WESWind Energy ScienceWESWind Energ. Sci.2366-7451Copernicus PublicationsGöttingen, Germany10.5194/wes-2-35-2017A methodology for the design and testing of atmospheric boundary
layer models for wind energy applicationsSanz RodrigoJavierjsrodrigo@cener.comhttps://orcid.org/0000-0003-0291-6429ChurchfieldMatthewKosovicBrankohttps://orcid.org/0000-0002-1746-0746Wind Energy department, National Renewable Energy Centre (CENER),
Sarriguren, 31621, SpainNational Wind Technology Center, National Renewable Energy Laboratory
(NREL), Golden, 80401 CO, USAResearch Applications Laboratory, National Center for Atmospheric
Research (NCAR), Boulder, 80307 CO, USAJavier Sanz Rodrigo (jsrodrigo@cener.com)9February201721355427July201619August201622December20166January2017This 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://wes.copernicus.org/articles/2/35/2017/wes-2-35-2017.htmlThe full text article is available as a PDF file from https://wes.copernicus.org/articles/2/35/2017/wes-2-35-2017.pdf
The GEWEX Atmospheric Boundary Layer Studies (GABLS) 1, 2 and 3 are used to
develop a methodology for the design and testing of Reynolds-averaged
Navier–Stokes (RANS) atmospheric boundary layer (ABL) models for wind energy
applications. The first two GABLS cases are based on idealized boundary
conditions and are suitable for verification purposes by comparing with
results from higher-fidelity models based on large-eddy simulation. Results
from three single-column RANS models, of 1st, 1.5th and 2nd turbulence
closure order, show high consistency in predicting the mean flow. The third
GABLS case is suitable for the study of these ABL models under realistic
forcing such that validation versus observations from the Cabauw
meteorological tower are possible. The case consists on a diurnal cycle that
leads to a nocturnal low-level jet and addresses fundamental questions
related to the definition of the large-scale forcing, the interaction of the
ABL with the surface and the evaluation of model results with observations.
The simulations are evaluated in terms of surface-layer fluxes and wind
energy quantities of interest: rotor equivalent wind speed, hub-height wind
direction, wind speed shear and wind direction veer. The characterization of
mesoscale forcing is based on spatially and temporally averaged momentum
budget terms from Weather Research and Forecasting (WRF) simulations. These
mesoscale tendencies are used to drive single-column models, which were
verified previously in the first two GABLS cases, to first demonstrate that
they can produce similar wind profile characteristics to the WRF simulations
even though the physics are more simplified. The added value of incorporating
different forcing mechanisms into microscale models is quantified by
systematically removing forcing terms in the momentum and heat equations.
This mesoscale-to-microscale modeling approach is affected, to a large
extent, by the input uncertainties of the mesoscale tendencies. Deviations
from the profile observations are reduced by introducing observational
nudging based on measurements that are typically available from wind energy
campaigns. This allows the discussion of the added value of using remote
sensing instruments versus tower measurements in the assessment of wind
profiles for tall wind turbines reaching heights of 200 m.
Introduction
Wind energy flow models are progressively incorporating more realistic
atmospheric physics in order to improve the simulation capacity of wind
turbine and wind farm design tools. Wind resource assessment and wind turbine
site suitability tools, dealing with the microscale flow around and within a
wind farm, have been traditionally based on site measurements and microscale
flow models relying on Monin–Obukhov similarity
theory (MOST; Monin and Obukhov,
1954) that assume steady-state and are typically applied in neutral
atmospheric conditions. At larger scales (than microscale), the long-term
wind climatology is typically determined from a combination of historical
measurements and simulations from mesoscale meteorological models at a
horizontal resolution of a few kilometers. The transition from mesoscale to
microscale to come up with a unified model chain is the main challenge at
stake for the next generation of wind assessment tools. In order to make this
possible, microscale models have to extend their range to simulate the entire
atmospheric boundary layer (ABL) and include relevant physics like Coriolis
as well as realistic large-scale forcing and appropriate turbulent scaling,
dependent on thermal stratification, from the surface layer to the free
atmosphere. The dynamics of these forcings determine the interplay between
the wind climatology, relevant for the assessment of the wind resource, and
the wind conditions relevant for wind turbine siting. Sanz Rodrigo et
al. (2016) reviews the state-of-the-art wind farm flow modeling,
methodologies and challenges for mesoscale–microscale coupling.
The design of ABL models for wind energy requires a systematic approach to
verification and validation in order to demonstrate consistency of the
computational code with the conceptual physical model and to quantifying
deviations with respect to the real world (Sanz Rodrigo et al., 2016). The
verification process is carried out using idealized test cases where the
solution is known from theory or from a higher-fidelity model (code-to-code
comparison). Sensitivity analysis in idealized conditions also helps
determine which are the main drivers of the model, which directly affect
the quantities of interest, and anticipate their main sources of
uncertainty. Validation, however, deals with code-to-observation
comparison to quantify the accuracy of the model at representing the real
world in terms of the application of interest. From the wind energy
perspective, the quantities of interest are the wind conditions that are
directly related to the production of energy and the design characteristics
of wind turbines.
The GEWEX Atmospheric Boundary Layer Studies (GABLS) were developed by the
atmospheric boundary layer community to benchmark single-column models, used
by meteorological models to parameterize the ABL (Holtslag et al., 2013).
While the cases are all based on observations of the ABL in relatively
stationary and horizontally homogeneous conditions, it is notoriously
difficult to define validation cases due to the interplay of a large number
of physical processes that can modify these relatively simple conditions.
Hence, the first two GABLS benchmarks used idealized conditions in order to
analyze the turbulent structure of the ABL without the influence of the
variability of the external large-scale forcing. GABLS1 simulated a quasi-steady
stable boundary layer resulting from 9 h of uniform surface cooling (Cuxart
et al., 2006). GABLS2 simulated a diurnal cycle, still with uniform
geostrophic forcing, by simplifying measurements from the CASES-99 experiment
in Kansas (Svensson et al., 2011). Under this idealized forcing, large-eddy
simulation (LES) models have shown high consistency at predicting the ABL
behavior (Beare et al., 2006). Therefore, they have been used to verify
reduced-order models based on Reynolds-averaged Navier–Stokes (RANS)
turbulence modeling. Hence, GABLS 1 and 2 are suitable verification cases for
demonstrating the simulation capacity of ABL models for incorporating thermal
stratification into turbulence modeling under uniform large-scale forcing and
using prescribed surface boundary conditions.
GABLS1 showed that many boundary layer parameterizations tend to overestimate
the turbulent mixing in stable conditions, leading to a too-deep
boundary layer compared to LES simulations (Cuxart et al., 2006). GABLS2
showed the difficulties of comparing observations with simulations under
idealized forcing and prescribed surface temperature. Holtslag et al. (2007)
showed that during stable conditions there is strong coupling between the
geostrophic wind speed and the surface temperature. Hence, prescribing the
surface temperature inhibits the interaction of the boundary layer with the
surface, which, for instance, results in large differences in the 2 m
temperature predicted by the models.
