lee of othermore complex terrain. For example, in regions ofcomplex three-dimensional topography, gap andmountain wave dynamics may both contribute tothe generation of strong low-level winds (Colleand Mass, 1998a).

Several distinct theories have been advancedto explain the origin of severe downslope wind-storms as reviewed by Durran (1990). It shouldbe noted that these theoretical treatments arealmost exclusively two-dimensional. Eliassenand Palm (1960) theorized that upward propagat-ing linear gravity waves are partially re¯ected bya layer containing strong vertical gradients inwind velocity and/or thermal strati®cation.Klemp and Lilly (1975) used linear perturbationtheory to investigate the resonant response ofhydrostatic waves in a multi-layer atmosphere.They hypothesized that gravity wave ampli®ca-tion is related to the partial re¯ection of upwardpropagating wave energy by static stabilityvariations at various interfaces resulting in anoptimal wave resonance or superpositioning.When the tropopause is located one-half verticalwavelength above the ground, the backgroundstate may be optimally tuned for maximumresponse.

Long (1953) theoretically addressed the simi-larity between downslope windstorms andhydraulic jumps. Applying this hydraulic per-spective, Durran (1986) proposed that anincrease in the velocity and decrease in theisentropic layer thickness, as the ¯uid ascendstoward the mountain peak, lead to a subcritical tosupercritical transition near the peak. The super-critical ¯ow accelerates along the lee slope andeventually evolves to a turbulent hydraulic jump

as the ¯ow returns to the downstream ambientconditions. This transcritical ¯ow can be sensi-tive to the height of an elevated inversion withenhanced low-level stability providing a favor-able environment for supercritical ¯ow and largedownslope windspeeds (Smith, 1985; Durran,1986). The two-dimensional analytic solution toLong's equation for a single ¯uid layer withuniform stability and winds indicates that wavebreaking will occur when the nondimensionalmountain height, h � Nhm=U (where N is theBrunt-V�ais�al�a frequency, U is the mountainnormal wind speed, and hm is the obstacleheight), exceeds 0.85 (Miles and Huppert,1969). Solutions to Long's equation indicate thatwave ampli®cation occurs when a critical layer ispresent at 1=4� n and 3=4� n vertical wave-lengths above the obstacle (Smith, 1985; Klempand Durran, 1987). A limitation of the hydraulicanalog is that the free surface assumptionprevents vertical gravity wave propagation.However, the fundamental dynamics of wind-storm conditions appear to be captured byinternal hydraulic theory (Smith, 1985; Durran,1986, 1992).

Nonlinear numerical simulations suggest thatvertically propagating waves may become stati-cally unstable and overturn above the tropopauseprior to acceleration along the lee-slope (e.g.,Clark and Peltier, 1977; Peltier and Clark, 1979).The wave-breaking region, which contains strongvertical mixing and local cross-mountain ¯owreversal, acts as a ` wave- or self-induced criticallayer'' and re¯ects vertically propagating wavesdownward. Peltier and Clark applied lineartheory to show that under certain conditions,the mountain wave becomes trapped betweenthe level of overturning and the surface, and aresonant wave ampli®cation occurs, resulting instrong surface lee-slope winds. The presence ofan environmental critical level may intensifydownslope winds (Colle and Mass, 1998b).

Strong downslope winds may occur whenfronts interact with steep topography, in partbecause of the large static stability within thefrontal inversions just above the mountain, andsigni®cant cross-barrier ¯ow (e.g., Durran,1990). Bjerknes and Solberg (1921) used detailedanalyses of surface observations to describe thevertical deformation and subsequent fracture of awarm frontal zone that resulted from the frontal

A multi-scale simulation of an extreme downslope windstorm over complex topography 85

interaction with the complex topography ofcentral Norway. Their analyses indicated thatstrong winds in the lee of the Norwegianhighlands often occurred as the near-surfacefrontal zone passed over the steep topography(e.g., Fig. 20b of Bjerknes and Solberg, 1921).Bjerknes and Solberg hypothesized that bothupstream blocking and adiabatic expansion uponlee-side descent contribute to frontal modi®cationas depicted in their conceptualization of a land-falling warm front passing a mountain ridge (Fig.2). These Norwegian events are similar to stronglee-side winds associated with Alpine foehnconditions, which are common in the pre cold-frontal environment characterized by strong cross-Alpine ¯ow (e.g., Hoinka, 1985; Seibert, 1990).

