ACPAtmospheric Chemistry and PhysicsACPAtmos. Chem. Phys.1680-7324Copernicus GmbHGöttingen, Germany10.5194/acp-15-11981-2015The impact of embedded valleys on daytime pollution transport over a mountain rangeLangM. N.moritz.n.lang@gmail.comhttps://orcid.org/0000-0002-2533-9903GohmA.https://orcid.org/0000-0003-4505-585XWagnerJ. S.Zentralanstalt für Meteorologie und Geodynamik, Vienna, AustriaInstitute of Atmospheric and Cryospheric Sciences, University of
Innsbruck, Innsbruck, AustriaDeutsches Zentrum für Luft- und
Raumfahrt, Oberpfaffenhofen, GermanyM. N. Lang (moritz.n.lang@gmail.com)28October20151520119811199816February201521May201530September201516October2015This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://acp.copernicus.org/articles/15/11981/2015/acp-15-11981-2015.htmlThe full text article is available as a PDF file from https://acp.copernicus.org/articles/15/11981/2015/acp-15-11981-2015.pdf
Idealized large-eddy simulations were performed to investigate the impact of
different mountain geometries on daytime pollution transport by thermally
driven winds. The main objective was to determine interactions between
plain-to-mountain and slope wind systems, and their influence on the
pollution distribution over complex terrain. For this purpose, tracer
analyses were conducted over a quasi-two-dimensional mountain range with
embedded valleys bordered by ridges with different crest heights and a flat
foreland in cross-mountain direction. The valley depth was varied
systematically. It was found that different flow regimes develop dependent on
the valley floor height. In the case of elevated valley floors, the
plain-to-mountain wind descends into the potentially warmer valley and
replaces the opposing upslope wind. This superimposed plain-to-mountain wind
increases the pollution transport towards the main ridge by an additional
20 % compared to the regime with a deep valley. Due to mountain and
advective venting, the vertical exchange is 3.6 times higher over complex
terrain than over a flat plain. However, the calculated vertical exchange is
strongly sensitive to the definition of the convective boundary layer height.
In summary, the impact of the terrain geometry on the mechanisms of pollution
transport confirms the necessity to account for topographic effects in future
boundary layer parameterization schemes.
Introduction
Daytime transport and mixing processes of air pollutants primarily occur
within the convective boundary layer (CBL) and are mostly well understood for
flat and homogeneous terrain . The typical CBL, which forms
under fair weather conditions over horizontally homogeneous and flat terrain,
consists of a superadiabatic surface layer, a mixed layer (ML), and a stably
stratified layer called the entrainment layer (EL); the latter separates the
CBL from the free atmosphere . Turbulent mixing in the ML
induced by rising thermals leads to nearly height-constant profiles of
conserved quantities, such as potential temperature and specific humidity up
to the EL . Inside the EL, overshooting
thermals cause mixing of potentially cooler air from the ML with air from the
stably stratified free atmosphere aloft. This relatively weak exchange with
the free atmosphere limits the vertical dispersion of pollutants mostly to
the ML. Over complex terrain, interactions between the terrain and the
overlying atmosphere lead to a horizontally inhomogeneous CBL structure
. Additionally, thermally driven flows increase the vertical
transport of pollutants, moisture, and other components. Often this transport
goes beyond the CBL top into the free atmosphere
e.g.,.
Thermally driven winds develop due to differential heating of adjacent air
masses and are characterized by a reversal of wind direction twice per day
. Generally, thermally driven winds can be divided into
three different types within respective boundary sub-layers, such as slope
winds within the slope layer, valley winds within the valley atmosphere, and
plain-to-mountain winds within the mountain atmosphere
. Under weak synoptic forcing, the interaction
of these three wind systems dominates the flow pattern over complex
terrain .
Observational and modeling studies have shown that thermally driven winds and
especially upslope winds can enhance the daytime vertical moisture and mass
exchange between the CBL and the free atmosphere over a valley by a factor of 3 to 4 compared to pure turbulent exchange processes over a plain
. By means of idealized simulations,
show that this increase in vertical transport to the free
atmosphere can even be up to 8 times larger depending on the CBL height
definition used as the reference surface for the vertical transport. In
addition to slope and valley winds, vertical transport can be further
enhanced by plain-to-mountain winds, which have been explored in the Vertical
Transport and Orography (VERTIKATOR) campaign and in
several modeling studies e.g.,. Plain-to-mountain
winds develop due to a horizontal temperature gradient between the mountain
ridge and the adjacent plain. This mesoscale flow transports low-level air
from the foreland to the mountain ridge. The slope winds superposed by the
plain-to-mountain winds transport the air further upslope and form vertical
updrafts above the mountain peaks. Under ideal conditions an upper-branch
return flow closes the circulation by blowing air from regions above the
peaks backwards in the direction of the foreland . This
transport process is referred to as mountain venting and can be an important
additional exchange mechanism between the CBL and the free atmosphere over
complex topography . In more detail,
differentiate between mountain venting and advective venting. Both are
mesoscale flows exporting CBL air to the free atmosphere, where mountain
venting is characterized by a vertical transport and advective venting by
a horizontal transport through the CBL top. Advective venting usually occurs
if an inclined CBL height exists and the mean wind direction is not parallel
to the CBL top .
Thermally driven flows not only provide a vertical transport mechanism; they
also impact the temperature and humidity distribution via horizontal and
vertical advection and hence the CBL height over complex terrain. When
determining the CBL height based on temperature profiles it is assumed that the
temperature structure is dominated by vertical mixing. This may often not be
the case over complex terrain. Several studies reported shallow
e.g., or non-existent
e.g., mixed layers in valleys, although convection
was present. Thus, the definition of the CBL height over complex terrain may
be often problematic e.g.,, and many
conventional concepts for the determination of the CBL height might not hold
for complex topography. Accordingly, the observational and modeling study of
shows that during the day, aerosol layer (AL) heights
detected with an airborne lidar differ from CBL heights determined by
temperature-based methods over complex terrain, whereas this is not the case
over homogeneous, flat terrain. Temperature-based CBL heights mostly show
a more terrain-following behavior and are lower than AL heights
.
