Idealized Sensitivity Study of Pollution Transport over Alpine Terrain

Transcription

1 Idealized Sensitivity Study of Pollution Transport over Alpine Terrain A diploma thesis submitted to the Institute of Meteorology and Geophysics, University of Innsbruck for the degree of Master of Natural Science presented by Manuela Lehner June 8

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3 Abstract A mesoscale model is used to perform simulations of pollution transport in an idealized D valley during daytime. This thesis is connected to the measurement campaigns INNAP and INNOX, which were conducted within the framework of the project ALPNAP and investigated the wintertime aerosol distribution in the Inn Valley, Austria, by means of airborne observations. The highly idealized model setup is chosen so as to roughly approximate typical wintertime conditions and the topography of the Inn Valley. Sensitivity tests systematically vary several parameters including, e.g., the atmospheric layering, the orientation of the valley, and the surface conditions (i.e., vegetation type and snow cover). The simulations evaluate the impact of the respective factor on the resulting transport of a tracer plume, which is initially inserted at the valley oor. The evolving slope-wind system and thermal stratication of the valley atmosphere are strongly inuenced by solar irradiation, which is again determined by the surface albedo and the orientation and inclination of the slopes with respect to the sun. During the day insolation causes upslope winds along the sunlit slope, which imply a vertical transport of the tracer material. A more stably stratied valley atmosphere dampens the slope-wind speeds and therewith the tracer transport along the mountain sides. Elevated layers of higher static stability induce a splitting of the ow at the lower boundary of this layer. The resulting cross-valley wind removes tracer material from the slope-wind layer and carries it towards the valley center. Furthermore, results show that an initial near-surface inversion causes a temporal delay of both the growth of the mixing layer and the tracer transport from the valley oor. A high surface albedo, induced by a potential snow cover, prevents the development of upslope winds and the morning break-up of the nighttime near-surface inversion. Tracer material at the valley oor becomes then trapped close to the ground, where, consequently, the concentrations remain high. The numerical model appears to be able to capture the essential atmospheric processes leading to the observed aerosol structure. But the ndings show also the strong sensitivity of the model performance and the resultant tracer distributions on the model's parameterization schemes (surface layer and diusion parameterization). i

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5 Contents Abstract Contents i iv Introduction. Motivation A short overview of previous research Goals and outline Model and setup 9. Boundary conditions Initial conditions Parameterizations Code modications Grid Rotation Surface layer parameterization Horizontal diusion Reference run 3. Meteorological parameters Numerical problems Tracer dispersion Sensitivity tests Horizontal tracer diusion Diuse radiation Valley orientation Thermal stratication Surface conditions Vegetation type Snow cover Plateau embedded in the south-exposed slope iii

6 iv CONTENTS 4.7 Continuous tracer release Discussion Typical ow and tracer-transport pattern Sensitivity tests Conclusions 95 A RAMS v4.4 code modications 97 A. Grid rotation A. Surface layer parameterization A.3 Horizontal diusion A.4 Diuse radiation A.5 Snow B Additional gures of the sensitivity simulations 9 Bibliography 55 Acknowledgments 57 Curriculum vitae 59

7 Chapter Introduction. Motivation The dispersion of pollutants in mountainous terrain is greatly inuenced by the topography and local meteorological phenomena. Strong nighttime temperature inversions that typically form within valleys in clear-sky conditions, particularly in wintertime, reduce vertical mixing. Pollutants near the ground can become trapped within these highly stable layers until their breakup (e.g., Anquetin et al. 999; Chazette et al. 5). Hence, continuous emission from, e.g., trac or urban areas at the valley oor can lead to high concentrations of air pollutants. Furthermore, the local wind system, namely valley and slope winds, which develop during daytime due to thermal forcing, can determine the transport of the pollutants, e.g., through carrying them up the irradiated mountain side (e.g., Whiteman 989; Bader and Whiteman 989). In order to investigate the eect of the above factors, i.e., the valley and slope winds and the thermal stratication, on the temporal evolution of the wintertime aerosol distribution, a eld campaign was realized in the Inn Valley, Austria, during January and February 6. This experiment was supported by the research projects INNAP (Boundary layer structure in the Inn Valley during high air pollution), IN- NOX (NO x -structure in the Inn Valley during high air pollution), and ALPNAP (Monitoring and Minimisation of Trac-Induced Noise and Air Pollution Along Major Alpine Transport Routes, Heimann et al. 7). Airborne aerosol backscatter lidar and in-situ measurements, of INNAP and INNOX, respectively, provided information on the aerosol structure in the lower Inn Valley on several ight days. Information on the projects and detailed results can be found in, e.g., Gohm et al. (6), Harnisch (7), and Harnisch et al. (8). Figure. presents two vertical cross sections of aerosol backscatter intensities near Schwaz in the Inn Valley (.7 E, N, 5 km to the east of Innsbruck) taken from Harnisch (7),