The challenges of the first two GABLS exercises inspired the setup of GABLS3,
which deals with a real diurnal case with a strong nocturnal low-level jet
(LLJ) at the Cabauw meteorological tower in the Netherlands (Baas et
al., 2009; Holtslag, 2014; Basu et al., 2011; Bosveld et al., 2014a). Here,
large-scale forcing is not constant throughout the diurnal cycle but depends
on time and height. Instead of prescribing the surface temperature, models
are allowed to make use of their land surface schemes in order to include the
dependencies between the ABL and the land surface models. The large-scale
forcing is prescribed based on piece-wise linear approximations of the real
forcing, derived from simulations with the Regional Atmospheric Climate Model
(RACMO) mesoscale
model and adjusted to match the observed surface geostrophic wind and the
wind speed at 200 m. These approximations are introduced to limit the impact
of the uncertainties associated with mesoscale geostrophic and advection
forcing.
Based on the GABLS benchmark series, the challenges of stable boundary layers
and diurnal cycles are reviewed by Holtslag et al. (2013): notably, the
relation between enhanced mixing in operational weather models performance,
the role of land surface heterogeneity in the coupling with the atmosphere,
the development of LES models with interactive land surface schemes, the
characterization of a climatology of boundary layer parameters (stability
classes, boundary layer depth and surface fluxes), and the development of
parameterizations for the very stable boundary layer when turbulence is not
the dominant driver. These challenges are also shared by wind energy
applications. Therefore, it is relevant to study the GABLS3 case within the
wind energy context as a validation case with focus on rotor-based quantities
of interest.
Revisiting GABLS3 for wind energy also means adopting a more pragmatic
approach when it comes to adding physical complexity. In the context of
developing a mesoscale-to-microscale model, it is important to identify which
are the first-order physics that need to be incorporated to improve
performance compared to current practices in the wind industry. For instance,
adding thermal effects on turbulence modeling is important compared to the
traditional hypothesis of neutral stratification, while the effects of
humidity may be initially neglected.
Reducing model-chain uncertainties by using on-site observations is also
particularly appealing for wind energy since it is standard practice to have
profile measurements at the site. Since these measurements are typically
affected by site effects, we propose introducing corrections at the microscale
level based on profile nudging. Hence, contrary to the original GABLS3
setup, for the sake of a more generalized mesoscale-to-microscale
methodology, we propose using the large-scale tendencies computed by a
mesoscale model as driving forces at microscale without introducing any
correction based on measurements. Then, at microscale, the simulation can be
dynamically relaxed to the profile observations to correct the hour-to-hour
bias. This is also a more natural way of dealing with the wind energy
model chain using an asynchronous coupling methodology where (1) a database
of input forcings is generated offline by a mesoscale model (in the context
of a regional wind atlas for instance), (2) site effects are simulated by a
microscale ABL model forced by these mesoscale inputs and introducing a high-resolution topographic model, and (3) deviations of the model with respect to
a reference observational site are corrected to remove the bias generated
throughout the downscaling process. It is important to note that strict
validation shall not include site observations to be able to quantify the
impact of the limited knowledge of the model. The final bias-correction step
allows the calibration of the model to reduce the bias and provide a more accurate
wind assessment in the application context. Quantifying the correction
introduced by the nudging terms in the modeling equations and their relative
weight with respect to the other terms can also be used to assess the
limitations of the model.
The methodology used by Bosveld et al. (2014a) to characterize large-scale
forcing from mesoscale simulations will be adopted here using simulations
from the Weather Research and Forecasting (WRF) model. At microscale, we use
a single-column model with three RANS turbulence closure schemes of 1st,
1.5th and 2nd order. This model chain was also used by Baas et al. (2009) to
design the GABLS3 case and perform a sensitivity analysis of various
single column model (SCM) settings. Following a similar philosophy, we evaluate
the impact of different mesoscale forcing terms and bias-correction
strategies on wind energy quantities of interest.
Models
We follow the same modeling approach used by Baas et al. (2010) to define a
microscale atmospheric boundary layer model driven by realistic mesoscale
forcing. This one-way meso–micro methodology allows the coupling of the models
offline, facilitating the generalization of the downscaling methodology to
any combination of mesoscale and microscale models working asynchronously.
The RANS equations in natural Cartesian coordinates (x→ north,
y→ east, z→ vertical) for the horizontal wind components
U and V are
1fc∂U∂t=-1fcU∂U∂x+V∂U∂y+W∂U∂z+V-Vg-1fc∂uw∂z1fc∂V∂t=-1fcU∂V∂x+V∂V∂y+W∂V∂z-U+Ug-1fc∂vw∂z,
where fc is the Coriolis parameter, W is the vertical wind
component, Ug and Vg are the components of the
geostrophic wind, and uw and vw are the kinematic horizontal turbulent
fluxes for momentum based on the fluctuations about the mean velocity
components u, v, and w. For convenience, all the components of
the RANS equations were divided by fc to define the
equations as the balance of different wind speed vectors:
Utend=Uadv+Ucor+Upg+UpblVtend=Vadv+Vcor+Vpg+Vpbl,
where Utend and Vtend are the tendencies of the wind
components, Uadv and Vadv are the advection wind
components, Ucor=V and Vcor=-U are
the Coriolis wind components, Upg=-Vg and
Vpg=Ug are the pressure gradient wind components,
and Upbl and Vpbl are the turbulent diffusion wind
components (equivalent to the so-called planetary-boundary layer (PBL) scheme
in mesoscale models). In a meso–micro offline coupled model, the RANS
equations are solved using mesoscale forcing as source terms in the
microscale model. In horizontally homogeneous conditions
1fc∂U∂t=Uadv+V+Upg-1fc∂uw∂z+Unud1fc∂V∂t=Vadv-U+Vpg-1fc∂vw∂z+Vnud,
where the advection and pressure gradient wind components are derived from
mesoscale simulations and vary with the time t and the height above
ground level z. Bias-correction nudging terms, Unud and
Vnud, were also incorporated to assimilate profile
observations available from a reference measurement campaign. Observational
nudging (or Newtonian relaxation) based on Stauffer and Seaman (1990) is
defined as
δnud=ωzfcδobs-δτnud,
where δnud is either Unud or Vnud,
δobs and δ are the corresponding observed and
simulated quantities, and τnud is the nudging timescale.
ωz is a weight function that is equal to 1 within the vertical
range of the observations, z1 < z < z2,
and it decreases linearly from 1 to 0 in the range
z2 < z< 2z2 and 0 elsewhere. Since the
nudging term is an artificial forcing, it should not be dominant compared to
the other terms in Eq. (3). Hence, it should be scaled by the time constant
τnud of the order of the slowest physical process of the ABL,
which, for a diurnal cycle, is the inertial oscillation introduced by the
Coriolis term. Hence,
τnud should be of the order of 1/fc. In
general τnud is typically between 103 and 104 s in
meteorological systems (Stauffer and Seaman, 1990).
Similar to the momentum equations, the energy equation in the absence of
radiative and phase-change heat transfer effects relates the tendency of
potential temperature with the mesoscale advective temperature
(Θadv), the diffusion and the nudging (Θnud)
terms.
∂Θ∂t=Θadv-∂wθ∂z+Θnud,
where wθ is the kinematic heat flux and Θnud is
defined in Eq. (3).