As about 50% of the earth's land surface consists of mountainous
terrain , differences in transport and mixing processes
over complex terrain and the flat plain are of great importance for regional
weather and climate studies. Today's operational global numerical weather
prediction and climate models have horizontal grid resolutions larger than
10 km, which is too coarse to properly resolve topographically
induced transport processes. Present-day boundary layer parameterization
schemes are not capable of accounting for these missing subgrid-scale effects
. It is therefore necessary to quantify these effects,
e.g., with high-resolution numerical simulations and, based on these results,
develop new boundary layer schemes for complex terrain. The need for such
a development has already been stressed by .
This paper relates to recent idealized studies
, which investigate the impact of different
valley topographies on the CBL structure, and the vertical exchange between
the CBL and the free atmosphere under idealized daytime conditions with a
constant surface sensible heat flux. The present work aims at investigating
interactions between plain-to-mountain and slope wind systems, and their
influence on daytime pollution transport and distribution over complex
terrain. This is achieved by tracer analyses over a quasi-two-dimensional
mountain range with embedded valleys and a flat foreland on each side of the
mountain in cross-mountain direction. The embedded valleys used in the
present simulations are bordered by two mountain ridges of different crest
heights. This is in line with a case study of transport processes in a valley
with similar asymmetric crest heights and extends recent
idealized simulations of to account
for a typical geometric feature of real terrain. Simulations for valleys with
different depths are performed and compared to a single-ridge topography to
quantify the impact of varying valley floor heights on different transport
processes of pollutants over complex terrain, e.g., mountain venting and
return flows in the free atmosphere.
The paper is organized as follows. In Sect. the numerical model
and the experimental setup are described. Section explains the
procedures of flow decomposition and averaging, and Sect.
summarizes the different CBL height definitions used in this study. The
simulation results are presented in Sect. , and a conclusion is
given in Sect. .
Model and setup
In this study, idealized large-eddy simulations (LES) of daytime thermally
driven flows are performed with the Advanced Research version of the Weather
Research and Forecasting model (WRF-ARW), version 3.4. The WRF model is
a fully compressible, non-hydrostatic, terrain-following numerical modeling
system, which can be run in LES mode .
A third-order Runge–Kutta (RK3) time integration scheme, a fifth-order
horizontal and a third-order vertical advection scheme are applied in the
numerical simulations . Subgrid-scale turbulence is
parameterized by a three-dimensional, 1.5-order turbulent kinetic energy
(TKE) closure . The fully turbulent flow is decomposed
into its resolved turbulent and mean advective parts according to the method
of , which is described in Sect. . A statistics
module for online averaging and flux computation has been implemented in the
WRF model which reduces the demand for data storage.
At the surface a Monin–Obukhov similarity scheme is used
to compute turbulent momentum fluxes. This scheme couples the surface and the
first model level using the four stability regimes of . The
surface roughness length is set to 0.16m. Following the approach
of , surface moisture fluxes are disabled, and a constant
sensible heat flux of 150Wm-2 is prescribed at the surface.
These quite substantial simplifications are supported by sensitivity tests
performed by , which reveal similar flow and CBL
developments over an idealized valley when prescribing either a constant or a
time-dependent surface sensible heat flux. Further, the recent study of
shows an approximately linear relation between the
amplitude of the sensible heat flux and the amplitude of the net shortwave
radiation. Hence, prescribing the heat flux instead of the radiative forcing
will not fundamentally change the results. The simulations are run for
6h. The resulting integrated heat input would be the same as
prescribing a more realistic sinusoidal heating with an amplitude of about
235Wm-2 that is reached after 6h, i.e., at noon.
Such heating conditions are typical for non-arid mid-latitude valleys
. The simulations are initialized
with an atmosphere at rest, with a potential temperature of 280K
at sea level height, and a constant vertical temperature gradient of
3Kkm-1. To avoid moist processes, the relative humidity is
set to a constant value of 40% at the beginning. To trigger
convection, randomly distributed temperature perturbations with amplitudes
≤0.5K are added to the lowermost five model levels. The Rossby
number for our problem is about one or larger
Ro=U/(Lf)∼1, with
typical values of U=3ms-1, L=30km, and f=10-4s-1.
suggesting that Coriolis force might play some
minor role. Nevertheless, for the sake of simplicity we neglect Coriolis
effects.
All simulations are performed with a horizontal mesh size of 100m
and 74 vertically stretched levels with a vertical grid spacing increasing
from 10m at the lowest level to 100m higher aloft. The
model top is defined at 6.2km with a Rayleigh damping layer
covering the uppermost 2km. Periodic lateral boundary conditions
are applied in both horizontal directions. The integrating time step is set
to 0.5s.
The analytical expression for the quasi-two-dimensional model terrain h(x)
is defined as the product of a large-scale mountain h*(x) with a half
width Lx/2 and a small-scale cosine-squared perturbation with n number
of wave cycles per length scale Lx:
h(x)=hmaxcos2xLxnπh*(x),
where
h*(x)=cos2xLxπ|x|≤X00|x|>X0,
and where hmax specifies the maximum height of the mountain
range. This setup is similar to mountain configurations with several ridges
used in previous studies . In this study, the
parameters are set to Lx=60km, X0=30km, and
n=0 or 4. This generates a symmetric, 60km broad mountain
range consisting of a single ridge for n=0, or three ridges with two
embedded valleys for n=4 (Fig. a). In the simulations with
three ridges, the ridge at x=-13.9km and the ridge at x=0km are hereafter referred to as the first and the main ridge,
respectively. The slopes are correspondingly counted from left to right:
slope 1 (-22.5km≤x≤-13.9km), slope 2
(-13.9km≤x≤-7.5km), and slope 3
(-7.5km≤x≤0km). A flat foreland extends
over 30km on each side of the mountain in cross-mountain direction
(see Fig. b). The scale of the embedded valleys is comparable
to real valleys such as the Inn Valley in the European Alps. For sensitivity
runs, mountain shapes with elevated valley floors are used, where the
topography is an extension of Eq. () and is specified by
a linear combination of an upper and lower envelope:
h(x)=(hmax-hmin)cos2xLxnπh*(x)+hminh*(x),
where h*(x) is the large-scale mountain of Eq. (), and
where hmax and hmin are the maximum heights of the
upper and lower envelope, respectively. When hmin becomes zero,
Eq. () is identical to Eq. (). In addition to
these mountain shapes, a simulation over a flat plain is performed. An
overview of the different model topographies with their maximum slope
inclinations is given in Table .