8 Introduction.5 Backscatter at 64 nm, 4 Jan 6 3:43: to 3:45:5 UTC.5 Backscatter at 64 nm, Feb 6 4:8:43 to 4::47 UTC Altitude (km MSL).5 Altitude (km MSL) Figure.: Vertical cross sections of aerosol backscatter intensities measured during the project INNAP at 345 UTC 4 January 6 and 4 UTC February 6. The orientation of the cross sections is from southeast (left) to northwest (right). Figures taken from Harnisch (7). who gives a thorough analysis of the observed aerosol distributions with regard to the relevant synoptical and local inuences. Figure.a is valid for 345 UTC 4 January 6. The asymmetry in backscatter intensities between the two mountain sides with higher values at the northwestern slope (right hand side) is explained through the orientation and the dierent snow cover of the slopes causing a stronger upslope transport at the northwestern (southeast-facing) mountain side. Furthermore, two elevated layers of high intensities become apparent between and m MSL and at 5 m MSL, respectively. Both layers occurred at a height, where a shallow inversion layer was present. At those heights a northerly wind was observed indicating a cross-valley ow that transported the aerosols away from the slope-wind layer. A similar circulation pattern was suggested by Vergeiner and Dreiseitl (987), who deduced the existence of cross-valley winds at the lower boundary of an inversion from the reduction of mass transport in the slope-wind layer due to the increased stability (Fig..). For the February (Fig..b) an alike distribution was obtained (Harnisch 7). On this day additional ights were conducted in the morning in order to explore the temporal evolution of the aerosol eld (not shown). In the morning, a strong near-surface inversion was present and the highest backscatter intensities occurred within the lowermost m to the ground. Horizontally, a fairly homogeneous distribution was detected, apart from slightly higher values along the northwestern slope, which were explained by a beginning upslope transport of pollutants at the already illuminated southeast-facing mountain side. In the afternoon at 4 UTC (Fig..b) the distribution became again highly

9 . A short overview of previous research 3 Figure.: Diagram showing the circulation induced by an elevated inversion layer and the subsequent reduction of the mass ux in the slope-wind layer (indicated by the dashed line). Figure taken from Vergeiner and Dreiseitl (987). asymmetric with the larger intensities along the southeast-exposed slope. Moreover, two elevated aerosol layers were observed, which corresponded to the existing inversion layers at about 95 and 5 m MSL, respectively. This structure was also obtained by tethered balloon soundings and car measurements along the slopes (see Heimann et al. 7). Motivated by the above observations, numerical simulations of pollution transport within an idealized D valley are performed in the framework of this thesis in order to investigate the inuence of various atmospheric, topographic, and surface parameters on the evolving slope winds, the development of the thermal stratication of the valley atmosphere, and therewith the resulting particle dispersion. In contrast to observational studies numerical simulations enable such a systematic approach, in which each factor can be considered individually. Furthermore, during the eld campaigns no measurements of the wind within the slope-wind layer were conducted, so that only assumptions can be made by means of the observed aerosol distributions. The simulations, however, yield the complete D wind eld in the valley cross section.. A short overview of previous research During the last decades research has dealt a lot with mountain and valley-specic meteorological features and their impact on the dispersion of pollutants. Both observational and modeling studies have been carried out. It is quite intuitive that the thermally induced local wind system is a major mechanism contributing to the pollution transport, particularly in conditions without or with only weak synopti-

10 4 Introduction cal inuence. Upslope winds resulting from buoyancy forces along the slope (e.g., Haiden 3), which form during the daytime due to the stronger heating of the air close to the surface compared to the air further away from the slope, can lead to a vertical transport of pollutants. Whiteman (989) conducted tracer experiments in the Brush Creek Valley, Colorado, in order to investigate the dispersion during the morning hours, shortly after sunrise. He showed that dierential heating of the mountain slopes due to their orientation with respect to the sun causes a cross-valley ow near the bottom, which carries the tracer towards the sunlit mountain side. Upslope winds can then transport the plume further up the slope. Numerical simulations within a D northwest-southeast orientated valley by Bader and Whiteman (989) yielded similar results for a summertime case. For a wintertime situation, however, the less unequal heating of the valley sides prevented the development of a cross-valley ow leading to a more symmetric tracer distribution within the valley cross section. The role of upslope winds on the pollution transport, whether they carry pollutants out of the convective boundary layer (CBL) or whether a return ow occurs that traps the pollutants within the CBL, was investigated by means of observations in the Lower Fraser Valley, Canada (Reuten et al. 5), and water tank studies (Reuten et al. 7). Another important aspect is the trapping of pollutants near the valley oor within inversion layers, which form frequently during nighttime. The daily evolution of the boundary layer over at terrain is well described (e.g., Stull 988). During nighttime in clear-sky conditions the lower atmospheric levels cool more than the levels above due to radiative losses of the surface. The resulting stable layering dampens turbulence and vertical movements; generally, low wind speeds are associated with such conditions. Hence, pollutants tend to disperse more or less horizontally, vertically conned within this layer. In the morning, after sunrise, solar heating of the surface leads to rising air temperatures near the ground and the evolution of a shallow unstable surface layer and on top of it a mixed layer with vertically constant potential temperature, which starts to destroy the nocturnal stable layer from below. In mountainous terrain, however, katabatic winds can additionally transport cold air towards the valley oor, which enhances the formation and strength of the stable layer. Often, a temperature inversion is found in the morning hours reaching up to about crest level (Whiteman 98). Whiteman (98) evaluated cases of morning inversion-breakup measurements in four valleys of the Rocky Mountains in western Colorado during a whole year, so as to gain results for all seasons. He classied three dierent idealized patterns of inversion destruction in a valley. His schematical diagram of the three patterns (his Fig. ) is shown in Fig..3. Pattern one corresponds to the classic breakup, which occurs over at terrain. Here, the solar heating forms a convective boundary layer

11 . A short overview of previous research 5 Figure.3: Figure taken from Whiteman (98). It displays his idealized patterns of inversion breakup in a valley. The left column shows proles of the potential temperature at time t, where t i indicates the time of sunrise and t D the time of the inversion breakup. In the right column the height of the convective boundary layer H(t) and the height of the inversion top h(t) are plotted.