The diffusion terms in Eqs. (1), (3) and (5) are simulated assuming an
isotropic eddy viscosity that relates turbulent fluxes with the gradients of
mean flow quantities:
uw=Km∂U∂z;vw=Km∂V∂z;wθ=Kmσt∂V∂z,
where the Prandtl number σt is assumed to be equal to 1. The eddy
viscosity Km is equivalent to the product of a mixing length
and velocity scales. Three turbulent closures will be used in this paper: 1st
order, based on an analytical function of the mixing length and a velocity
scale based on the strain rate (S-l) (Sanz Rodrigo and Anderson, 2013);
1.5th order, based on the same mixing length function and a velocity scale
based on a transport equation of the turbulent kinetic energy (k-l)
(Sanz Rodrigo and Anderson, 2013); and 2nd order, based on two transport
equations for the turbulent dissipation rate and the turbulent kinetic energy
(k-ε) (Sogachev et al., 2012; Koblitz et al., 2013).
The S-l turbulence model assumes a semiempirical analytical
expression for the turbulent mixing length lm:
lm=κzφmζ+κzλ,
and scales the mixing velocity with the strain rate to obtain the eddy
viscosity:
Km=lm2∂U∂z2+∂V∂z21/2,
where κ= 0.41 is the von Kármán constant, λ= 0.00037
Sg0/|fc| is the maximum mixing length in neutral conditions,
proportional to the surface pressure gradient (Blackadar, 1962).
φm is an empirical function that depends on the local
stability parameter ζ=z/L based on the Obukhov length L.
Functional relationships from Dyer (1974) are commonly used:
φmζ=1-5ζ-1/4ζ<01+5ζζ≥0.
Transport equations for the turbulent kinetic energy k and dissipation
rate ε are
∂k∂t=P+B-ε+∂∂zKmσk∂k∂z,∂ε∂t=εkCε1∗P-Cε2ε+Cε3B+∂∂zKmσε∂ε∂z,
where σk and σε are the Schmidt numbers for
k and ε, P and B are the rate of shear and buoyancy
production of k, and Cε2 and Cε3 are
model coefficients.
Then, the eddy viscosity is defined as
Km=lmk1/2Cμ1/4
for the k-l model and
Km=Cμ1/4lmk1/2=Cμk2ε
for the k-ε model, where Cμ is a coefficient equal to
the square of the ratio of the shear stress and k in equilibrium.
Sogachev et al. (2012) define a modified Cε1 coefficient as
follows:
Cε1∗=Cε1+(Cε2-Cε1)lmlmax,
with a length-scale limiter following Mellor and Yamada (1974):
lmax=Cλ∫0∞zk1/2dz∫0∞k1/2dz,
where Cλ= 0.075 in order to obtain Blackadar's lmax=λ in neutral conditions, consistent with Apsley and
Castro (1997). Sogachev et al. (2012) introduce a rather complex additional
diffusion term in the Eq. (11) to make the k-ε model
equivalent to a k-ω model. For simplicity, this term is not
included here.
In neutral conditions, a relationship amongst k-ε
coefficients is prescribed to obtain consistency with well-established log
profiles in surface-layer neutral conditions (Richards and Hoxey, 1993):
σε=κ2Cμ1/2(Cε2-Cε1).
In non-neutral conditions, Sogachev et al. (2012) introduce a Cε3 coefficient that depends on the local stability conditions:
Cε3=(Cε1-Cε2)αB+1,
with
αB=1-lm/lmaxifRi>01-1+Cε2-1/Cε2-Cε1lm/lmaxifRi<0,
where Ri=B/P is the local gradient Richardson number. With the
relationships of Eqs. (16) and (17), the following set of model coefficients
are used: Cε1= 1.52, Cε2= 1.833,
σk= 2.95,
σε= 2.95 and Cμ= 0.03.
GABLS1 (a) and GABLS2 (b) time series of boundary
layer height hτ and surface-layer friction velocity u×0,
kinematic heat flux wΘ0, Obukhov length L0, and stability
parameter z/L0. Comparison between SCM simulations using three
turbulent closures (S-l, k-l and k-ε) and the k-l
model of Weng and Taylor (2006), SCM simulations of Svensson et al. (2011),
and LES simulations of Beare et al. (2006) and Kumar et al. (2010).
Surface boundary conditions are defined based on MOST using the simulated
surface-layer friction velocity u∗0 and heat flux
wθ0. The potential temperature at the surface
Θ0 is either prescribed or inferred from the 2 m
temperature Θ2:
Θ0=Θ2-θ∗0κlg2z0t+Ψh2L0,withθ∗0=-wθ0u∗0,
where a thermal roughness length z0t=z0/100 (Bosveld et al.,
2014a) and Dyer's integral form of the stability function for heat
ψh(ζ) are adopted.
The GABLS1 case setup is described in Cuxart et al. (2006), based on LES
simulations presented by Kosovic and Curry (2000), where the boundary layer
is driven by a prescribed uniform geostrophic wind and surface cooling rate
over a horizontally homogeneous ice surface. The following initial and
boundary conditions are used: fc= 1.39 × 10-4 s-1, Ug= 8 m s-1,
Vg= 0 and
Θ0= 265 K for the first 100 m and then increasing
at Γ= 0.01 K m-1; k= 0.4(1-z/250)3 m2 s-2 for the first 250 m with a minimum value of
10-9 m2 s-2 above. The surface temperature
Θ0 starts at 265 K and decreases at a cooling rate of
0.25 K h-1. The roughness length for momentum and heat is set to
z0= 0.1 m.
Single-column model simulations are run for 9 h using a 1 km high
log-linear grid of 301 points and a time step of 1 s (Sanz Rodrigo and
Anderson, 2013). Figure 1 (left) shows surface fluxes and boundary layer
height, based on shear stress, for the three turbulence models and compared
with the k-l model of Weng and Taylor (2006) and LES simulations from
Beare et al. (2006). Figure 2 shows the quasi-steady profiles resulting at
the end of the 9 h cooling. The three models are consistent with the
reference simulations. While the S-l and k-l models produce almost
identical results, the k-ε model produces slightly smaller
surface momentum flux leading to a slightly lower boundary layer height.
Nevertheless, the differences are small.
GABLS1 quasi-steady vertical profiles of horizontal wind speed S= (U2+V2)1/2, potential temperature Θ, shear
stress τ and kinematic heat flux wΘ. Comparison between SCM
simulations using three turbulent closures (S-l, k-l and
k-ε) and the k-l model of Weng and Taylor (2006) and the
LES simulations of Beare et al. (2006).
A sensitivity analysis of quasi-steady ABL profiles is shown in Fig. 3,
following the same simulation approach as GABLS1 and varying the surface
cooling rate CR and the geostrophic wind Sg. In order to use
a more representative wind energy context, the inputs correspond to the
Fino-1 offshore site conditions, with fc= 1.2 × 10-4 s-1 and Γ= 0.001 K m-1.
The roughness length is proportional to the square of the surface friction
velocity through the Charnock relation (Charnock, 1955), calibrated for
Fino-1 conditions in Sanz Rodrigo (2011), with z0= 0.0002 m being a
representative value. Contours of quantities of interest are presented at a
reference “hub height” of 70 m and a reference “rotor range” between 33
and 90 m. The stability parameter z/L at the reference height is also
plotted following the stability classes defined in Sanz Rodrigo et
al. (2015), where sonic measurements of the at Fino-1 show a stability range
at 80 m from ζ=-2 to ζ=2. In unstable conditions the boundary
layer height is of the order of 1 km and the reference wind speed is almost
independent of the cooling rate. Turbulence decreases and wind shear
increases as neutral conditions are approached. In stable conditions the
boundary layer height is of the order of a few hundred meters and the wind
conditions are more strongly correlated to the local stability parameter. In
very stable conditions turbulence is low and a LLJ develops with high shear.