Numerous observational studies (e.g., M�ullerand Sladkovic, 1990; Volkert et al., 1991) andnumerical studies (e.g., Bannon, 1984, Williamset al., 1992) have shown that fronts tend toweaken on the windward sides of mountains andstrengthen again on the lee slopes. Fronts have atendency to steepen on the downslope side andbecome distorted in the presence of strong ¯ow(Zong and Xu, 1997). Schuman (1987) noted thatthe impedance and deformation of a low-levelfrontal zone by orography will be greater when his large, a shallow and intense baroclinic zoneexists, the front-normal velocity is small, and themean-state strati®cation is large. The scalingparameters that control atmospheric ¯ow response

to a front impinging on an obstacle include h andthe Rossy number �Ro � U=fL�; where f is theCoriolis parameter, and L is the mountain half-width scale. As a result of this balanced response,the maximum extent of the decelerated regionupstream of a mountain associated with blockingis on the order of the Rossby deformation radius�LR � Nhm=f � (Pierrehumbert and Wyman,1985).

3. Model architecture

The atmospheric portion of the Navy's CoupledOcean-Atmospheric Mesoscale Prediction Sys-tem (COAMPS) (Hodur, 1997) was used tosimulate the Oppdal windstorm. COAMPS is a®nite-difference approximation to the fullycompressible, nonhydrostatic equations that gov-ern atmospheric motions. In this study, theequations are solved in three dimensons on fournested grid meshes with a terrain-followingvertical coordinate, �z (Gal-Chen and Somer-ville, 1975). The ®nite difference schemes are ofsecond order accuracy in time and space. A timespliting technique that features a semi-implicittreatment in the vertical for the acoustic modesenables ef®cient integration of the compressibleequations (Klemp and Wilhelmson, 1978; Durranand Klemp, 1983).

The short- and long-wave radiative processesare parameterized following Harshvardhan et al.(1987). The planetary boundary layer and free-atmospheric turbulent mixing and diffusion aremodeled using a prognostic equation for theturbulent kinetic energy (TKE) budget based onthe level 2.5 formulation of Therry andLaCarr�ere (1983). Counter gradient correctionterms to the vertical ¯uxes are included for thepotential temperature and water vapor equations.The surface ¯uxes are computed following theLouis (1979) formulation, which makes use ofthe ¯ux-pro®le relationships and Monin-Obu-khov similarity theory. The surface energybudget is based on the force-restore method.The subgrid-scale moist convective processes areparameterized using an approach following Kainand Fritsch (1993). The grid-scale evolution ofthe moist processes are explicitly predicted frombudget equations for cloud water, cloud ice,raindrops, snow¯akes, and water vapor (Rutledgeand Hobbs, 1983).

Fig. 2. Schematic depiction of topograhic blocking anddeformation of a warm front making landfall in Norway.From Bjerknes and Solberg (1921)


The computational domain for the presentstudy was con®gured with four horizontallynested grids of 85� 85, 73� 73, 97� 97, and145� 145 points, respectively. The locations ofthe grid meshes are shown in Fig. 1. Thehorizontal grid increments of the computationalmeshes were 27 km, 9 km, 3 km, and 1 km,respectively. The model top was at 31 km with 38irregularly spaced vertical levels and 14 levels inthe lowest 1.5 km to suf®ciently resolve theboundary-layer processes. Re¯ection of waves atthe upper boundary was suppressed by a gravitywave absorbing layer using a Rayleigh dampingtechnique in the upper 13 km of the modeldomain based on the work of Durran and Klemp(1983).

A 24-h COAMPS simulation, beginning at0000 UTC 31 January 1995, utilized an incre-mental update data-assimilation procedure thatenabled mesoscale circulations to be retained inthe analysis increment ®elds. The initial ®elds forthe nonhydrostatic model were created frommulti-variate optimum interpolation analyses ofupper-air sounding, surface, aircraft, and satellitedata that were quality controlled and blendedwith the 12-h COAMPS forecast ®elds based onthe incremental update methodology. Real-datalateral boundary conditions made use of NavyOperational Global Atmospheric and PredictionSystem (NOGAPS, Hogan et al., 1991) forecast®elds following Davies (1976). It follows that useof COAMPS in this type of application closelyemulated a real-time numerical prediction sys-tem in spite of the simulations being performedin a hindcast mode.