12 6 Introduction (CBL) near the ground, which grows steadily upwards until it reaches the top of the initial inversion. He observed this pattern once in a wide valley of the Colorado Mountains, too. The second pattern shows only little growth of the CBL, at the beginning, which then stops at a certain height. The greater part of the dissolving is caused by the descending inversion top, which eects a warming of the entire valley atmosphere, too, according to the vertical advection of potentially warmer air. Evolving usplope winds along the slopes lead to compensatory subsidence over the valley due to mass continuity. Air near the valley oor, which is carried upwards, is replaced by air with higher values of potential temperature from levels further above. Pattern three combines both the growing CBL and the descending inversion top. It was the most observed one by Whiteman (98) in the Colorado Mountains, independent of the season. Pattern two was found twice in winter when snow cover was present (Whiteman 98) or in moist conditions with a high latent heat ux within an Alpine basin (Whiteman et al. 4). In both cases the sensible heat ux was comparatively small. Since the development of this classication scheme various numerical simulations have been performed (Whiteman and McKee 98; Bader and McKee 983), reproducing the idealized patterns. Sensitivity studies with dierent model codes evaluated the impact of, e.g., valley width and orientation, static stability, surface albedo, surface heating rate (Bader and McKee 985), season (Anquetin et al. 998, 999), and shading by the surrounding topography (Colette et al. 3). Princevac et al. (6) conducted experiments of inversion breakup in a water tank showing the additional factor of detrainment from the slope-wind layer. Apart from the above radiative mechanisms, also dynamical ones, i.e., advective processes, can play a signicant role (Zängl 5). Chazette et al. (5) described observations of pollution distributions in the Chamonix and Maurienne valley, France, during wintertime. They encountered a near-surface inversion, within which the pollutants were trapped. By means of a differential snow cover between the two valleys they showed that a closed snow cover hinders the breakup of the inversion due to a smaller sensible heat ux and therewith less vertical mixing. Furthermore, they observed elevated aerosol layers, which occured in connection with elevated inversions. Model simulations by Anquetin et al. (999) showed also the reduction of vertical mixing within near-surface inversion layers. The primarily interesting area concerning the emission and distribution of air pollution is the region close to the surface, i.e., close to human habitation. Within the framework of MAP (Mesoscale Alpine Programme) several projects dealt with the boundary layer over mountainous terrain (Rotach and Zardi 7). Rotach and Zardi (7) give also a short overview of some crucial points with respect to the numerical modeling of the boundary layer in complex terrain, such as the

13 .3 Goals and outline 7 necessity of a horizontal resolution that is of the order of m. De Wekker et al. (5) compared results from simulations with the mesoscale model RAMS (which is also used for this thesis) with observational data gained in the Riviera Valley, Switzerland, during MAP. They mention among other things the initialization of the soil moisture as an important factor for the modeling of the boundary layer and additionally, the shadowing eect of the surrounding topography (also Colette et al. 3; Chow et al. 6). The inuence of the soil moisture on the katabatic ow was shown by (Banta and Gannon 995). Zängl et al. (7) evaluated the impact of the height of the lowest model level above ground and the boundary-layer parameterization on the model performance..3 Goals and outline Observations from the projects INNAP and INNOX yielded data of the wintertime aerosol distribution in the Inn Valley during high air pollution periods (Harnisch 7; Harnisch et al. 8). This thesis uses the Regional Atmospheric Modeling System (RAMS) in combination with a highly idealized setup (regarding, e.g., topography and initialization of the atmospheric conditions) in order to perform D simulations. The dispersion of a tracer plume, which is inserted in the morning at the valley oor, is analyzed during daytime. It is investigated whether the model can reproduce qualitatively some of the ow patterns, that cause a tracer distribution that is similar to the observed aerosol structure. Hence, the model topography is chosen in close resemblance to the topography of the Inn Valley, concerning its height, steepness, and orientation. An initially stagnant atmosphere ensures that the dispersion of the tracer material results mainly from the local slope-wind system, which develops due to solar irradiation. On the basis of these ndings some parameters are varied systematically, so as to illustrate the response of the model to the dierent conditions and to highlight the involved processes. Furthermore, the impact of some numerical and model related factors is tested. In chapter the model and the numerical setup for the reference simulation, including the modications to the RAMS model code, are described. Results from the reference run are dealt with in chapter 3. Chapter 4 shows the ndings of the sensitivity experiments. Simulations are presented which treat the inuence of the horizontal tracer diusion, the diuse shortwave radiation, the valley orientation, the initial atmospheric stability, or the vegetation class on the dispersion of the tracer. Additional experiments are performed in which a snow cover is included, a plateau embedded in the more strongly illuminated mountain side, and a continuous tracer release used instead of an instantaneous one. Finally, the results are discussed and summarized in chapter 6. The exact code of the modications is given in appendix A.