Sensitivity analysis of quasi-steady profiles at different cooling rates
CR and geostrophic wind speed Sg in offshore conditions
(z0∼ 0.0002 m) with an inversion lapse rate of
Γ=1 K km-1. All simulations based on the GABLS1
setup of 9 h uniform surface cooling, averaged over the last hour to
obtain the quasi-steady profiles. Power-law shear exponent based on 33 and
90 m levels. Atmospheric stability based on the local Obukhov parameter
ζ=z/L at a reference height of 70 m. Stability levels according
to Sanz Rodrigo et al. (2014): near neutral (white): 0<ζ<0.02, weakly stable: 0.02<ζ<0.2, stable
0.2<ζ<0.6, very stable 0.6<ζ<2, extremely stable ζ>2 (symmetric range in
unstable conditions in red).
It is important to note that the quasi-steady profiles resulting from the
sensitivity analysis almost never happen in real conditions. They are
canonical cases that help us parameterize the ABL without dynamical effects
so that we can more easily study the relationship between the main drivers
of the ABL. In real conditions, the ABL is a transient phenomena that not
only depends on the actual boundary conditions but also on the hours to days
of history leading to them.
GABLS2: Idealized diurnal cycle
While the second GABLS exercise was more strongly based on observations from
the CASES-99 experiment in Kansas, from the ABL forcing perspective it can
still be regarded as idealized. The case corresponds to 2 consecutive
clear and dry days with a strong diurnal cycle. Since the focus of the study
was the intercomparison of boundary layer schemes, the forcing conditions
were simplified to facilitate the comparison among the various turbulent
closures rather than an assessment of their accuracy against the actual
observations.
The case setup and model intercomparison is described in Svensson et
al. (2011). The boundary conditions are prescribed in terms of a uniform
geostrophic wind of Sg= 9.5 m s-1 and a prescribed
surface temperature derived from observations. The roughness lengths are set
to z0= 0.03 m and z0t=z0/10. A small subsidence
linearly increasing with height up to -0.005 m s-1 at 1000 m is
also introduced but it will be neglected here for simplicity. For the same
reason, humidity will not be modeled here since its effect on wind profiles
is not significant. Initial profiles are defined at 16:00 LT of the
22 October 1999 and the simulation runs for 59 h. The target evaluation day
in the GABLS2 benchmark was the 23 October. This leaves only 8 h of spin-up
time before the target day for the models to reach equilibrium with the
initial conditions. Koblitz et al. (2013) indicate that this short spin-up
period is not enough for the diurnal cycle to reach equilibrium with the
boundary conditions. An alternative approach is to run a periodic diurnal
cycle for several days until equilibrium is reached, i.e., 2 consecutive
days show the same diurnal cycle. This cyclic approach is also followed here
based on the 48 h period of surface temperature shown in Fig. 4. After five
cycles, the maximum difference in potential temperature with the forth cycle
is 0.2 K and the velocity field is in equilibrium. A 4 km log-linear grid
of 301 points is used with a time step of 1 s.
GABLS2 surface temperature profile (Svensson et al., 2011) and
alternative 48 h periodic cycle used to obtain a diurnal cycle independent
of initial conditions.
GABLS2 time–height contour plots of wind velocity S (top raw),
turbulent kinetic energy k (middle) and potential temperature Θ
(bottom) for the SCM simulation based on S-l (first column), k-l
(second) and k-ε (third) turbulence closure after five cyclic
simulations.
Figure 1 (right) shows the surface fluxes and stability parameter of the
three turbulence models compared with the SCM results of the GABLS2 model
intercomparison of Svensson et al. (2011) and the LES results of Kumar et
al. (2010). The three models are within the scatter of the SCM reference
results and close to the LES results. Compared to the LES simulations, the
k-ε model overpredicts the heat flux in unstable conditions
and in stable conditions over the second night. Figure 5 shows time–height
contour plots of mean velocity, turbulent kinetic energy and potential
temperature for the three models. As the closure order is increased, higher
turbulent kinetic energy is observed. Higher mixing during diurnal unstable
conditions results in a faster evening transition to nocturnal stable
conditions and a higher LLJ, i.e., lower wind shear in the rotor area.
ValidationGABLS3: Real diurnal cycle
The GABLS3 setup is described in Bosveld et al. (2014a). The case analyzes
the period from 12:00 UTC 1 July to 12:00 UTC 2 July 2006 at the Cabauw
Experimental Site for Atmospheric Research (CESAR), located in the
Netherlands (51.971∘ N, 4.927∘ E), with a distance of
50 km to the North Sea in the WNW direction (van Ulden and Wieringa, 1996).
The elevation of the site is approximately -0.7 m, surrounded by
relatively flat terrain characterized by grassland, fields and some scattered
tree lines and villages (Fig. 6). The mesoscale roughness length for the
sector of interest (60–120∘) is 15 cm.
Roughness map for a 30 × 30 km area centered at the Cabauw
site. Grassland (green) dominates the surface conditions with local values of
the roughness length of around 3 cm. For the 60–120∘ sector of
interest, the mesoscale roughness length is around 15 cm, characteristic of
scattered rough terrain (Verkaik and Holtslag, 2007). This value is also
found in the default land use model of WRF, based on the US Geological Survey
(USGS, 2011). Figure reprinted from KNMI's Hydra Project website (KNMI,
2016).
Time–height contour plots of the longitudinal wind component U and
momentum budget terms: Utend=Uadv+Ucor+Upg+Upbl from the WRF–YSU
simulation.
The CESAR measurements are carried out at a 200 m tower, free of obstacles
up to a few hundred meters in all directions. The measurements include
10 min averaged vertical profiles of wind speed, wind direction, temperature
and humidity at heights 10, 20, 40, 80, 140 and 200 m, as well as surface
radiation and energy budgets. Turbulence fluxes are also monitored at four
heights: 3, 60, 100 and 180 m. A RASS profiler measures wind speed, wind
direction and virtual temperature above 200 m.
The selection criteria for GABLS3 consisted of the following filters applied
to a database of 6 years (2001–2006): stationary synoptic conditions, clear
skies (net long-wave cooling > 30 W m-2 at night), no fog,
moderate geostrophic winds (5 to 10 m s-1, with less than
3 m s-1 variation at night) and small thermal advective tendencies.
Out of the nine diurnal cycles resulting from this filtering process, the one
that seemed more suitable was finally selected: 12:00 UTC 1 July to
12:00 UTC 2 July 2006.
Mesoscale forcing from WRF
Mesoscale forcing is derived from simulations with the Advanced Research
Weather Forecasting model (WRF), version 3.8 (Skamarock et al., 2008).
Kleczek et al. (2014) made a sensitivity study of WRF for different grid
setups, boundary layer schemes, boundary conditions and spin-up time.
Reasonably good results of the vertical wind profile in stable conditions (at
midnight) are obtained, although the dependency on the PBL scheme and grid
setup is important.