The topograhic data were taken from the U.S.Defense Mapping Agency's 100-m resolutiondata set. The model terrain ®elds for the third��x � 3 km� and fourth mesh ��x � 1 km�,shown in Fig. 3, indicate that numerous steepcanyons and valleys are embedded in theNorwegian highlands and further underscoresthe complex nature of the topography of thisregion. The Oppdal Valley and the village ofOppdal are located on the northern slope of theNorwegian massif and downstream from thehighlands of the Dovre region. The modeltopographic data is representative of the complexlocal topography, with several mountain peaks tothe south of the Oppdal Valley > 1800 m and a1500 m mountain located immediately to the

north of the valley and downstream of the low-level ¯ow.

4. Synoptic-scale and frontal-scale perspective

The discussion of the synoptic-scale and frontal-scale evolution is based on the 24-h COAMPSsimulation. The surface and 850-hPa ®elds forthe 6-h, 12-h, and 18-h simulation times areshown in Figs. 4, 5, and 6, respectively. Theresults for 0600 UTC 31 January 1995 (Fig. 4a)show a mature cyclone with a minimum central

Fig. 3. Terrain ®eld (shaded and contoured every 200 m)and noteworthy elevations for the (a) 3-km and (b) 1-kmresolution grids


pressure of 964 hPa located in the NorwegianSea between Norway and Iceland. A noteworthyfeature of this situation is the well-de®ned warmfront, which extends from the cyclone centersoutheastward to the east coast of Scotland. The850-hPa potential temperature ®eld at 0600 UTC(Fig. 4b) shows the moderate baroclinicity of thewarm front situated between the westerly ¯owover the North Atlantic and southerly ¯ow overthe Norwegian Sea. A well-de®ned arctic front inlow-level potential temperature and vorticity(Figs. 4a and 4c) extended from the northerncoast of Norway to south of Iceland and is not afocus of this study. The 850-hPa wind ®eld at0600 UTC (Fig. 4c) shows the strong cyclonicshear within the warm front and associated

southerly jet with a maximum > 40 msÿ1 in thecold air ahead of the front. Cyclonic vorticitymaxima at the surface (Fig. 4a) and 850-hPa(Fig. 4c) are collocated with the baroclinicity ofthe warm front. Numerous near-surface observa-tions from commercial petroleum drilling plat-forms in the North Sea show southerly winds >25 msÿ1 preceding the surface front (Fig. 4a) inclose agreement with the simulated low-levelwinds.

By 1200 UTC 31 January (12 h), the warmfront had progressed eastward toward the coast,where it was deformed by the steep topographyof southern and central Norway with an enhance-ment of the pre-frontal jet (Fig. 5). The simulatedsea-level pressure gradient and surface geo-

Fig. 4. The simulated a mean sea-level pressure and 10-mabsolute vorticity (shaded > 2:0� 10ÿ4 sÿ1), b 850-hPapotential temperature and winds, and c 850-hPa wind speedand absolute vorticity (shaded > 3:0� 10ÿ4 sÿ1) for 0600UTC 31 January 1995 (6 h). The isobar interval in a is 4hPa, the isotherm interval in b is 2 K, and the isotachinterval in c is 5msÿ1. Selected surface wind observationsare shown in (a) and radiosonde observations in (b). Onefull wind barb is equivalent to 10msÿ1


strophic winds immediately upstream of thesteep topography increased by � 25% duringthe previous 6-h (Fig. 5a). Surface observationsover the North Sea document distinct cyclonicshear across the warm front, with southwesterly¯ow in the cold air. The frontal baroclinicity andambient ¯ow associated with the low-level jetintensi®ed as the warm front approached theNorwegian coast (Fig. 5b). The realism of thesimulated mesoscale structures is attested to bythe close agreement between the model and theobserved 850-hPa winds (Fig. 5b). As thesoutherly low-level jet ascended the steepNorwegian orography, a substantial mountain-wave disturbance formed in the vicinity ofOppdal, leeward of the mountainous region. An

850-hPa wind-speed maximum > 50 msÿ1 devel-oped along the lee slopes concurrent with anintensi®cation of the low-level cyclonic shearand vorticity (Fig. 5c). In response to ¯owblocking and frontal contraction processes, thelow-level jet attained a maximum speed of� 56 msÿ1 at 0900 UTC 31 January (9 h). Thewarm/cold dipole in the 850-mb potentialtemperature ®eld was a manifestation of thelow-level mountain wave (Figs. 5b). The pre-sence of mountain waves and correspondingstrong descent in the lee of the Norwegianhighlands is consistent with a well-de®ned cloud-free region in the 1223 UTC 31 January infraredsatellite image (Fig. 7). A large area of cloudswas present along the warm front and extended

Fig. 5. As in Fig. 4 except for 1200 UTC 31 January 1995(12 h)


eastward in a region of sloped ascent along thefrontal zone, overriding the relatively cool airover Scandinavia.