14 8 Introduction Appendix B displays a set of additional gures for each of the sensitivity simulations.

15 Chapter Model and setup The numerical model used for this study is the Regional Atmospheric Modeling System RAMS, version 4.4. RAMS is the result of two formerly independent codes, a cloud model by William R. Cotton and a mesoscale model by Roger A. Pielke. Its present code was developed at the Colorado State University and the ASTER division of Mission Research Corporation and is currently maintained by ATMET. It is mostly written in Fortran 9 with some parts in C. An overview of the model options and possible applications is given by Pielke et al. (99) and Cotton et al. (3). De Wekker et al. (5) investigated the applicability of RAMS within complex mountainous terrain through a comparison of model results with observational data from the Riviera Valley, Switzerland. Gohm and Mayr (5) and Gohm et al. (8) used RAMS for the numerical simulations of their case studies of bora winds. The following sections describe the model in general, as well as the parameterizations and the basic setup for the reference simulation, and the modications to the model code.. Boundary conditions The code is based on the nonhydrostatic, compressible primitive equations. In the vertical terrain-following σ z coordinates (Gal-Chen and Sommerville 975) are used and in the horizontal a polar stereographic projection is applied. The simulations are all performed on a single grid using a pseudo D setup with 3 grid points in x-direction and 5 grid points in y-direction. This conguration becomes necessary with the introduction of a tracer in the form of an additional prognostic scalar, which is not possible for a real D simulation with only one grid point in y-direction. In x-direction the lateral boundary condition for the velocity component perpendicular to the boundary (u) is a radiative condition by Klemp and Wilhelmson (978) with a constant phase speed. For the other prognostic variables 9

16 Model and setup zero gradient inow and outow is considered. In y-direction a cyclic boundary condition is applied. Horizontal grid spacing is m, yielding a 6-km wide model domain. Both the center of the grid and the projection point are located at N and.7 E, corresponding to the site of Innsbruck. According to the location of the grid's center the position of the sun is determined, and therewith solar radiation. In the vertical 7 grid points are used, beginning with a grid point distance of m near the bottom. The spacing is stretched by a ratio of.5 until a maximum value of 4 m is attained at approximately 3 m MSL. Altogether, the model domain reaches up to a height of roughly 98 m MSL. On the top a damping Rayleigh friction layer comprises the upper levels, starting at 4 m MSL. The idealized valley topography (shown in Fig..) is described by two sinusoidal shaped mountains of the form h (x) = h max [sin ( x L v L m )], (.) where h is the topography height at point x. The width of the at valley oor L v is km, the width of the adjacent mountains L m is km, and the maximum mountain height h max is 7 m, corresponding approximately to the height dierence between Innsbruck and its surrounding orography. In y-direction the height is taken to be constant. The geographic orientation of the topography is north-south, i.e., the assumed valley axis lies in west-east direction in rough approximation to the orientation of the Inn Valley. Here, the x-axis applies to north-south and the y- axis to west-east, consequently. Sensitivity simulations with dierent orientations (east-west and northeast-southwest) are considered in section Initial conditions The atmosphere is initialized horizontally homogeneous with a single sounding (Fig..). Relative humidity is set to 9% at the bottom, it decreases linearly to 8% at m MSL and thereafter to % at 8 m MSL, which is an idealization of mostly realistic atmospheric conditions. Proles of the temperature T and the potential temperature θ are dened via the Brunt-Väisälä frequency N: N = g θ θ z, (.) with g =9.8 m s being the acceleration of gravity. Constant values of N are considered within certain height intervals, namely.3,.,., and. s

17 . Initial conditions North North West West gp 3 gp 7 South South East East gp Figure.: Model topography and initial tracer source at 83 UTC (black square). Directions are indicated identical to the orientation of all vertical cross sections shown hereafter. 3.5 a) Temperature (K) Potential temperature (K) b) Brunt Vaisala frequency (s ) 3 c).5 Relative Humidity (%) d) Soil temperature (K) e) Altitude (km MSL) Altitude (km MSL) Depth (m) Figure.: Initial proles of temperature (K), potential temperature (K), (c) Brunt-Väisälä frequency (s ) (up to 3 km MSL), (d) relative humidity (%) (up to 9 km MSL) and (e) soil temperature (K) (up to a depth of m). between and m MSL, and m MSL, and m MSL, and up to the top of the model domain, respectively. This yields a strong near-surface inversion in the lowermost parts and a second weak inversion, nearly isothermal, at the height of the ridgetops. The prole is created in this way so as to partly approximate the conditions of static stability measured in Innsbruck in the morning of 4 January 6. The initial temperature at the bottom is 7 K and the whole atmosphere is taken to be stagnant, with the wind speed set to zero. Some sensitivity simulations with various potential temperature proles are run in order to evaluate the impact of atmospheric layering (section 4.4). The simulations span the time from 6 UTC 4 January 6 to 8 UTC. Major variables are written to les every half an hour. Since the rst few hours