Idealized model topography of the reference run HMIN0 as (a) vertical cross section (gray shading) and (b)
plan view (showing the full domain). Additional topography setups with three ridges and different elevated valley floor heights, and with a single ridge are used in
sensitivity simulations and are shown in (a) as dashed, dotted and solid lines (compare Table ).
Overview and abbreviations of model topographies as described by Eqs. (1)
and (). HMIN0 corresponds to the reference run. All mountain
topographies consist of a 60km broad symmetric mountain range with
a 30km wide flat foreland on each side (see Fig. ).
hmax and hmin are the maximum heights of the upper
and lower envelope, respectively. hv is the effective height of
the valley floor and max(α) the maximum slope inclination. The cases
S-RIDGE and PLAIN refer to sensitivity runs with a single ridge and a flat
plain, respectively.
Due to the flat foreland on each side of the mountain range,
a plain-to-mountain wind system develops during the simulation. The model
topography consists of infinitely long ridges and valleys of constant height
in y direction; hence, no valley winds develop in this setup. The
computational domain has an extent of 10km in the along-ridge
direction and 120km in the cross-mountain direction. The idealized
terrain in this study is a step towards a more realistic setup compared to
recently used idealized topographies consisting of a single valley between
two ridges of identical height
e.g..
Tracer analyses are performed to quantify the impact of different terrain
geometries on daytime pollution transport and distribution over a mountain
range compared to flat terrain. In all simulations, a passive tracer is
constantly emitted over the whole y direction within different
cross-mountain subdomains, depending on the focus of the analysis. In the
vertical, the tracer source covers the lowermost eight model levels (up to an
altitude of approximately 110 m), which is comparable to pollution
layer depths typically observed in the morning in the Inn Valley
e.g.,. The emission has an arbitrary magnitude. The
tracer particles are transported by three-dimensional winds and dispersed by
atmospheric turbulence and diffusion.
LES averaging method
In order to distinguish between different heating processes, the flow is
decomposed into its mean advective, resolved turbulent, and subgrid-scale
parts following the approach of and .
The fully turbulent variable ψ̃(x,t) is divided into
a model grid-box average ψ‾(x,t) and a subgrid-scale
part ψ′(x,t):
ψ̃(x,t)=ψ‾(x,t)+ψ′(x,t).
By means of Reynolds averaging, the model output
ψ‾(x,t) can be formally separated into a mean and
a fluctuating part. Therefore, the resolved turbulent part
ψ′′(x,t) can be computed from the grid-box average
by
ψ′′(x,t)=ψ‾(x,t)-〈ψ‾(x,t)〉,
where the time and along-mountain averaging operator 〈〉 is
defined as
〈〉=1TLy∫t-T/2t+T/2∫0Lyψ‾(x,t)dydt,
with an averaging interval in time of T=40min and in space
parallel to mountain range of Ly=10km. Time averaging is
based on a sample interval of 1 min. In order to better compare the mean
cross-mountain structure of the different sensitivity runs, all variables
shown in this study are averaged in time and space (along y direction)
according to Eq. ().
The decomposed vertical fluxes are computed according to the method described
in . The computation of mean vertical profiles over the
valley requires an interpolation from model levels to Cartesian coordinates
along constant height levels which have a vertical grid spacing of
20m.
CBL height detection
In this study, we distinguish between AL and CBL heights, marking the top of
the tracer distribution and the top of the nearly height-constant potential
temperature profile, respectively. Conventionally, both definitions are
synonymously used for the CBL height detection over homogenous and flat
terrain. Observational and numerical studies indicate, however, that the
heights of the AL and CBL are different over mountainous terrain
.
In the present work, the AL height is determined by a gradient method
computing the vertical gradient extremum
Technically, the term
gradient extremum specifies the minimum value of the negative vertical
aerosol gradient.
of aerosol concentration moving upwards from the surface
. We use three different methods to compute the CBL height.
The first one (CBL1) is determined as the height at which the potential
temperature gradient exceeds a threshold of 0.001Km-1. This
gradient method is also used by and
, whereby the threshold value is chosen
following . To compare our results with
, we compute a second CBL height (CBL2) by using the same
Richardson-number-based method following . For this
purpose, a modified bulk Richardson number is calculated on every vertical
model level starting from the surface. The CBL2 height is then derived as the
height where the Richardson number reaches a critical value of 0.25. A more detailed description is given in
. criticize that the
Richardson-method of adds a surface excess temperature
to an already existing superadiabatic layer above the ground; therefore, they
conclude that the calculated CBL2 height might be slightly overestimated. For
comparison, an additional CBL height (CBL3) is calculated based on
a Richardson number method without an additional excess temperature
. The temporal evolution of horizontally averaged AL and
CBL heights, vertical sensible heat flux profiles, and normalized tracer
mixing ratios over the PLAIN are shown in Fig. . Due to the
definition of the CBL1 height, it marks the top of the ML and is located
slightly below the altitude of the vertical heat flux minimum. This is also
in line with CBL heights obtained by and
. The CBL2 height follows the top of the EL and
therefore lies above the CBL1 height (see Fig. ). During the
whole simulation, the vertical position of the CBL3 is situated in the middle
of the EL and is about the same as the AL height in the PLAIN simulation with
a homogeneous tracer source near the surface between -30km≤x≤0 km (see Sect. ).
Temporal evolution of mean boundary layer heights of the PLAIN
simulation. Shown are three different temperature-based CBL heights and the
AL height (see Sect. ). Thin green contour lines display
horizontally averaged normalized tracer mixing ratios (0.1 increment) for
a horizontally homogeneous tracer source at the surface. Color contours
represent total vertical sensible heat flux profiles of the PLAIN simulation.