The presence of topographically-generatedgravity waves in the lee and blocking upstreamof the central Norwegian mountains is particu-larly evident in the 18-h simulation of sea-levelpressure and 10-m vorticity for 1800 UTC 31Janaury (Fig. 6a). The warm front was signi®-cantly distorted, and its eastward movement atlow levels was impeded by the Norwegian topo-graphy to the west and south (Fig. 6b), similar tothat described by Bjerknes and Solberg (1921)(e.g., Fig. 2). Adiabatic descent and warmingcontributed to the distortion of frontal propertiesin the lee. The observations show that strong

near-surface ¯ow > 25 msÿ1 (Fig. 6a) was presentin the vicinity of the warm front. The portion ofthe warm front over the adjacent Norwegian Searetained its integrity, including the strong 850-hPa thermal gradient (Fig. 6b), and attendantlow-level jet, and vorticity ®lament (Fig. 6c).

The evolution of the vertical structure of thewarm frontal zone and the modulation bytopography is illustrated by a series of verticalsections oriented normal to the low-level bar-oclinic zone, along vertical projection line AA0

(Figs. 4c, 5c, and 6c). At 0600 UTC 31 January(6 h), the cross section of potential temperature(Fig. 8a) indicates that prior to landfall, the low-level thermal gradient of the warm front wasdiffuse, with a weak static stability layer aloft

Fig. 6. As in Fig. 4 except for 1800 UTC 31 January 1995(18 h)


arising from the vertical gradient of latentheating above the front. A well-de®ned low-leveljet � 36 msÿ1 was situated on the cold side of thebaroclinic zone (Fig. 8b). By 1200 UTC (12 h),the topographic blocking led to a signi®cantsteepening of the front slope, as well as adoubling of the 800-hPa potential temperaturegradient located just above the mountain top(Fig. 8c). The front-normal wind component ofthe low-level jet (Fig. 8d) increased from36 msÿ1 to � 43 msÿ1 simultaneously with thefrontal contraction. At 1800 UTC (18 h), topo-graphic deformation of the warm front thermalgradient (Fig. 8e) and cross-front vorticity (Fig.8f) was evident. A narrow front-normal wind-speed maximum was maintained along theupwind slope, while the main core of the low-level jet moved in the lee of the mountain peaks(Fig. 8f).

The role of the topography in deforming thewarm front is further illustrated by a comparisonof the simulations with and without topography,shown along the vertical projection line BB0 (Fig.6c) of Figs. 9a and b, respectively. The simula-tion with topography (Fig. 9a) has characteristicsin common with the Bjerknes and Solberg (1921)schematic (Fig. 2):

iii) the impedance of the lower portion of thewarm front upwind of the mountains,

iii) the more rapid downstream movement of theupper-portion of the front, and

iii) a mountain wave signature that separates theprecipitation and clouds into two distinctregions.

One portion of the precipitation remainednearly stationary above the low-level warm frontand upwind side of the coastal topography,whereas a second region was forced by frontal-scale ascent that propagated eastward with theupper portion of the warm front. The frontretained a more continuous vertical structure inthe absence of topography (Fig. 9b) similar to thewarm front in the offshore stage (Fig. 8a).

In order to investigate the kinematics of frontaldeformation by topography, consider the Lagran-gian rate of change of the gradient of the virtualpotential temperature ��v� through the kinematicfrontogenesis equation for virtual potential tem-perature, de®ned as:

d

dtjr��j � jr��jÿ1

ÿ @��@x

ÿ �2@u@x� @��

@y

� �2@�@y

� �ÿ @��

@x@��@y

@v@x� @u

@y

� �h i8><>:

9>=>;ÿ jr��jÿ1 @��

@x

@��@p

� �@!

@x� @��

@y

@��@p

� �@!