18 Model and setup are needed as a start-up time, which is necessary for the slope winds to evolve, the tracer source is not inserted until 83 UTC,.5 h after the simulation starts. The pollutants are represented by a prognostic scalar quantity, which can be both advected by the local ow and diused. The introduced cubic source covers the whole valley oor and reaches up to about 8 m with a mixing ratio of kg kg. This is an arbitrary value, since absolute concentrations are not of interest for this study. Rather the qualitative dispersion and mixing ratios relative to the initial value are considered. Fig.. shows the situation at 83 UTC, one second, i.e., one timestep after the insertion of the scalar..3 Parameterizations The bottom boundary is represented by the interactions between soil, surface, and atmosphere. The soil model LEAF (Land Ecosystem-Atmosphere Feedback) is coupled to the atmospheric model in order to compute soil parameters and uxes to and from the atmosphere. The version LEAF-, which is implemented in RAMS version 4.4, is described in detail by Walko et al. (). It contains prognostic equations for the internal energy of the soil and snow layers, for vegetation and canopy air temperature, soil moisture, and mass of the snowcover. Canopy air can be described as the air surrounding the vegetation. Water, heat, and radiative uxes between ground and atmosphere, as well as between the LEAF- components and layers, contributing to the prognostic equations, are parameterized. The term ground is here used to describe the entire system containing the vegetation, the surrounding canopy air, and the soil, which may again be covered by snow to various degrees. Both vegetation and soil absorb solar radiation and are in immediate exchange of longwave radiation with the atmosphere and with each other. The interaction between the soil and the canopy air, as well as between the vegetation and the canopy air is given through heat uxes. Finally, the resulting uxes of momentum, heat, and water vapor are evaluated between the canopy air and the atmosphere. The computation of the turbulent uxes is based on the Blackadar scheme (Zhang and Anthes 98). It was adopted from the Pennsylvania State University - National Center for Atmospheric Research mesoscale model MM5. A short description of the parameterization and a comparison with the original RAMS scheme based on Louis et al. (98) are given in section.4.. RAMS yields the option to choose between various soil and vegetation classes, which are characterized by several parameters each, e.g., saturation moisture content, density and thermal diusivity of dry soil, albedo, leaf area index, displacement height, roughness height or fractional coverage of vegetation (including its seasonal dependence). The grid cells may be divided into a water area and several land

19 .4 Code modications 3 patches, each containing dierent vegetation and soil. For this study a vegetational coverage with short grass is considered, for soil texture sandy clay loam is used. In the model short grass has a roughness length of. m, a displacement height of. m, and an albedo of 6%. 3 soil layers are applied at a depth of, 3, 6, 9,, 6,, 5, 3, 4, 5, 7, and cm with a positive temperature oset, compared to the air temperature at the lowest level, of.,.7,.3,.7, 3., 3.3, 3.7, 4., 4.3, 4.8, 5.3, 6., and 7. C, respectively. Measured soil temperatures at a depth of 5 cm in Innsbruck and Jenbach (.78 E, 47.4 N, 3 km to the east of Innsbruck) showed values of approximately - C in January 6. The temperature prole is plotted in Fig... Soil moisture is initialized with 35% of the saturation moisture content, independent of depth. Longwave and shortwave radiation are computed using the scheme by Chen and Cotton (983). It accounts for the interaction between radiation and condensates occurring in the atmosphere, but makes no distinction between the various forms of condensate. Since only water vapor is allowed in these simulations, this does not aect the results. Turbulent subgrid scale uxes are parameterized via K-theory. According to the grid spacing horizontal and vertical mixing coecients are computed separately, based on the scheme by Smagorinsky (963) with further modications by Hill (974) and Lilly (96). It is a so-called local deformation scheme, since the coecients are a function of the wind shear at the local grid point only. Horizontal turbulent diusion has shown a major impact on numerical stability, but also on the general results obtained by the model within this valley geometry. In section.4.3 horizontal diusion and particularly the treatment of the prognostic scalars is discussed in more detail, including the code modications done in order to gain sensible results..4 Code modications.4. Grid Rotation In this setup with an initially stagnant atmosphere without any synoptical inuences the formation and evolution of the slope-wind system is mostly due to diurnal changes in solar irradiation. Since the incident shortwave radiation is also dependent on the topography, RAMS applies a correction which takes into account the orientation and inclination of the surface with respect to the position of the sun. Starting from the radiation that would impinge on a horizontal surface, the ground receives the fraction perpendicular to the actual topography. The incidence angle i