Due to technical reasons (time averaging), values are only shown for
simulation times after 1.5h.
For quantifying the vertical transport from the CBL to the free atmosphere,
the time dependent CBL1 height is used as reference height. Vertical
transport of CBL air beyond this reference height can occur either by
turbulent exchange in the EL or by thermally induced circulations.
Simulation resultsFlow structure
In this section, the sensitivity of the flow structure on the terrain
geometry is assessed. In all simulations the instantaneous flow is fully
turbulent after 2h of simulation (not shown), and the flow pattern
shows similar characteristics to the results in . Over the
flat foreland a CBL layer and a plain-to-mountain wind is established. Inside
the valleys, thermally driven upslope winds develop at the beginning of the
simulations.
Cross sections of averaged (a–d) cross-mountain wind speed
and (e–h) vertical wind speed as color contours after 6h
of simulation for four different mountain shapes: (from top to bottom) HMIN0,
HMIN0.5, HMIN1, and S-RIDGE (cf. Table ). Potential temperature
as black contour lines (0.25K increment) and wind vectors for
components parallel to the cross section. Variables are averaged in time and
space (along y direction). The black solid line shows the reference CBL
height (CBL1).
Vertical profiles of temporally and spatially averaged
cross-mountain wind speed at (a) the middle of slope 1 (x=-18.2km), (b) the middle of slope 2 (x=-10.7km), and the middle of slope 3 (x=-3.7km) for
the mountain shapes HMIN0 (solid lines) and HMIN0.5 (dashed lines). Black and
blue lines are valid for 2 and 4h of simulation, respectively.
Red lines in the inset show the location of the profiles. The averaging in time and space is done according to Eq. (5).
Cross sections of averaged potential temperature as contour lines
(increments of 0.25K) after (a)2h and
(b)4h of simulation for the HMIN0.5 mountain shape and
(c) after 4h for the reference run (HMIN0). Wind vectors
for components parallel to the cross section. Variables are averaged in time
and space (along y direction).
In order to better compare the mean flow structure of the different
sensitivity runs, the flow fields are temporally and spatially averaged, and
shown as cross sections after 6h of simulation in
Fig. . In all simulations, a CBL develops over the foreland up
to 1.5km. Despite the different valley depths, all simulations
with valleys (Fig. a–c) have similar CBL1 heights of 1.5 to
1.7km over the crest of the first ridge and approximately
2.5km over the crest of the main ridge. However, in the reference
run (HMIN0, Fig. a), due to updrafts in the upper part of
slope 2 (cf. naming convention in Sect. ), the CBL1 height is up
to 600m higher over slope 2 and nearly horizontal over the valley
region. In the single-ridge simulation (S-RIDGE, Fig. d), the
CBL1 height is comparable to the one in the simulations with elevated
valleys, but the depth
The CBL depth is defined as the CBL height
minus the terrain height.
of the CBL is considerably smaller.
Mean vertical profiles of potential temperature after (a)2h and (b)6h of simulation for the mountain
shapes HMIN0 (solid line), HMIN0.5 (dashed line), and HMIN1 (dotted line).
The vertical profiles are vertically interpolated from model levels to
constant height levels and horizontally averaged between the first and main
ridge (-13.9km≤x≤0km, see red area in
insets). Variables are averaged in time and space (along y direction) according to Eq. (5).
Evolution of density-weighted and volume-averaged heat budget
components for (a) the HMIN0 and (b) the HMIN1 simulation.
The total tendency (TOT) is equal to the sum of surface sensible heat flux
(SHF), mean flow advection (ADV), and turbulent exchange (TRB). Both control
volumes extend from the first to the main ridge and from the surface to an
altitude of 2.1km. Due to technical reasons (time averaging),
values are only shown after 1.5h of simulation.
Depending on the valley floor height, two different flow regimes develop in
the simulations with embedded valleys. The first one occurs in the reference
run with the deepest valley and the second one in the two simulations with
elevated valley floors. In the reference run (HMIN0, Fig. a),
upslope winds develop over all mountain slopes with cross-mountain wind
speeds of up to 2.1ms-1 after 6h of simulation. In
the upper part of slope 2 and above the main ridge updrafts form due to
converging upslope winds blowing from both sides of the mountain
(Fig. e). The convergence zones lead to mean vertical wind
speeds of up to 1.3ms-1 and horizontal return flows towards
the foreland above the CBL1 height. Above the valley region, subsidence
exists with vertical wind speeds of approximately -0.3ms-1.
Over the foreland of the reference run, a plain-to-mountain circulation
develops, which surmounts the first ridge and converges over slope 2 with the
upslope winds.
Cross sections of tracer concentrations (color contours) after
6h of simulation for all simulations: (a) PLAIN,
(b) HMIN0, (c) HMIN0.5, (d) HMIN1, and
(e) S-RIDGE. A passive tracer has been constantly emitted over the
whole along-mountain domain within the region of -30km≤x≤0 km on the lowermost eight model levels (up to an altitude of
approximately 110 m). Mixing ratios are averaged in time and space
(along y direction), and normalized by their corresponding maximum value.
CBL heights CBL1, CBL2, CBL3, and AL are plotted as black solid, dashed,
dotted, and green solid lines, respectively (see also the legend shown in
Fig. e). Potential temperature is shown as black contour lines
(0.25K increment). Additionally, vertically integrated tracer
masses are shown for 2, 4, and 6h of simulation as dotted,
dashed, and solid lines in the bottom panels, respectively. These relative
mass values are calculated by splitting the x direction into bins of
1km and determining the percentage of total amount of tracers
within these cross-mountain intervals (% km-1).