@y

� �� jr��jÿ1 @��

@x

@

@x

d��dt

� �� @��@y

@

@y

d��dt

� �� where ! is the vertical velocity, and u and v arethe horizontal wind components. The ®rst twoterms on the right-hand side of (1) represent thecontribution of the deformation ®eld to thefrontogenesis and include both horizontal con-¯uence and horizontal shear effects. The twistingor tilting term is denoted by the third term. Thefourth term on the right-hand side represents thefrontogenesis due to horizontal gradients ofdiabatic heating.

The terms in the frontogenesis equation wereevaluated for the full physics simulation and asimulation without topography. The results for1500 UTC 31 January (15 h), shown in Fig. 10,reveal the complex mesoscale response to steeptopography. The warm front is strengthened,especially in the lee, by topographic deformationassociated with the high-amplitude mountain

Fig. 7. Infrared satellite image for 1223 UTC 31 January1995


Fig. 8. Vertical section along line AA0 (Figs. 4c, 5c, and 6c) of potential temperature (3 K) (a, c, e) and section-normal winds�5msÿ1� (b, d, f) for 0600 UTC (a, b), 1200 UTC (c, d) and 1800 UTC (e, f) 31 January 1995. The relative humidity > 90% isshaded


wave (Fig. 10a). Contribution of the tilting termleads to an intense region of frontolysis imme-diately downstream of the strongest region offrontogenesis. This frontogenesis/frontolysisdipole, which is a result of the vertical motionand static stability anomalies associated withthe large-amplitude mountain wave, acts tostrengthen and deform the warm front in thehorizontal as well as the vertical. Enhancedregions of frontogenesis are apparent upstream ofthe steepest topography as a result of low-level

blocking effects. The simulation without topo-graphy has a quasi-linear frontal structure at 850hPa with locally weaker frontogenesis in centralNorway (Fig. 10b). The maximum 850-hPathermal gradient is strengthened by a factor of

Fig. 9. Vertical cross section along line BB0 (Fig. 6c) ofpotential temperature and along section winds for the a full-physics simulation and b simulation without topography for1800 UTC (18 h) 31 January 1995. The relative humidity> 90% is shaded. The isotherm interval is 3 K. The windarrows are plotted every 10 grid points. The heavy solid linedenotes the warm front inversion

Fig. 10. The 850-hPa potential temperature for the a full-physics and b no-terrain simulations for a portion of thecoarse mesh domain for 1500 UTC (15 h) 31 January 1995.The isotherm interval is 1 K. Frontogenesis > 5 K�10 km 6 h�ÿ1 is denoted by the hatched region, and <ÿ5 K �10 km 6 h�ÿ1 is represented by the dark shadedregion


three through the topographic deformation pro-cesses in the lee of the highest topography. Insummary, the strengthening of the mesoscalethermal gradients is clearly tied to frontogenesisthrough differential vertical motion or tilting.

5. Fine-scale windstorm aspects

At 1200 UTC 31 January (12 h), the 300-m AGLwind ®eld for the 3-km resolution grid (Fig. 11a)

indicates a maximum speed of > 60 msÿ1

located within the Oppdal Valley. Several otherareas contain wind speeds > 50 msÿ1, inparticular to the north and west of the OppdalValley. All regions of high wind speed arelocated in the lee of the highest topographywithin the Norwegian massif. Orographic block-ing and de¯ection are apparent upstream of themountain peaks, resulting in easterly valley¯ows. The 300-m AGL wind ®eld valid at 1400UTC (14 h) for a sub-domain of the 1-km grid(Fig. 11b) indicates that, despite the knowndif®culties in predicting low-level winds incomplex terrain, the model simulated maximumwind speed is coincident within the region ofobserved windstorm damage in the OppdalValley. Observational estimates from the damagesurvey suggest that the windstorm occurred atapproximately 1500 UTC with wind gusts> 60 msÿ1 (Harstveit et al., 1995).

Figure 12 presents a sequence of south-northoriented vertical cross sections of potentialtemperature and horizontal wind speed, con-structed parallel to the low-level ¯ow and alongvertical projection line CC0 of Fig. 11a. The 0600UTC (6-h) potential temperature cross section(Fig. 12a) reveals a two-layer structure within thetroposphere, with high stability in the low-levelsbelow 600 hPa associated with the warm frontalinversion, and weaker stability aloft in the 300±400 hPa layer. The 0600 UTC (6-h) wind-speedcross section (Fig. 12b) indicates that a layer ofsigni®cant low-level wind speeds > 25 msÿ1 waspresent below � 700 hPa, with weaker cross-mountain wind speeds less than 10 msÿ1 above500 hPa. The maximum cross-mountain windspeeds are present near the mountain peak (Fig.12b).