Mesoscale simulations are reproduced here using the same domain setup used as
reference by Kleczek et al. based on three concentric square domains centered
at the Cabauw site. The model is driven by 6-hourly ERA Interim reanalysis
data from ECMWF (European Centre for Medium-Range Weather Forecasts), which
come at a resolution of approximately 80 km. Three domains, all with
183 × 183 grid points, are nested at horizontal resolutions of 9, 3
and 1 km. The vertical grid, approximately 13 km high, is based on 46
terrain-following (eta) levels with 24 levels in the first 1000 m, the first
level at approximately 13 m, a uniform spacing of 25 m over the first
300 m and then stretched to a uniform resolution of 600 m in the upper
part. The US Geological Survey (USGS) land use surface data, which come by
default with the WRF model, are used together with the unified Noah land
surface model to define the boundary conditions at the surface. Other
physical parameterizations used are the rapid radiative transfer model
(RRTM), the Dudhia radiation scheme and the Yonsei University (YSU)
first-order PBL scheme. The WRF setup follows the reference configuration of
Kleczek et al. except for the input data (Kleczek et al. uses ECMWF
analysis), the horizontal resolution (Kleczek et al. use 27, 9 and 3 km) and
the vertical grid (Kleczek et al. use 34 levels, 15 in the lowest 1000 m).
Differences in the grid settings are due to a further study with additional
nested domains with large-eddy simulation to study turbulent processes in the
ABL. Following Kletzeck et al. we use a spin-up time of 24 h, i.e., the
model is initialized 1 day before the target evaluation day in order to allow
enough time to develop mesoscale processes in equilibrium with the initial
and boundary conditions of the reanalysis data.
To derive mesoscale forcing, the momentum budget components (also called
tendencies) are directly extracted from WRF since they are computed by the
solver (Lehner, 2012). Curvature, due to the curvilinear coordinate system in
WRF, and horizontal diffusion tendencies were neglected since they are
comparatively small with respect to the other terms of the momentum budget.
Figure 7 shows contour plots of the longitudinal wind component and the
momentum budget terms of Eq. (2). These quantities have been spatially and
temporally averaged to filter out microscale fluctuations. The spatial filter
is based on 4 × 4 grid points surrounding the site from the second
WRF domain, which defines a typical size of a microscale domain
(Lavg= 9 km square box). A centered rolling average of
tavg= 60 min is also applied in order to remove high-frequency fluctuations in the lower part of the boundary layer.
Magnitude S and direction WD of the wind vector, pressure
gradient, advective and nudging forcing vertically averaged over a rotor span
between 40 and 200 m. Sensitivities to spatial averaging Lavg
and nudging timescale τnud.
Figure 8 shows the effect of Lavg on the mesoscale forcing,
vertically averaged over a 40–200 m layer, which is approximately the span
of a large wind turbine of 8 MW (diameter D= 160 m, hub height
zhub= 120 m). If site-interpolated values are used
(Lavg= 0 km), large fluctuations can be observed in the
mesoscale forcing during convective conditions at the beginning of the cycle.
Here, the fluctuations are filtered out when a spatial averaging of
Lavg= 9 km is introduced, which indicates that the scale of
these disturbances is smaller than this size. Extending the spatial averaging
to Lavg= 30 km does not show significant variations with
respect to the 9 km case. It is interesting to note that even though the
mean wind speed profiles do not show any dependency on the spatial averaging,
and one could conclude that horizontally homogeneous conditions prevail,
there is a quite significant spatial variability of mesoscale forcing within
the averaging box.
The derived mesoscale forcing is consistent with that obtained by Bosveld et
al. (2014a), based on simulations with the RACMO model at a horizontal
resolution of 18 km. Advection tendencies show narrower peaks compared to
those from Bosveld et al. (2014a). It is difficult to say where these
differences come from since we used different input data and horizontal
and temporal resolutions. In order to facilitate the implementation and
interpretation of the mesoscale forcing in the GABLS3 SCM intercomparison,
simplified mesoscale forcing was defined by adjusting piecewise linear
approximations of the RACMO tendencies to obtain a reasonable agreement of
the wind speed at 200 m.
Despite the filtering process, the resulting smooth fields in Fig. 7
still show large mesoscale disturbances in the advective tendencies,
especially during nighttime conditions at greater heights where vertical
diffusion is low. The geostrophic wind is more uniform, showing some decrease
in intensity with height (baroclinicity). At rotor level (Fig. 8) the
pressure gradient force is quite stationary throughout the whole cycle, with a
sudden change of 50∘ in wind direction happening a midnight. The
advective wind speed peaks at this time, reaching similar values to the
geostrophic wind. Interestingly, the advective wind direction makes a
360∘ turn throughout the cycle, although at relatively small
advection speed.
The dynamical origin of the nocturnal low-level jet was originally described
by Blackadar (1957) as an inertial oscillation that develops in flat terrain
due to rapid stabilization of the ABL during the evening transition under
relatively dry and cloud-free conditions (see also Baas et al., 2011; van de
Wiel et al., 2010). The daytime equilibrium of pressure gradient, Coriolis
and frictional forces is followed by a sudden decrease in vertical mixing due
to radiative cooling during the evening transition. This results in an
imbalance of forces. The residual mixed layer in the upper part of the ABL is
decoupled from the surface and the Coriolis force induces an oscillation in
the wind vector around the geostrophic wind, producing an acceleration of the
upper air that is manifested as a low-level jet at relatively low heights.
At Cabauw this happens 20 % of the nights, with jet heights between 140
and 260 m and jet speeds of 6–10 m s-1 (Baas et al., 2009).
: Time–height contour plots of wind velocity S (top raw), wind
direction WD (middle) and potential temperature Θ (bottom) for the
WRF simulation (first column), SCM simulation based on WRF mesoscale forcing
and k-ε turbulence closure without (second) and with (third)
velocity nudging between 40 and 200 m, and observations (fourth). A
reference rotor span (40–200 m) is delimited by the dashed lines.
Quantities of interest
Revisiting the GABLS3 in wind energy terms means evaluating the performance
of the models with application-specific quantities of interest. These
quantities are evaluated across a reference rotor span of 160 m, between 40
and 200 m, characteristic of an 8 MW large wind turbine. Aside from hub-height
wind speed Shub and direction WDhub, it is relevant
to consider the rotor equivalent wind speed REWS, the turbulence intensity
(not evaluated here), the wind speed shear
α, and the wind direction shear or veer ψ.
The rotor equivalent wind speed is specially suitable for accounting for wind
shear in wind turbine power performance tests (Wagner et al., 2014). The
REWS is the wind speed corresponding to the kinetic energy flux through the
swept rotor area, when accounting for the vertical shear:
REWS=1A∑iAiSi3cosβi1/3,
where A is the rotor area and Ai are the horizontal segments that
separate vertical measurement points of horizontal wind speed Si
across the rotor plane. The REWS is weighted here by the cosine of the
angle βi of the wind direction WDi with respect to the
hub-height wind direction to account for the effect of wind veer.
Wind shear is defined by fitting a power-law curve across the rotor wind
speed points Si:
Si=Shubzizhubα.
Similarly, wind veer is defined as the slope ψ of the linear
fit of the wind direction difference with respect to hub height:
βi=ψWDi-WDhub.