In the second flow regime (HMIN0.5, HMIN1 Fig. b, c), the
plain-to-mountain wind penetrates down to the valley floor. Hence, it
replaces the upslope flow over slope 2 and intensifies the upslope wind over
the main ridge. The superimposed plain-to-mountain flow leads to slightly
higher wind speeds and a significantly deeper slope wind layer of up to
0.5km compared to the HMIN0 run. Furthermore, the deeper slope
wind layer prevents subsidence in the center of the valley. Due to the
absence of a convergence zone above the first ridge in the HMIN0.5 and HMIN1
simulation, updrafts and return flows only develop over the main ridge. This
leads to a single return flow above the CBL1 height towards the foreland with
wind speeds up to 2.2ms-1 (between 1.4 and
2.6km), whereas in the reference run (HMIN0), two nearly separated
return flows develop over the foreland with wind speeds less than
1.9ms-1 (between 1.4 and 1.8km, and between
2.1 and 2.5km).
In the S-RIDGE simulation, an upslope wind layer superposed by the
plain-to-mountain wind develops with wind speeds up to
2.4ms-1 and a layer depth of approximately 400m.
The return flow towards the foreland is divided into two clearly separated
wind layers: an upper one above crest height (between 2.2 and
2.9km), which is deeper and has stronger winds (up to
1.4ms-1), and a lower one, which is located slightly above
the CBL1 height with wind speeds below 0.6ms-1.
The two different flow regimes are also visible in vertical profiles of mean
cross-mountain winds at the middle of the slopes (Fig. ).
Shown are profiles for the reference run (HMIN0) and for HMIN0.5 as
a representative for the simulations with elevated valleys. After
2h of simulation, upslope winds of up to 1.7ms-1
have established in both simulations over all slopes. The depth of the slope
wind layer is shallower over slope 3 (Fig. c) than over
slope 1 and 2 (Fig. a, b). 's
analytical slope-wind model predicts shallower
slope winds for steeper slopes and higher static stability of the background
atmosphere. This is in agreement with our simulations in which the background
stability and the slope angle are higher over the slope of the main ridge
than over the slopes of the first ridge. In HMIN0.5, after 4 h of
simulation, the plain-to-mountain flow overruns the first peak, accelerates
over slope 2 and finally reaches the elevated valley floor. The downslope
flow has a speed of about 3.8ms-1 and a depth of
approximately 500m (Fig. b). In the reference run,
however, the upslope wind regime persists throughout the simulation and
hinders the plain-to-mountain wind to penetrate into the valley. The
evolution of different flow regimes was mainly caused by different
temperature structures. This is discussed in detail in
Sect. .
Temperature structure
Relative tracer mass located above (dark gray) and below (light
gray) the reference CBL height (CBL1) as a function of time. A tracer has
been constantly emitted near the surface over the half space of the mountain
range within the region of -30km≤x≤0 km (see
Fig. ). Shown are all simulations (from left to right) between
2 and 6h: PLAIN, HMIN0, HMIN0.5, HMIN1, and S-RIDGE.
In this section, differences in the temperature structure due to varying
terrain geometries are described and explained by means of differences in
heating rates. To demonstrate the evolution of the downslope wind within the
elevated valley, cross sections of potential temperature are displayed for
the HMIN0 and HMIN0.5 simulation in Fig. . After 2h in
the HMIN0.5 simulation (Fig. a), the air over the first ridge,
advected by the plain-to-mountain flow from the foreland, is potentially
cooler than the valley air and therefore able to descend into the valley. Due
to a weakening of the upslope wind over slope 2, the convergence zone is
continuously shifted towards the valley floor and the downslope flow
eventually replaces the local slope wind circulation after 4 h of
simulation (Fig. b). In the reference run after 4 h of
simulation (Fig. c), the advected air at crest height over the
first ridge has about the same potential temperature than the air in the
upslope flow advected from the valley. Due to the deeper valley in HMIN0
compared to the elevated valleys in HMIN0.5 and HMIN1, a more distinctive
upslope circulation establishes over slope 2. Both facts prevent the
plain-to-mountain wind to descend to the valley floor during the entire
simulation.
The convergence zone is characterized by two thermally driven opposing flows
that separate from the surface. Flow separation may also occur over steep
slopes for dynamical reasons without the need of a strong counter current in
the valley. This has been shown in several studies of stably stratified flows
past a valley based on idealized simulations e.g., and
laboratory experiments e.g.,. For example, a
critical valley depth may exist beyond which the valley atmosphere becomes
decoupled from the imposed background flow aloft e.g.,.
However, a more detailed study to clarify the dependence of the depth of flow
penetration into the valley as a function of the valley depth would go beyond
the scope of this paper.
Mean vertical profiles of potential temperature over the valley region are
shown for all simulations with valleys in Fig. . After
2h of simulation (Fig. a), potential temperatures
near the valley floor are approximately 1 to 2K colder in the
reference run (HMIN0) compared to the simulations with elevated valleys
(HMIN0.5, HMIN1). The mean potential temperature profile of the reference run
shows a three-layer thermal structure over the valley region with
a well-mixed layer (CBL1), a valley inversion layer and an upper weakly
stable layer . After 6h of
simulation (Fig. b), all profiles show nearly identical mean
potential temperatures with a well-mixed CBL1 up to approximately
1.8km.
As in Fig. for the (a) HMIN0, (b)
HMIN0.5, and (c) S-RIDGE simulation, but a tracer has been
constantly emitted within the region between -4km≤x≤-3km.
As in Fig. for the (a) HMIN0 and (b)
HMIN0.5 simulation, but a tracer has been constantly emitted at the foot of
the mountain range between -23km≤x≤-22km.
Relative tracer mass located left (light gray) and right (dark gray)
of the first ridge (x=-13.9km) as a function of time.
A tracer has been constantly emitted at the foot of the mountain range
(-23km≤x≤-22 km, see Fig. ). Shown are
the simulations HMIN0, HMIN0.5, HMIN1, and S-RIDGE between 2 and
6h of simulation.
To investigate the reason for these different potential temperature profiles,
density-weighted and volume-averaged heating rates are computed for the
largest (HMIN0) and the smallest valley volume (HMIN1) according to the
method of . Both control volumes extend from the first to
the main ridge and from the surface to an altitude of 2.1km. In
Fig. , the evolution of all heat budget components is
shown, where the total tendency (TOT) is equal to the sum of the
contributions due to the surface sensible heat flux (SHF), the mean flow
advection (ADV), and the turbulent heat exchange between the valley volume
and the free atmosphere (TRB). Due to the flux computation method used in
this study, which involves averaging in time, no heating rates could be
calculated before 1.5h of simulation. Nevertheless, potential
temperature profiles indicate that in the early phase (before 2h)
the heating is stronger for smaller valley volumes than for larger ones (cf.