20 4 Model and setup is dened as cos i = cos α cos ζ + sin α sin ζ cos (β γ), (.3) where α is the slope angle, γ the slope azimuth, β the sun's azimuth, and ζ the sun's zenith angle (Pielke 984). The above correction is applied to the total shortwave radiation, i.e., direct plus diuse. Hence, a steep north-exposed slope may receive no radiation at all. Shadows cast by the surrounding topography are not considered, which can lead to an overestimation of the net radiation in the morning and evening (De Wekker et al. 5). Colette et al. (3) applied an algorithm to the model ARPS (Advanced Regional Prediction System) which takes into account the shadowing eect of the surrounding topography. They observed a delay in the onset of upslope winds and the inversion breakup due to the additional shading. The Inn Valley has a mainly east-west orientation with a small north-south component. In order to obtain similar irradiation conditions as in reality the direction of the D model domain was chosen to be north-south for most of the cases. The eect of valley orientation and the according irradiation conditions is further discussed in section 4.3. By default the x-direction in RAMS applies to east-west and the y-direction to north-south. The rotation of the grid is achieved by changing the slope azimuth in the radiation computation by 9. This means that only the shortwave radiation is modied according to the orientation of the topography and all other parameters, which depend on the geographical location, remain unchanged. The approach is justiable, since the longitudinal and latitudinal variations of solar radiation can be neglected due to the small model domain of 6 km. Appendix A. gives details on the appropriate modications of the RAMS model code. The second method to change the orientation of the valley is to turn the whole model domain, including the topography. This means to use only 5 grid points in x-direction and 3 grid points in y-direction with the topography height being a function of y instead of x. Since this allows no further possibilities than east-west and north-south orientation, only one simulation was performed to be used as a control for the results of the rst approach. A direct comparison of the incident shortwave radiation at three dierent grid points within the valley (Fig..3) shows nearly the same values for the two approaches, diering by no more than.5 W m at the south-facing slope. Hence, the alteration of the slope azimuth can be said to be an adequate way for the rotation of the topography in the present study..4. Surface layer parameterization The uxes of heat w T and moisture w r are determined from similarity theory and summed over all patches within a grid box. The partial uxes are weighted by the

21 .4 Code modications Reference Valley center Northern slope Southern slope Rotated grid Valley center Northern slope Southern slope 9 8 (c) Difference Valley center Northern slope Southern slope Shortwave radiation (W m ) Shortwave radiation (W m ).5 Shortwave radiation (W m ) Figure.3: and Shortwave incoming radiation at three grid points at the valley oor, the northern (south-exposed), and the southern (north-exposed) slope for the reference run and the grid rotated control run. (c) Dierence in shortwave incoming radiation between the two simulations. fraction of area covered by the respective patch: n p w T = f p (u T ) p, (.4) p= n p w r = f p (u r ) p, (.5) p= with n p being the number of patches within the grid box and f p the appropriate fraction of area (Walko et al. ). The original RAMS parameterization of the scaling velocity u, temperature T, and water vapor mixing ratio r based on Louis et al. (98) was replaced by the Blackadar scheme (Zhang and Anthes 98). Zhang and Anthes (98) dierentiate between a nocturnal, mostly stable regime and a regime of free convection. The distinction is made through z P BL, with z L P BL being the height of the mixed layer and L the Monin-Obukhov length, which is dened as L = c pm ρ θ a u 3 κ g SH, (.6) where c pm is the specic heat capacity of moist air, ρ the air density, θ a the potential temperature at the rst atmospheric level, g the acceleration of gravity, κ the von Kármán constant, and SH the sensible heat ux SH = c pm ρ u T. (.7)

22 6 Model and setup 5 Reference Louis 98 5 (c) Difference Energy flux (W m ) 5 5 Energy flux (W m ) Energy flux (W m ) SH Valley center SH Southern slope SH Northern slope 35 LH Valley center LH Southern slope LH Northern slope Figure.4: and Sensible heat ux (SH) and latent heat ux (LH) at three grid points at the valley oor, the northern (south-exposed), and the southern (north-exposed) slope for the reference run using the Blackadar parameterization and the Louis parameterization. (c) Dierence in SH and LH between the two simulations. See the legend in for and (c) too. The nocturnal regime distinguishes again between three dierent cases, depending on the bulk Richardson number Ri B = gz a θ a θ va θ vg V, (.8) where the index a denotes again the rst atmospheric σ z -level and the index g the ground (represented by the canopy air), z a is thus the height of the rst σ z -level above ground level; θ v the virtual potential temperature and V the horizontal wind speed. A stable regime without any turbulence is considered for Ri B., mechanically driven turbulence for Ri B <., and forced convection for Ri B <. Finally, u, T, and r read u = κv ( ), (.9) z ln a z ψ m T = κ r = κ θ a θ ( ) g, z ln a z ψ h (.) r a r g ln ( κu z a ), + za.4 5. ψh (.) with z being the roughness length and r the water vapor mixing ratio. The stability functions ψ h and ψ m are evaluated depending on which of the four stability classes is applicable. The exact model code for this surface layer parameterization is described in appendix A.. Fig..4a and b show a comparison of the sensible heat ux (SH) and the latent heat ux (LH) between the Blackadar and the Louis parameterization scheme. SH