In order to evaluate simulations and measurements consistently, these
quantities are obtained by linear interpolation, velocity
and wind direction vertical profiles at 10 points across the rotor area after resampling and
then computing the REWS and the shear functional fits. While these fitting
functions are commonly used in wind energy, their suitability in LLJ
conditions is questionable. The regression coefficient from the fitting can
be used to determine this suitability.
Metrics
Validation results can be quantified based on the mean absolute error MAE
metric:
MAE=1N∑i=1Nχpred-χobs,
where χ is any of the abovementioned quantities of interest,
predicted (pred) or observed (obs), and N is the number of samples
evaluated in the time series.
It is important to note that the errors computed here are particular for this
diurnal cycle test case and cannot be associated with the general accuracy of
the SCM in other situations. It is more important to discuss the results in
relative terms to explain, for instance, the impact of adding modeling
complexity as we go from idealized to more realistic forcing. Then, if a
simulation is used as a reference to quantify this relative improvement, it
is convenient to use a normalized MAE (NMAE) by dividing with respect to the MAE
of the reference simulation:
NMAE=MAEMAEref.
Results
Table 1 shows a list of the simulations performed with the single-column
model using different settings in terms of surface boundary conditions and
mesoscale forcing. The SCM simulations have been run with the same grid setup
of GABLS2, i.e., 4 km long log-linear grid with 301 levels and a time step
of 1 s. The simulations are grouped according to different model evaluation
objectives as described in the last column of Table 1. Table 2 shows the
MAE and normalized MAE, with respect to the reference k-ε
SCM simulation (ke_T2: tendencies from WRF, no nudging, surface
boundary conditions based on prescribed WRF 2 m temperature) for the
rotor-based quantities integrated throughout the diurnal cycle. Time series
of surface fluxes are plotted in Fig. 11 and quantities of interest in
Fig. 12. ERA-Interim and WRF
simulations are included in the plots in order to show how the mesoscale
model transforms the inputs from the reanalysis data and then is used as
input to the microscale model simulations in the meso–micro model chain. As
we did with the mesoscale forcing, a centered rolling average of 60 min is
applied to simulations and observations in order to have all the quantities
evaluated in a common time frame.
List of simulations and objectives for the sensitivity analysis of
single-column models.
Turb.Surface BC1Forcing2ObjectivesWRF–YSUYSUNoahERA InterimDemonstrateconsistency of onlineke_T2 (reference)k-εWRF T2WRF tendencies(WRF) vs. asynchronousmeso–micro couplingSl_T2S-lWRF T2WRF tendenciesEvaluate the choice ofturbulent closure withkl_T2k-lWRF T2WRF tendenciesrealistic forcingke_T2wtk-εWRF T2 and wθ0WRF tendenciesQuantify the impact ofthe choice of surfaceke_Tskk-εWRF Θ0WRF tendenciesboundary conditions onke_T2obsk-εObserved T2WRF tendenciesfluxes and quantitiesof interestnoTadvk-εWRF T2Without Θadv tendencyQuantify the relativeimportance ofnoTadvUadvk-εWRF T2Without advection tendenciesmesoscale tendencies onnoTadvUadv_Sg0k-εWRF T2Only surface pressure gradientquantities of interestUVTnud80k-εObserved T2U,V: 10–80 m; Θ: 2–80 m; τnud=60 minAssess bias correctionUVTnud120k-εObserved T2U,V: 10–120 m; Θ: 2–120 m; τnud= 60 minnudging method usingUVTnud200k-εObserved T2U,V: 10–200 m; Θ: 2–200 m; τnud= 60 mintypical wind energyUVTnud200_tau10k-εObserved T2U,V: 10–200 m; Θ: 2–200 m; τnud= 10 minmast configurationsUVnud400k-εWRF T2U,V: 40–400 m, τnud=60 minAssess bias correctionUVnud200k-εWRF T2U,V: 40–200 m, τnud= 60 minnudging method usingUVnud200_tau30k-εWRF T2U,V: 40–200 m, τnud= 30 mintypical wind energyUVnud200_tau10k-εWRF T2U,V: 40–200 m, τnud= 10 minlidar configurations
1 All based on Monin–Obukhov land surface model. 2 All use the same WRF tendencies, adding nudging or modified tendencies as indicated.
MAE and normalized MAE with respect to the reference k-ε SCM
simulation.
Time–height contour plots of wind velocity S (top raw), wind
direction WD (middle) and potential temperature Θ (bottom) for four
k-ε SCM simulations: with all the forcing terms (first
column), without Θadv (second), without Θadv, Uadv, and Vadv (third), and without
advection, and assuming that the geostrophic wind only varies with time
following the surface pressure gradient Sg0 (fourth).
Consistency of mesoscale tendencies and nudging
bias-correction methods from a model-chain perspective
Figure 9 shows time–height contour plots of wind velocity, wind direction
and potential temperature for the WRF simulation, the reference SCM simulation
without nudging (ke_T2) and with wind speed nudging between 40 and
200 m (UVnud200_tau10), and the observations. The reference rotor
span, between 40 and 200 m, is delimited with dashed lines. By comparing the
first two columns in Fig. 9 we can see that the SCM shows similar structure
to the mesoscale model even though more simplified physics is used. In terms
of REWS, the MAE due to offline coupling is only 4 % of the error of
the WRF model itself (Table 2). This confirms the consistency of the
asynchronous coupling methodology based on mesoscale tendencies. Compared to
observations, we can distinguish a LLJ of longer duration in the simulations
than in the models; the simulations show a double peak while observations
show a more distinct velocity maxima. The evening and morning transitions are
more gradual in the mesoscale model than in the observations.
At the rotor area, the peak of the REWS is well predicted by both the
mesoscale and the ke_T2 SCM, while they both tend to overpredict in
the convective and transitional parts of the cycle (Fig. 12). The LLJ lives
longer in the simulations than in the observations. This is attributed to an
incorrect timing of the advection tendencies. Switching off these tendencies
in the SCM sifts the LLJ peak of wind speed and direction 3 h ahead. Wind
shear is not predicted well by the models. The reanalysis data predict
surprisingly well the wind shear, but due to the very coarse vertical
resolution of the data, this is considered an artefact from the linear
interpolation. Wind veer suffers the consequences of the phase error in the
wind direction, underpredicting the maximum wind veer. Wind direction is
reasonably well predicted by the reanalysis input data, with a ramp starting
at 18:00 UTC 1 July and peaking at 06:00 UTC 2 July. However, the mesoscale
model presents a sudden change around midnight, which is apparent in both the
pressure gradient and advective forcing in Fig. 8, and it results in a broader
wind direction peak. This peak has larger amplitude and shorter duration in
the observations. The potential temperature fields are also reasonably well
characterized by the input data during daytime conditions. At night the
cooling is underpredicted by the reanalysis data but overpredicted by the
mesoscale model (Fig. 11).
By introducing profile nudging, these deviations are corrected to a large
extent in the lower part of the ABL. Since the weighting function of the
nudging terms ωz decays linearly up to 400 m we can see how the
bias correction is gradually introduced and the simulation is not affected by
nudging in the upper levels (Fig. 9). In terms of NMAE, using velocity
profile nudging leads to error reductions of up to 80 % in the REWS
with respect to the reference simulation (no nudging). A more detailed
assessment of profile nudging for different measurement strategies is
discussed later.