HMIN1 and HMIN0 in Fig. a). The result is in agreement with
the concept of the valley-volume effect which states that for a given amount
of energy input, the heating rate is stronger the smaller the volume
e.g.,. This explains why the heating rate contribution
from the surface sensible heat flux (SHF) is permanently higher in the
simulation with smaller valley volume (HMIN1) compared to the reference run
with larger valley volume (HMIN0, cf. Fig. ), although
the surface sensible heat flux itself is the same in both simulations.
Figure shows that the surface sensible heat flux is the
main heating source of the valley atmosphere in both simulations, whereas
mean-flow advection (ADV) cools the valley volume, and the turbulent
contributions (TRB) are negligible. In contrast to the early phase, the total
heating rate (TOT) of the HMIN1 simulation is smaller than of the HMIN0 run
after about 1.5h (Fig. ). The reason is that
the plain-to-mountain flow enters the control volume of the HMIN1 run and
leads to a much stronger cold-air advection (ADV) than in HMIN0.
Consequently, advection overcompensates the volume effect. This striking
heating pattern leads to the almost same potential temperatures in the CBL
until the end of all simulations (see Fig. b), despite the
different valley volumes.
Pollution distribution
By means of tracer analyses, the impact of varying terrain geometries on
daytime pollution distribution over a mountain range compared to the one over
a flat plain is described in this section. Here, we focus on the interaction
between the plain-to-mountain flow and the slope wind system which affects
the vertical distribution of pollutants. The focus of the next section,
Sect. , is on the impact of the valley floor height on processes
of pollution transport over complex terrain.
In the first step, a passive tracer is constantly emitted at the surface over
the half space of the mountain range within the region of -30km≤x≤0 km (see Sect. ). Figure shows
cross sections of normalized tracer mixing ratios, and the AL and CBL heights
for all simulations after 6h of integration. The mixing ratio has
been normalized by its maximum value occurring in the shown domain at the
given time. Additionally, vertically integrated tracer masses are shown for
2, 4, and 6h of simulation. In the PLAIN simulation
(Fig. a), the turbulent transport results in a nearly
homogeneous distribution of tracer particles inside the CBL up the EL.
The CBL1 height marks the top of the nearly height-constant potential
temperatures at 1.7km. The altitude of the AL height is located at
approximately 1.9km and lies between the heights of the CBL2 and
CBL3. The almost identical CBL and AL heights over the plain qualitatively
confirm results of . The vertically integrated tracer
mass is homogeneously distributed with approximately
3.3%km-1. This results in slightly less than
100% tracer mass when integrating between -30km≤x≤0 km, as a small part of tracer mass is horizontally transported
out of this subdomain due to turbulent diffusion. In the reference run
(Fig. b), tracer particles are advected towards both ridges by
upslope winds. After 6h of simulation, concentration maxima exist
in regions of updrafts over slope 2 (-13km≤x≤-11 km) and in the upper part of slope 3 (-1km≤x≤-0 km). Therefore, the largest tracer masses are found with up to
5.9%km-1 over the valley region after 6h
of simulation. The AL and CBL heights over the foreland are in all
simulations similar to the ones in the plain simulation. Over the valley
region of the reference run (-9km≤x≤-3 km), the AL
height is considerably higher (up to 0.8km for CBL1) than the CBL
heights. In the HMIN0.5 (Fig. c) and HMIN1 (Fig. d)
run, the superimposed plain-to-mountain flow leads to a less complex tracer
distribution than in the HMIN0 case with a rather continuous horizontal
increase in tracer mass towards the main ridge. In the region x<-8 km, the AL heights are considerably higher (up to 0.9km
for CBL1) than the CBL heights. As in the reference run, this implies
a tracer transport towards higher altitudes than the temperature-based CBL
heights. In the S-RIDGE simulation a second tracer maximum above crest height
exists at approximately 2.5km. The total horizontal mass flux of
tracer particles in the return flow above the CBL is only sightly higher in
the S-RIDGE run than in the other simulations (not shown) and, hence, cannot
explain the formation of the elevated layer of tracers in S-RIDGE. However,
the center of the return flow is located about 500m higher in
S-RIDGE which favors the formation of a pollution layer at this height
compared to the other runs (cf. Figs. and ).
Generally, similar elevated pollution maxima were modeled by
and elevated moist layers downstream of mountain ridges
related to advective venting were observed by .
These results corroborate the concept of an additional transport between the
CBL and the free atmosphere over complex terrain in comparison to a pure
convective exchange process . The CBL heights show a more
terrain-following behavior than the AL height for all simulations except for
the HMIN0 run. In that simulation, the different CBL heights are nearly
horizontal over the valley region as a result of a strong updraft over
slope 2 (cf. Sect. ). Nevertheless, the CBL heights are still
lower than the AL height. The comparison of the present results with those of
, who used the same CBL height definition as our CBL2,
shows similar differences between the AL and CBL2 heights (up to
0.4km) for various terrain geometries.
The topographically induced tracer transport in relation to the PLAIN
simulation is quantified in Fig. . In the CBL over a flat
plain, the only process to transport pollutants into the free atmosphere is
turbulent mixing in the EL. Therefore, in the PLAIN simulation nearly all of the
tracer particles (up to 85%) stay below the CBL1 height
throughout the entire simulation. In contrast to the PLAIN run, approximately
40% of tracer mass is located above the CBL1 height after
2h in the simulations with mountains. Until the end of the
simulation, the vertical transport beyond the CBL1 height increases up to
50% for the HMIN1 case and up to 55% for the S-RIDGE
simulation. In the reference run, the relative tracer mass above the CBL1
height compared to the relative tracer mass within the CBL slightly decreases
to 35% until the simulation end. This decrease in relative tracer
mass above the CBL1 height is due to the fact that the constant tracer source
at the surface is stronger than the vertical tracer transport through the CBL
top. In summary, topographically induced vertical tracer transport from the
surface to the free atmosphere can be up to 2.5 to 3.7 times larger than
pure turbulent exchange over a flat plain. Similar results were found for the
vertical transport out of a valley in the real-case study of
and in the idealized modeling study of
. Repeating the same analysis of tracer exchange for the
CBL3 as a reference height instead of CBL1 leads to the same qualitative
results. However, in terms of quantitative exchange, the vertical transport is
three times (5.5 to 10.3) higher for CBL3 than for CBL1. This result
demonstrates the strong sensitivity of the magnitude of the vertical exchange
on the definition of the CBL height.