23 .4 Code modications 7 and LH are plotted for the valley center and for both mountain slopes within the valley. Positive values depict a ux to the surface and negative values a ux to the atmosphere. Contrary to the Louis parameterization, the Blackadar scheme does not allow latent heat uxes directed to the ground. Hence, no positive values occur in Fig..4a, whereas with the Louis scheme (Fig..4b) the south-facing slope shows a short period of a very weak LH directed to the surface in the morning after about 3 hours (9 UTC). The dierence between the two simulations is displayed in Fig..4c. Here, a negative sign indicates higher values in the Blackadar case, i.e., more energy gain or less energy loss by the surface. The increased sensible heat uxes (in both directions) in the Blackadar scheme reinforce the coupling between the lower atmospheric levels and the ground. This may avoid numerical instability through extensive cooling of the vegetation and its surrounding canopy air. Thorough testing showed a general reduction both in the strength and the amount of occurrence of these cases compared to the original Louis scheme. Unrealistic surface cooling in stable nocturnal conditions and the impact of the sensible heat ux were investigated, e.g., by Poulos and Burns (3) or Derbyshire (999)..4.3 Horizontal diusion In the original RAMS code, considering the current setup options, the subgrid scale tendencies of momentum and scalar quantities (potential temperature θ, water vapor mixing ratio r, and the passive tracer) due to horizontal diusion are calculated using K-theory. They can be written in the following form, where momentum is denoted by the index m and scalars φ by the index s, the index h means horizontal: φ t diuse,h = h ( K sh h φ), (.) u i t diuse,h = h ( K vh h u i ), (.3) where u i is the respective wind component. The gradients of momentum and scalars are not calculated along σ z levels, but derived on a true horizontal plane after interpolating the values to the appropriate vertical level rst. The scalar mixing coecient K sh is three times the value for momentum K mh with K mh = max (K min, K h ), (.4) where K h is a function of grid point distance x and horizontal wind shear: [ ( u ) K h = (C x x) { + x ( ) ] ( v v + y x + u ) }.5. (.5) y

24 8 Model and setup The parameter C x is set to.3 as it is proposed for the case that strong diusion is needed. K min imposes a minimum value on the mixing coecient eld in areas, where originally low values occur due to weak wind velocities, K min =.75 K A ( x) 4 3. (.6) The parameter K A allows to apply a minimum horizontal diusion in order to avoid numerical instability. Here K A is set to.5, which results in a minimum scalar mixing coecient of m s, considering the grid point distance of m. No modications are made to momentum diusion, therefore it is not regarded hereafter. The prognostic scalars potential temperature, water vapor mixing ratio, and the tracer are each treated separately. In the case of the tracer the high threshold value K min, which is necessary for θ to guarantee numerical stability, may become more inuential on the dispersion than the wind eld. It may even force the pollutants to propagate up the slope against downslope winds, if they are not strong enough. But similarly to θ a certain minimum diusion is needed for stability reasons nevertheless. Hence, K min is switched o for the tracer and instead, an additional 4 th order-derivative diusion term is applied, for which the derivations are taken along σ z levels, ( φ t 4 φ diuse,h = h (K sh h φ) K x x + K 4 y The discretization of the fourth derivative at grid point i reads ( ) 4 φ x 4 i ) 4 φ. (.7) y 4 6φ i 4 (φ i+ + φ i ) + φ i+ + φ i ( x) 4. (.8) Parameters K x and K y are weighted by the slope of the σ z levels, so as to reduce the diusion in areas, where the height dierence between neighbouring grid points is particularly high: c K x = K 4 c + 4 z 4. (.9) ( x4 ) c x K y is obtained analogue, the derivations taken with respect to y. K 4 is a constant with its coecients adopted from (.6), K 4 =.75 K B ( x) 4 4 t. (.) The constant factor c is set to, c to 3 m, and K B to.8. A 6 th order diusion term instead of the 4 th order diusion was tested as well, but did not yield

25 .4 Code modications 9 any further improvements. Contrary to the other prognostic variables, horizontal tracer gradients for the second-order term are taken along σ z levels in combination with vertical gradients, since diusion with gradients on a true horizontal plane happened to produce mass along the mountain slope surface. Likewise, the second-order scheme tends to produce unrealistic cooling at locally conned regions along the mountain slopes. This seems to be caused by the inuence of the rst model level, located below the surface, which is also taken into account for vertical interpolation. Therefore, the second-order diusion for all other scalars but the tracer is turned o for the lowest seven atmospheric levels, setting the corresponding tendencies to zero. The necessity to consider that many layers arises from the high inclination of the topography and the low vertical grid point distances near the ground. For stability reasons the fourth-order diusion term is added to the tendencies at these grid points, instead. Here, the derivations for θ are taken for a perturbation potential temperature based on Zängl (), which means that a mean value according to the vertical θ-gradient γ = θ is subtracted from the θ-eld z rst. The perturbation potential temperature θ reads θ = θ [θ + γ (z z )], (.) where the index indicates a constant reference state. γ is assumed to be horizontally homogenous over the ve grid points which are considered for the discretization, the one at which the diusion is computed and two to each side. 4 θ x 4 = 4 θ x 4 γ 4 z x 4 (.) A detailed view of the modications to the model code and the implementation of the above equations is given in appendix A.3. Vertical diusion Although no alterations to the vertical diusion computation are made, it shall be shortly described here, so as to have an overview of the entire diusion parameterization. The vertical (index v) diusion terms for momentum and scalar quantities read ( ) u i u i K sm, (.3) t diuse,v = z φ t diuse,v = z z ( φ K sv z ). (.4)

26 Model and setup The mixing coecient K mv is calculated similar to (.5), except for two additional modications, which take into account the atmospheric layering, K mv = κ z [ S κ z + { ] [ (.5 max (, F B ) min, max, K )] }.5 sv Ri, + K δ mv (.5) where S contains the vertical shear of the horizontal wind components u and v: S = ( ) u + z ( ) v. (.6) z The factor δ is the square of the vertical grid point distance z multiplied by the parameter C z, which is set to.3, analogue to the horizontal diusion, δ = max { (C z z), min [ 3, (C x x ) ]}. (.7) The correction term containing the squared Brunt-Väisälä frequency F B = g θ v is θ v z based on Hill (974). In the unstable case (F B < ) F B is added to the deformation rate S. The second modication (Lilly 96) considers the Richardson number Ri multiplied by the ratio of the scalar mixing coecient to the momentum mixing coecient, which is again set to three. The Richardson number is thereby dened as { [ Ri = max min F B max (S, 5 ), K sv K mv ] },. (.8)