The 1200 UTC (12-h) potential temperaturecross section (Fig. 12c) valid near the time of theobserved windstorm indicates that the strati®ca-tion below � 600 hPa increases concurrent withdestabilization in the 350±500 hPa layer. Thewarm frontal inversion above the mountain top,often associated with downslope windstormevents (e.g., Colson, 1954; Brinkman, 1974;Durran, 1990), has undergone substantial verticaldistortion. Wave ampli®cation within the OppdalValley is noted below 500 hPa with the maximumamplitude > 2:5 km height deviation of the 297 Kisentropic surface. In this case, the wave is

Fig. 11. The simulated 300-m AGL wind ®eld for the a 3-km resolution and b a subdomain of 1-km resolution grids.The isotachs are shown > 45msÿ1 at an interval of 5msÿ1

in (a) and 2:5msÿ1 in (b). The terrain ®eld for the 3-km and1-km resolution meshes are represented by the shading in(a) and (b), respectively. Wind arrows are plotted everythird point in (a) and every point in (b)


Fig. 12. Vertical section along line CC0 (Fig. 11a) of the potential temperature (3 K) (a, c, e) and along-section wind speed�5msÿ1� for 0600 UTC (a, b), 1200 UTC (c, d) and 1800 UTC (e, f) 31 January 1995


con®ned to the lower troposphere, unlike the fulltroposphere, large-amplitude waves found in othercases (e.g., Lilly, 1978). The lack of substantialvertical wave tilt throughout the wave life cycle(e.g., Figs. 12a and 12c) suggests that the verticalpropagation of the gravity wave energy may betrapped. The largest cross-mountain wind speedsat 1200 UTC (12 h) (Fig. 12d) are > 55 msÿ1 at300 m above the valley. Large vertical shear isapparent in the cross section, with the meancross-mountain wind speed � 35 msÿ1 below700 hPa and < 20 msÿ1 above 600 hPa.

By 1800 UTC (18 h), the low-level strati®ca-tion remains large, and the 400±550 hPa staticstability continues to weaken (Fig. 12e). How-ever, the cross-mountain wind speed (Fig. 12f)indicates that despite the depth of the strong low-level ¯ow �> 30 msÿ1� increasing slightly, thewindstorm in the lee diminishes to < 45 msÿ1

over the previous 6 h as the low-level warm frontdeforms (Fig. 9a).

Figure 13 shows the time-height evolution ofthe cross-mountain wind speed and potentialtemperature at a grid point (3-km resolution grid)

Fig. 13. Time-pressure section of thea cross-mountain wind speed and bpotential temperature from 0000UTC 31 January through 0000 UTC01 February 1995 (0±24 h) for a gridpoint near Oppdal on the 3-kmresolution grid. The isotach intervalis 5msÿ1 in (a), and the isotherminterval is 5 K in (b)


within the region of the windstorm damage. Therapid increase of the cross-mountain wind speedmaximum and its descent to near the surface areapparent between 0300 UTC (3 h) and 1200 UTC(12 h) (Fig. 13a). Between 0900 UTC (9 h) and1200 UTC (12 h), the 550±650 hPa cross-mountain ¯ow decreases by > 10 msÿ1 andreverses, such that large vertical shear �40msÿ1=100 hPa� develops in the 700±800 hPalayer. An increase in the low-level strati®cationbelow 750 hPa and a decrease between 500±700hPa preceded the largest cross-mountain windspeeds (Fig. 13b). Overturning of the 600±750hPa isentropic layer, a likely signature of low-level gravity wave ampli®cation and breakdown,is apparent above the vertical shear layer duringthe time period when the cross-mountain windspeeds are > 50 msÿ1.

The 1200 UTC (12 h) mean structure of thetroposphere is represented (Fig. 14a) by verticalpro®les of potential temperature and the cross-mountain wind component, averaged over a 25-grid point region upstream of the windstorm(location shown by the star in Fig. 11a). Thepro®les contain a two-layer structure character-ized by i) large static stability below 700 hPa, ii)weak stability in the 350±500 hPa layer, and iii)strong southerly ¯ow in excess of 30 msÿ1 below650 hPa.