Pollution transport processes
This section focuses on the impact of embedded valleys and varying valley
floor heights on different transport mechanisms, such as mountain venting in
updrafts and advective venting by horizontal return flows. To isolate
individual horizontal and vertical transport processes, a passive tracer is
constantly emitted within three different subdomains: over the slope within
the mountain range, at the foot of the mountain range, and over the valley
floor, respectively.
As in Fig. for the (a) HMIN0 and (b)
HMIN0.5 simulation, but a tracer has been constantly emitted at the valley
floor between -8km≤x≤-7km.
Relative tracer mass located above (dark gray) and below (light
gray) the reference CBL height (CBL1) as a function of time. A tracer has
been constantly emitted at the valley floor (-8km≤x≤-7km, see Fig. ). Shown are all simulations with
valleys (from left to right) between 2 and 6h: HMIN0, HMIN0.5,
and HMIN1.
Conceptual diagram of the flow pattern for (a) a deep
valley (HMIN0) and (b) an elevated valley (e.g., HMIN0.5) after
6h of simulation. The black and gray solid lines mark the
temperature-based CBL and the AL height, respectively. Thick, solid arrows
represent the cross-mountain flow, and thin, solid arrows mark the turbulent
exchange in the entrainment layer over the foreland and the valley region.
Dashed, double-lined arrows indicate the vertical transport through the CBL
top as a result of horizontal flow convergence. V denotes mountain and
advective venting and B indicates flow blocking.
To study the pollution transport over a slope within the mountain range,
a passive tracer is emitted near the surface between -4km≤x≤-3 km which corresponds to the center of the slope 3 in the
simulations with valleys. Figure shows the vertical transport
between the CBL and the free atmosphere over the main ridge for the reference
run (HMIN0) and for HMIN0.5, and compares it to the vertical transport over
the upper part of the single ridge (S-RIDGE). In all three simulations,
tracers are transported within the slope wind layer towards the mountain peak
and within the updrafts to the free troposphere. From there, they are
captured by the horizontal return flow and are transported towards the
foreland. In the simulations with valleys, the rather strong vertical
updrafts transport most of the tracers vertically through the CBL top
(Fig. a, b). Therefore, according to the definition of
, mainly mountain venting occurs in these
simulations. Closer inspections (not shown) of the flow structure indicate,
that in the S-RIDGE simulation, both mountain and advective venting occur to
the same extent (cf. Figs. and c).
As previously noticed, difference in the return flow structure (cf.
Fig. ) cause different patterns of horizontal tracer transport
from the main ridge towards the foreland (Fig. ). In the HMIN0
simulation (Fig. a), the additional venting process over slope 2
prevents a horizontal transport of pollutants from the main ridge towards the
foreland beyond the valley region. Due to the absence of updrafts over the
smaller ridge in the HMIN0.5 simulation (Fig. b), the tracers
are transported by the more homogeneous return flow almost twice the
horizontal distance towards the foreland compared to the HMIN0 run. In the
S-RIDGE simulation (Fig. c), a distinct return flow develops,
which extends approximately 500m higher up to about 3km
than in the other simulations. This leads to the previously mentioned
elevated tracer layer shown in Fig. . These different
distribution patterns are also represented in the vertically integrated
tracer masses. At the end of the simulation, the integrated tracer mass in
the HMIN0.5 and S-RIDGE is more evenly distributed between -20km≤x≤0 km and -30km≤x≤0 km,
respectively, whereas in the HMIN0 run a non-uniform tracer distribution
remains with a mass maximum over the valley region.
To investigate the pollution transport from the foreland towards the mountain
crest, a passive tracer is emitted at the foot of the mountain range between
-23km≤x≤-22 km, which is shown for the HMIN0 and
HMIN0.5 simulation in Fig. . Until the end of the HMIN0
simulation (Fig. a), tracer particles are transported
horizontally by the plain-to-mountain flow up to the convergence zone in the
upper part of slope 2 (x≃-12 km). From there, particles are
transported to higher altitudes within the updraft. Apart from this
pronounced and stationary updraft, moving thermals distribute the tracers
relatively homogeneously in the vertical up to the CBL1 height. In contrast
to the reference run, the tracer particles in the HMIN0.5 simulation are
transported horizontally up to the main ridge (x=0km) until
the end of the simulation (Fig. b).
The different transport patterns are quantified in Fig. for
all mountain simulations. Shown are the relative tracer masses, which are
located on the left- and right-hand side of the first ridge (x=-13.9km) as a function of time. For purposes of comparison, the
relative mass transport to the left and right of x=-13.9 km is also
shown for the S-RIDGE simulation. In the reference run, less than
30% of the emitted tracers are transported to the right side of
the first ridge until the end of the simulation. In the HMIN0.5 and HMIN1
simulations, approximately 50% of the tracer mass is located
right of the first ridge after 6h. The reason for these different
transport patterns is the upslope wind along the second slope
(-13.9km≤x≤-7.5km) in the HMIN0 simulation,
which opposes the plain-to-mountain wind and therefore acts as an effective
“barrier” between the foreland and the main ridge (cf.
Fig. ). This blocking of the plain-to-mountain flow persists
during the entire simulation and allows only little tracer transport towards
the main ridge. In the simulations with elevated valleys, the
plain-to-mountain flow eliminates the opposing upslope winds and enhances the
horizontal tracer transport to the main ridge compared to the reference run.