27 Chapter 3 Reference run The reference simulation, whose setup is specied in chapter, yields the basis for further comparisons with several sensitivity tests and for the evaluation of the inuence of various parameters. It displays major features of atmospheric development, wind systems, and their eect on particle dispersion in mountainous area. The main results are described here in detail, comprising the meteorological parameters, e.g., energy uxes, slope winds, and atmospheric layering, as well as the transport and dispersion of a tracer plume within the valley. Furthermore, a short note on numerical problems is made. 3. Meteorological parameters Incoming solar radiation depends on the time of the day and the orientation and inclination of the mountain slopes. The resultant dierential heating of the mountain sides leads to varying driving forces for the slope winds and alterations of the circulation pattern. Segal et al. (987) investigated the inuence of dierences in solar irradiation between a north and south-exposed slope on the upslope winds during the day. Figure 3. shows the energy uxes of the radiational components and the sensible and latent heat ux at the surface. Fluxes to the system soil-vegetation-canopy air are indicated through a positive sign and uxes to the atmosphere through a negative one. Since all the uxes have a value of W m at the beginning (6 UTC), the rst data shown are from half an hour later, at 63 UTC. The three considered grid points are located within the valley, since this is the area of major interest. Grid point 5 (gp 5) represents the center of the model domain at the valley oor, the grid point at the south-facing slope (gp 3) and the north-facing slope (gp 7) have a terrain height of 6.4 m each. See Fig.. for the exact location of gp 3 and 7. In y-direction all of the following time series for a specic site and all of the vertical cross sections are taken from gp 3.

28 Reference run After sunrise at 7 UTC incident shortwave radiation becomes positive, both at the south-facing slope and the valley oor, only the north-facing slope remains shaded from solar irradiation during the whole simulation period. Sunset occurs shortly after 53 UTC on a horizontal plane. Due to the inclination of the topography and the large zenith angle of the sun in January the slope receives much more solar radiation than the at terrain. At the valley center the maximum value is 4 W m, which is reached shortly before UTC, while it is more than two times as high at grid point 3. The reected shortwave radiation is dictated by the surface albedo, which has a nearly constant value of %. The longwave radiation shows no noteworthy diurnal variability, with a downwards directed component of 7 W m and an upwards directed component, which is about 5 W m higher. Altogether this yields a positive net radiation balance during the day, when the solar shortwave irradiation compensates for the negative longwave balance, except for the north-facing slope, where the net radiational loss persists. The energy input from the absorbed radiation leads to a diurnal cycle of soil and near-surface temperatures (Fig. 3.). Vegetation and canopy air react most strongly to the variations in radiation. While the air at the valley center (Fig. 3.a) reaches a maximum of 3 C at 6 UTC, vegetation and canopy air attain values of 5.5 C and 4. C, one hour earlier. In the afternoon cooling is equally stronger. Soil temperatures respond with the highest amplitude in the upper layers to the irradiation during daytime. The deeper layers roughly maintain their initial values. Grid point 3 (Fig. 3.b) yields a dierent picture. Vegetation, canopy air, and the uppermost soil layers show a diurnal cycle according to the radiation, whereas the air temperature increases during the whole day except for short uctuations. At 8 UTC a nal temperature of -.7 C is obtained. Due to the fact that the vegetation and the ambient air become warmer than the atmosphere above an upwards directed sensible heat ux occurs with maximum values of more than 35 W m (Fig. 3.b). Evaporation causes a latent heat ux of up to W m. In spite of the large turbulent uxes the rise in air temperature remains relatively weak with a continuous increase of roughly.5 C h. During the day strong upslope winds advect potentially colder air from below and counteract the heat ux from the ground. The daily evolution and strength of the slope winds are described further below. Before and after sunrise, when the sensible heat ux becomes nearly zero and directed to the surface, the slope winds reverse and advect potentially warmer air from above. Therefore, air temperature mounts steadily. The individual contributions to the heating rate from advection and sensible heat ux are in the range of C h, whereas radiation is an order of magnitude smaller. Since the north-facing slope (gp 7, Fig. 3.c) receives no shortwave radia-

29 3. Meteorological parameters 3 Reference, Grid Point 5 8 SW d SW u Energy flux (W m ) 6 4 LW d LW u R net SH LH Reference, Grid Point 3 (c) Reference, Grid Point 7 8 SW d SW u 8 SW d SW u LW d LW d Energy flux (W m ) 6 4 LW u R net SH LH Energy flux (W m ) 6 4 LW u R net SH LH Figure 3.: Surface energy balance components (W m ) at the valley center (gp 5), the south-facing slope (gp 3), and (c) the north-facing slope (gp 7): Incident shortwave radiation (SW d ), reected shortwave radiation (SW u ), downward longwave radiation (LW d ), upward longwave radiation (LW u ), net radiation (R net ), sensible heat ux (SH), and latent heat ux (LH).