Further general insight into the dynamics ofthis windstorm may be gained by considering thelinear response to the mean state structure.Scorer (1949) made use of linear theory to showthat wave energy may be trapped due to verticalvariations in the mean state velocity and stability.For two-dimensional, inviscid, Boussinesq ¯owwith no rotation � f � 0�, the linearized, steady-state equations can be reduced to form a second-order partial differential equation for the pertur-bation vertical velocity (e.g., Scorer 1949; Alaka1960)

@2w

@x2� @

2w

@z2� l 2w � 0; �2�

where l is the Scorer parameter, de®ned as

l2 � N2

U2ÿ 1

U

@2U

@z2: �3�

Following Scorer (1949) and Durran and Klemp(1982), the necessary condition for the existenceof mountain wave energy trapping for a two-layer

Fig. 14. Vertical pro®les of a potential temperature (solid,K) and the v-wind component �dashed; msÿ1�; bl2��10ÿ6 mÿ2�, and c potential temperature (K) for thesimulation without latent heating. The pro®les are averagedover 25 grid points centered at the `?' in Fig. 11a


¯uid that contains a discontinuity in l occurswhen

l2L ÿ l2U >

�2

4H2: �4�

For the present situation, a mean pro®le of l 2 iscomputed upstream of the Oppdal Valley valid at1200 UTC (12 h) (Fig. 14b). Here, the Scorerparameter is characterized by a near two-layerstructure with a rapid decrease with height abovethe lower troposphere. The criterion for trappedwave energy is satis®ed in this highly idealizedsetting assuming H � 1200 m, l2

L � 2:2� 10ÿ6

mÿ2, and l2U � 0:2� 10ÿ6 mÿ2. However, the

applicability of this highly idealized theory to acomplex, three-dimensional ¯ow is clearly lim-ited. It is noteworthy that the two-layer meanstate structure and ensuing windstorm dynamicsare in marked agreement with the idealizednumerical simulations of downslope windstormspresented in Durran (1986).

The origin of the strong low-level winds andenhanced static stability in the Oppdal Valley isclearly tied to the presence of the warm front.The sloping frontal inversion and vertical shearassociated with the low-level jet contribute to thetwo-layer characteristics of the Scorer pro®le.Additionally, the weak stability aloft acts toreduce l in the upper layer. The origin of thislayer of weak stability arises through thedestabilizing effect of the vertical gradient in

latent heat associated with the maximum ascentabove the warm front, as previously discussed(Figs. 8 and 9).

In order to gain further insight into thedestabilizing effect of differential latent heating,a simulation was performed excluding the latentheating of condensation. The 1200 UTC (12-h)mean vertical pro®le of potential temperature(Fig. 14c) from this simulation upstream of thewindstorm reveals a signi®cantly larger 350±500hPa static stability relative to the full-physicssimulation (Fig. 14a). Trajectory analysis (notshown) provides further con®rmation of thedestabilization in the upper-levels resulting fromthe differential diabatic processes. In the full-physics simulation, latent heating contributed toa 6 K warming just above the warm front con-current with adiabatic ¯ow near the tropopause.This is also evident in the comparison of thecross sections of potential temperature and cross-mountain wind speed for the no-latent heating(Figs. 15a-b) and full-physics (Figs. 12c-d)simulations, valid near the time of the observedwindstorm (1200 UTC). Note that in the absenceof latent heating (Fig. 15), the wave amplitudesand cross mountain wind speeds, particularlywithin the Oppdal Valley, are signi®cantlyreduced in contrast to the full-physics simulation(Figs. 12c-d). Calculations of the Richardsonnumber, Ri, �N2=�dU=dz�2� indicate that the full-physics simulation is characterized by a smaller

Fig. 15. Vertical section along line CC0 (Fig. 11a) of a potential temperature (3 K) and b along-section wind speed �5msÿ1�for 1200 UTC 31 January 1995 (12 h) for the simulation without latent heat processes


midtropospheric Ri minimum than the simulationwithout latent heating. The mitigation of thedownslope windstorm in this simulation withoutlatent heating is apparently related to a resonantresponse to the modi®ed mean-state stability andcross-mountain wind pro®les. For example,Durran and Klemp (1982) found that in thepresence of mid-level moisture, such as in thepresent study, lee waves may amplify when theheight of the trapping interface is reduced due toresonant effects.