In the HMIN1 simulation the plain-to-mountain flow penetrates towards the
valley floor earlier than in the HMIN0.5 run. Therefore, the horizontal
transport in the HMIN1 run is significantly faster than in the HMIN0.5 run.
In the S-RIDGE simulation, a similar horizontal tracer transport develops as
in the HMIN0.5 and HMIN1 runs. However, due to the more homogeneous upslope
flow in the S-RIDGE simulation, the tracer transport is less variable and,
hence, leads to a rather continuous increase in time in tracer mass towards
the main ridge.
To study the pollution transport within a mountain valley, a passive tracer
is emitted at the valley floor between -8km≤x≤-7 km, which is shown in Fig. for the HMIN0 and HMIN0.5
simulation. Due to the existence of the typical slope wind system within the
valley in the reference run (Fig. a), subsidence above the
valley center mainly limits the tracer transport to the valley region and
most tracer particles remain below the CBL1 height during the whole
simulation. In the HMIN0.5 run (Fig. b), tracers are transported
by the superimposed plain-to-mountain wind towards the main peak and within
the updraft to the free troposphere. From there, the tracer is transported by
the return flow towards the foreland.
The vertical part of this transport by mountain and advective venting is
quantified for all simulations with valleys in Fig. . After
2h, the turbulent transport by convection is the dominant process
for the tracer distribution and barely 20 to 25% of the tracer
mass is mixed beyond the CBL1 height. After 3h in the HMIN1 and
5h in the HMIN0.5 simulation, the distribution pattern changes due
to the additional tracer transport by the plain-to-mountain wind within the
valley. Therefore, until the end of the simulations with elevated valleys
(HMIN0.5, HMIN1), up to 60% of the tracer particles are advected
beyond the CBL1 height. However, in the reference run only 30% of
the emitted tracer mass is located above the CBL1 height due to subsidence in
the valley center and a missing superimposed cross-mountain flow. Comparing
tracer emissions within different cross-mountain subdomains (e.g.,
Figs. and ), reveals that in all simulations with
valleys mountain and advective venting occurs; but whether pollutants emitted
at the valley floor are transported out of the valley depends on the
interactions between the plain-to-mountain and the slope wind systems.
Conclusions
In this study we performed idealized LES with the WRF model to investigate
the interaction between plain-to-mountain and slope wind systems, and their
influence on daytime pollution distribution over complex terrain. Simulations
over a mountain range with embedded valleys bordered by ridges with different crest heights were compared to simulations with a single ridge and a flat plain by means of tracer analyses.
These analyses show differences in thermally driven flows and
resultant pollution transport dependent on the valley floor heights. To
illustrate the observed two main flow patterns, a conceptual diagram is shown
in Fig. . In the situation of a deep valley (reference run
HMIN0, Fig. a), the upslope wind system within the valley
opposes the plain-to-mountain wind and therefore acts as an effective
“barrier” between the foreland and the main ridge. In the situation of
a shallow, elevated valley (e.g., HMIN0.5, Fig. b), the
plain-to-mountain flow passes the crest of the first (smaller) ridge,
descends into the potentially warmer valley, and eventually replaces the
opposing upslope wind. These two differing flow structures lead to different
transport patterns. In the reference run, less than 30% of tracer
particles emitted over the foreland are advected beyond the first ridge
towards the main ridge until the end of the simulation. However, in the
simulations with elevated valleys, the relative tracer mass located on the
right-hand side of the first ridge is similar to that of a simulation with
a single ridge and amounts to approximately 50%.
The simulation results show that mountain and advective venting are important
mechanisms of pollution transport from the surface to the free atmosphere in
addition to the turbulent exchange by convection. Pollutants are transported
within the slope wind layers towards the mountain ridges, and within the
vertical updrafts above the CBL height. From there, the pollutants are
captured by the horizontal return flow and are advected towards the foreland.
The determination whether mountain or advective venting occurs strongly
depends on the reference surface through which the transport is assessed. It
also depends on which part of the updraft is considered (the center or the
outflow region). The simulations show that independent of this detail, the
exchange by venting, be it mountain or advective venting, is caused by the
same stationary updraft as a result of horizontal flow convergence over the
ridges. Therefore, we suggest that at least for purely thermally driven winds
without a large-scale flow no distinction between mountain and advective
venting is needed, as already done, e.g., in . In
the simulations with elevated valleys, the plain-to-mountain flow covers the
whole mountain range and therefore prevents the development of venting over
the first ridge.
The detected AL and CBL heights are in line with the results obtained by
. Over the flat plain, the spread between the temperature-based CBL heights and the AL height is rather small. However, over complex
terrain, the CBL heights are up to 0.9km lower and rather
terrain-following than the AL height. In the present simulations, the
mountain induced vertical transport beyond the CBL1 height is up to 3.6 times
larger than pure turbulent exchange over a flat plain. Even though the
quantification of the vertical exchange strongly depends on the definition of
the CBL, the significant transport beyond the CBL1 height in the present
simulations demonstrates the need to consider the AL height rather than
temperature-based CBL heights as the relevant parameter for air pollution
studies over mountainous terrain.
The results of this study extend those of , and
confirm that the terrain geometry has a large impact on the flow structure
and the resultant transport processes over a mountain range. The change of
the flow regime due to minor changes in the topography demonstrates the
necessity to account for these topographically induced effects in future
boundary layer parameterization schemes. Furthermore, the findings confirm
a mountain-induced vertical transport of pollutants beyond the temperature-based CBL height and therefore imply a reconsideration of the conventional
CBL height detection methods over mountainous terrain. However, to generalize
present findings, further investigations with inhomogeneous land-use
properties, time and space dependent surface forcings, and varying
atmospheric background conditions will be necessary.
Acknowledgements
This work was supported by the Austrian Science Fund (FWF) under grant
P23918-N21 and by the Austrian Federal Ministry of Science Research and Economy (BMWF) as part of the
Uni-Infrastrukturprogramm of the Research Platform Scientific Computing
at the University of Innsbruck. We greatly appreciate the comments of two anonymous reviewers,
which have considerably improved the paper.Edited by: W. Birmili
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