Choice of turbulence closure
The k-ε closure is chosen as reference with respect to the
other turbulence models because it is expected to be more generally
applicable in heterogeneous terrain conditions, where the mixing length is
modeled through the ε equation. In the GABLS2 case we could see
some differences between the three models in the prediction of turbulent
kinetic energy when simulating the CASES-99 diurnal case. Here, we quantify
the impact of the choice of turbulence model on the quantities of interest by
using the same boundary conditions and mesoscale forcing. The S-l and
k-l models are almost equivalent but show around 30 % higher MAE than
the k-ε model. Some improvement, of the order of 10 %, is
observed for lower-order models in the hub-height wind direction and wind
veer, but this does not compensate the error increase of 20 % in
hub-height wind speed and 40 % in wind shear.
Choice of surface boundary conditions
The third objective in the model evaluation strategy of Table 1 is to
determine if there is a choice of boundary condition for the energy equation
that is more adequate in the prediction of quantities of interest. Basu et
al. (2008) demonstrated using MOST arguments that using a prescribed surface
heat flux as a boundary condition in stable conditions should be avoided. MOST
is imposed at the surface by prescribing the mesoscale 2 m temperature
(ke_T2), the 2 m temperature and surface heat flux
(ke_T2wt) or the surface skin temperature (ke-Tsk).
Figure 11 shows time series of surface-layer fluxes (at 3 m height) and 2 m
temperature along the diurnal cycle. A large bias was observed in the 2 m
temperature of the WRF simulation, which was also found in the GABLS3 model
intercomparison (Bosveld et al., 2014b) and WRF sensitivity study of Kleczek
et al. (2014). Using the WRF skin temperature instead of the 2 m temperature
is equivalent in terms of predicting the surface-layer fluxes. This is not a
surprise since the Noah land surface model in WRF is also based on MOST
surface-layer parameterization and the roughness lengths in WRF and SCM
simulations are the same. However, in terms of REWS, using skin temperature
instead of 2 m temperature results in a 15 % increase in the MAE. Adding
the WRF heat flux as an additional prescribed quantity also has no effect on
the surface fluxes and little impact on the quantities of interest.
Interestingly enough, prescribing the observed 2 m temperature instead of
the mesoscale 2 m temperature results in a 23 % increase in REWS MAE.
This is due to a mismatch between the surface (observed) and top (simulated)
boundary conditions, which leads to a less accurate prediction of potential
temperature gradients throughout the ABL. In effect, despite the large
bias in the prediction of the potential temperature, the mesoscale simulation
still does a good job of simulating the diurnal evolution of vertical
potential temperature gradients, which are ultimately the main feedback in
the simulation of the wind speed fields via the buoyancy term in the
turbulence equations. Then, using the mesoscale 2 m temperature as indirect
surface boundary condition seems to be the most appropriate choice. This is a
standard output in meteorological models and surface stations; therefore, it makes
sense to use it for practical reasons and as a standard in wind energy
campaigns and flow models.
Time series of surface-layer characteristics using different surface
boundary conditions for potential temperature with the k-ε
model and compared with ERA Interim input data, mesoscale model simulation
and observations.
GABLS3 time series of rotor-based quantities of interest from top
to bottom: rotor equivalent wind speed REWS, hub-height wind direction
WDhub, wind shear α and wind veer ψ. Sensitivity of
the k-ε SCM to different nudging strategies, as per Table 1,
assimilating wind speed observations “UV” (left), wind speed and air
temperature observations “UVT” (right), and comparison with the reference SCM
(without nudging, ke_T2), the WRF simulation, the ERA Interim input data and
the observations.
Added value of more realistic forcing
Adding mesoscale tendencies to microscale ABL simulations requires the
generation of tendencies from a mesoscale model. The question is how
important these tendencies are in the assessment of quantities of interest.
This is the fourth objective in the model evaluation strategy of Table 1. The
modulation of the LLJ evolution by the mesoscale tendencies in the GABLS3
episode is discussed by Baas et al. (2010) and Bosveld et al. (2014a). They
use a SCM to switch on and off different forcing mechanisms and show their
relative impact on the evolution of the LLJ. Figure 10 shows time–height
plots of different SCM simulations: with all mesoscale tendencies included
(T2_ke), without
Θadv (noTadv), without Θadv, Uadv, and Vadv (noTadvUadv),
and without advection tendencies, and assuming that the geostrophic wind only
varies with time following the surface pressure gradient
(noTadvUadv_Sg0). The next step in terms of simplifying the forcing
would be to impose a uniform geostrophic wind throughout the entire episode,
which is the idealized setup of GABLS2.
In the first 100 m above the ground, where turbulence diffusion is
important, advection tendencies are relatively small and using surface
geostrophic forcing provides a realistic evolution of the diurnal cycle.
Above 100 m advective tendencies become a dominant force in the modulation
of the equilibrium between Coriolis and pressure gradient forces. If only
surface geostrophic forcing is applied at greater heights, the wind speed and
direction are way off. In terms of the REWS NMAE, removing potential
temperature tendencies does not have a significant impact, while additionally
removing momentum tendencies results in a 24 % increase in error. Using
just the surface geostrophic wind as forcing increases the error by an
additional 100 %. Hence, realistic forcing requires the characterization
of the horizontal pressure gradient variations with time and height as the main
drivers. Then, even though advection tendencies come with high uncertainty,
introducing mesoscale momentum advection still results in significant
improvement. Potential temperature advection in this case shows some
improvement in the wind direction and wind shear, but this is compensated for with
a deterioration of wind speed and wind veer; therefore, the overall impact on REWS
is not significant.
Assessment of bias correction for different profile nudging
strategies
In homogeneous terrain conditions, such as those of the GABLS3 case, we
should not expect improvements when using the offline meso–micro simulations
with a RANS model with respect to online mesoscale simulations with a
boundary layer scheme since the surface conditions have not changed and the
turbulence models are similar. Instead, by using the same surface conditions,
we demonstrated that using mesoscale tendencies was an effective solution to
drive a microscale ABL model offline without introducing significant
additional uncertainties due to the coupling between the models. It is also
not surprising to find large errors in the WRF model hour to hour, sometimes
even larger than in the reanalysis input data, since the higher resolution of
the model brings additional variability that is physically realistic but
is not necessarily well represented by the models (Baas et al., 2010; Bosveld
et al., 2014). In aggregated terms, it has been demonstrated that adding
mesoscale-generated advection tendencies was beneficial for the SCM
simulations, even though their hourly contribution was not obvious due
to phase errors for instance. A way of improving the transient behavior
of the microscale model is to introduce bias correction through nudging.
Here, we explore the profile nudging method of Eq. (4), which depends on the
timescale τnud and the range and type of observations
assimilated in the simulations.
Two scenarios of nudging are considered in Table 1, making use of the Cabauw
instrumentation as a proxy for typical setups that could be used in the wind
energy context. The first scenario corresponds to mast-based instrumentation
where we can routinely measure and assimilate in the model wind speed and
temperature. By convention, temperature measurements start at 2 m and wind
speed measurements at 10 m. Then, the mast height is varied from 80 m
(ke_T2obs_UVTnud80) to 200 m. Since temperature nudging starts at
2 m, the observed 2 m temperature is prescribed in the surface boundary
condition. By default, the nudging timescale is set to 1 h. In terms of
REWS, using nudging with an 80 m mast does not improve the aggregated
error for a large rotor in the range of 40–200 m. Using 120 or 200 m results
in improvements of 12 and 50 %, respectively. If the timescale is reduced
to 10 min, a much stronger correction is introduced every time step and the
REWS error decreases to almost 90 %.