Figure 16 shows a south-north oriented verticalsection of the wind speed and potential tempera-ture, valid at 1345 UTC (13.75 h), for the 1-kmresolution grid. The largest amplitude wave issituated above the Oppdal Valley, with character-istics consistent with the internal hydraulicampli®cation processes illustrated in the idealizedsimulations of Durran (1986). For the presentstudy, qualitative analysis of the model resultsindicates the presence of supercritical ¯ow in thelee concurrent with downward displacement of thelow-level frontal inversion in the Oppdal Valley.Considering the three-dimensionality of the topo-graphy over Norway evident in Fig. 16 and the

complexity of the ¯ow, the model predictive skillof the windstorm event is remarkable.

6. Concluding remarks

A mesoscale numerical simulation of an extremedownslope windstorm over the mountains ofcentral Norway was undertaken to test the abilityof a sophisticated numerical weather predictionsystem (COAMPS) to forecast extremely loca-lized topographic ¯ow over highly complexterrain. The simulation was used to identify keysynoptic-scale and mesoscale characteristics ofthe event and to establish links with observa-tional and theoretical studies of similar topo-graphic ¯ows. Since there were no directobservations to evaluate the representativenessof the simulation, indirect con®rmation of theextreme wind event was inferred from wide-spread destruction of substantial buildingsthroughout the Oppdal valley. Clearly, thepresent study is not de®nitive in that few, ifany, observations con®rm the three-dimensionalevolution of the mountain-wave ampli®cationevent. However, the study does reaf®rm the

Fig. 16. Three-dimensional depiction ofthe 1-km resolution mesh results for asouth-north vertical section of potentialtemperature (2 K) and wind speed (colorshading) as viewed from the northeastfor 1345 UTC 31 January 1995 (13.75h). Red shading corresponding to windspeeds > 55msÿ1 and blue shading< 15msÿ1


ability of high-resolution models to simulatefrontal-scale contraction and associated diabaticprocesses, and the consequence of their interac-tion with complex orography.

The key ®ndings and new insights arising fromthis study are

i) mountain wave resonance and ampli®cationarising from the interaction of a surface-based warm front and attendant lower tropo-spheric jet with complex orography,

ii) sensitivity of the wave response to differ-ential diabatic heating (vertical) gradients inthe layer bounded by the tropopause andwarm frontal ascent,

iii) in contrast to previously studied idealizedand observed windstorms characterized bystrong ¯ow response in the lower-strato-sphere (e.g., Lilly, 1978; Clark and Peltier,1977; Peltier and Clark, 1983), the waveresponse for the present study is trappedwithin the layer of large frontal strati®cationin the lower troposphere, and

iv) wave ampli®cation is consistent with thetheoretically established two-layer hydraulicanalogue (e.g., Durran, 1986).

It is imperative that future high-resolutionsimulations be evaluated with comparablyresolved in situ and remote-sensing observingsystems, such as will be deployed in support ofgravity wave studies in the Mesoscale AlpineProgramme (MAP) (Houze et al., 1998). Finally,the results of the study highlight the promisingfuture for the utilization of high-resolutionnumerical simulations in advancing our under-standing and predictability of three-dimensionalcomplex topographic ¯ows.

Acknowledgements

The research support for the ®rst author was provided bythe Naval Research Laboratory's (NRL) Orographic andFetch-Limited Flows Research Option sponsored by theOf®ce of Naval Research (ONR) grant N0001499F0068.The second author expresses appreciation to NRL-Mon-terey for sponsoring his collaborative visits to NRL throughthe support of ONR program element 0602435N. Comput-ing time was supported in part by a grant of HPC timefrom the Department of Defense Shared ResourceCenter, Stennis Space Center, MS, and performed on aCray T-90. Bene®cial discussions with Dale Durran andRichard Reed are greatly appreciated. We thank SigbjornGrùn�as and Knut Helge Midtbù for valuable discussions

concerning observational aspects of the Oppdal downslopewindstorms.

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Authors' addresses: James D. Doyle, Naval ResearchLaboratory, Marine Meteorology Division, 7 Grace HopperAvenue, Monterey, CA 93943-5502 USA (E-Mail:[email protected]); M. A. Shapiro, National Centerfor Atmospheric Reserch/NOAA/ERL Environmental Tech-nology Laboratory, Boulder, CO, 80301 USA


a multi-scale simulation of an extreme downslope windstorm ... · the mountain wave becomes trapped...

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