The second scenario corresponds to a lidar setup whose range typically
starts from 40 m and goes up to 200–400 m. Here, only wind speed profiles
are assimilated. Again, considering a default nudging timescale of 1 h, an improvement of 53 and 58 %
is observed when assimilating data up to
200 and 400 m, respectively. Measuring above the rotor range has
little benefit in this case. Comparing the two scenarios, mast or lidar, for a nudging
range up to 200 m, it is observed that the main advantage of assimilating
potential temperature profiles is in improving the wind shear and veer
predictions. This is also observed at shorter nudging timescales,
particularly during the morning transition (Fig. 12). Figure 8 shows the
magnitude and direction of the nudging correction, vertically averaged over
the rotor range and compared to the other forcing terms. Using a nudging
timescale of 60 min results in corrections of less than 1 m s-1,
which are comparatively small with respect to the pressure gradient forcing at around
8 m s-1. This correction increases occasionally to up to
2 m s-1 for a timescale of 30 min and up to 4 m s-1 for a
timescale of 10 min. The direction of the nudging term shows how the
correction mainly follows the advection forcing, which comes with higher
uncertainty than the pressure gradient force.
Vertical profiles of horizontal wind speed S and wind direction WD
at 2 July 2006 00:00:00 (a) and 06:00:00 (b) using
different nudging strategies as per Table 1 and compared with the reference
SCM (without nudging, ke_T2), the WRF simulation, the ERA Interim input data
and the observations.
Figure 13 shows the vertical wind profiles of horizontal wind speed and wind
direction at midnight and during the morning transition. At midnight, the WRF
model performs reasonably well at developing the nocturnal LLJ and the
nudging corrections mainly affect the wind direction profile. In
contrast, the morning transition is not well captured by the model and large
nudging corrections are needed in both wind speed and direction. In both
cases, the transition at 400 m between the corrected and
uncorrected parts of the profile is apparent. Using a linear decaying weight of the
nudging correction above 200 m produces a reasonably smooth transition.
Discussion and conclusions
The series of GABLS test cases for the evaluation of ABL models have been
used for the design of a single-column model that uses realistic forcing by
means of mesoscale tendencies and nudging at microscale. The model includes
three different turbulent closures that produce consistent results in the
idealized cases GABLS cases 1 and 2. A sensitivity analysis of quasi-steady
simulations following the GABLS 1 approach shows how the wind conditions at
rotor heights are correlated mostly with the geostrophic wind in unstable
conditions and with the local atmospheric stability in stable conditions.
The main difference between the models in the GABLS 2 diurnal case resides
in a larger turbulent kinetic energy as the order of the closure model is
increased.
The GABLS3 diurnal cycle case has been revisited and evaluated in terms of
wind energy specific metrics. Instead of using the adjusted mesoscale
tendencies of the original GABLS3 setup, the mesoscale tendencies computed by
WRF are directly used to force the SCM. Momentum budget analysis shows the
relative importance of the different forcing terms in the momentum equations.
Through spatial and temporal averaging, the high-frequency fluctuations due
to microscale effects are filtered out. Compared to the WRF simulation, we use mesoscale tendencies to drive SCM simulations, resulting in consistent flow fields despite the more simplified physics of the ABL.
Using sensitivity analysis on the mesoscale tendencies, it is shown that the
main driver of the ABL is the time- and height-dependent horizontal pressure
gradient. Advection terms come with high uncertainties and hour to hour they
can lead to large errors. Nevertheless, their impact in terms of aggregated errors in quantities
of interest is positive.
The k-ε model of Sogachev et al. (2012) presents better
performance than the lower-order turbulence closure models. Considering
surface boundary conditions for the potential temperature equation,
prescribing the surface temperature by indirectly introducing the WRF 2 m
temperature with MOST is more adequate than using the skin temperature or the
observed 2 m temperature.
Instead of adjusting at mesoscale, corrections are introduced at microscale
through observational profile nudging to make use of the routine
measurements collected in wind energy campaigns. Mast-based and lidar-based
profiler setups are compared to show the added value of measuring at
greater heights than the hub height, which is the main advantage of lidar systems.
Sensitivity to the nudging timescale is large, especially to compensate
errors introduced by the mesoscale advection forcing.
The GABLS cases show the complexity of interpreting mesoscale forcing. While
the pressure gradient force is dominated by large scales and is
reasonably well captured in the reanalysis data, advection tendencies depend
on the physical parameterizations of the mesoscale model. Baas et al. (2010)
presented an alternative case based on the ensemble averaging of nine diurnal
cycles that meet the GABLS3 selection criteria. This composite case, like the
presented GABLS3 case, is entirely based on forcing from a mesoscale model,
and facilitates the assessment of the main features of the diurnal cycle by
canceling out the mesoscale disturbances of the individual days. As a
result, the composite case shows great improvement versus considering any
single day separately. Hence, the assessment of mesoscale to microscale
methodologies is more appropriate in a climatological rather than a deterministic
sense. Otherwise, dynamical corrections like profile nudging would be
required.
SCM simulations over horizontally homogeneous terrain are a convenient
methodology for the design of ABL models given their simpler code
implementation and interpretation of results compared to a three-dimensional setting in
heterogeneous conditions. This allows testing surface boundary conditions,
turbulence models and large-scale forcings more efficiently before
implementing them in a three-dimensional microscale model. In a three-dimensional model, advection would be
solved by the model through surface heterogeneities and velocity gradients
across the lateral boundaries. Spatially averaged, height- and time-dependent
mesoscale forcing from horizontal pressure gradients could be introduced as a
column body force throughout the three-dimensional domain similar to how it was done in
GABLS3. By spatial averaging over a larger scale than the microscale domain,
we expect to filter out disturbances in the pressure gradient due to
unresolved topography in the mesoscale model. These topographic effects will
be modeled with a high-resolution topographic model in the three-dimensional microscale
simulation. Such a model chain would still assume that the mesoscale forcing is
horizontally homogeneous throughout the microscale domain but with changes in
height and time through source terms in the momentum equations. Nudging local
corrections would be introduced through horizontal and vertical weight
functions that limit the correction to the local vicinity of the observation
sites as it is done in mesoscale models (Stauffer and Seaman, 1990). This
relatively simple implementation of meso–micro coupling is valid for RANS and
LES models and allows easier characterization of mesoscale inputs than using
three-dimensional fields.
Data availability
The original GABLS3 input and validation data can be found on the KNMI GABLS
website (http://projects.knmi.nl/gabls/). A benchmark for wind energy
ABL models based on the KNMI dataset and mesoscale tendencies published in
this paper is available from the Windbench portal
(http://windbench.net/gabls-3).
The authors declare that they have no conflict of
interest.
Acknowledgements
This article was produced with funding from the “MesoWake” Marie Curie
International Outgoing Fellowship (FP7-PEOPLE-2013-IOF, European Commission's
grant agreement number 624562). Edited by:
J. Meyers Reviewed by: B. Holtslag and two anonymous referees
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