Introduction
In the past decade, there has been a significant increase in installed wind
power capacity in forested areas across northern Europe
. This has been made possible due to the increased hub
heights and improved technologies of modern turbines .
However, these forested sites typically represent a challenging environment
for wind turbines because of high turbulence and wind shear levels
. The forested landscape is rarely homogeneous,
containing both forest edges and roughness changes that affect shear and
turbulence and can produce sharp gradients in the flow
e.g.. This, in turn, makes the accurate siting of wind
turbines in forested areas critical. For all of these reasons, it is
important to parametrize forest effects correctly in wind models aimed at the
application of wind turbine siting. The aim of the current study is twofold:
(1) to introduce a new and automated way of using highly detailed forest
information with the WAsP method and (2) to investigate how
prediction errors change when using different maps to represent the forest.
Starting with the second aim, a short background for the research in forest
wind meteorology is given. In surface layer theory, the effect of a
homogeneous forested area on the wind speed U is parametrized through a
suitable value for the roughness length z0 as well as a displacement
height d in the well-known logarithmic wind profile:
U=u*κ[lnz-dz0-Ψm],
where u* is the friction velocity, z is the height above ground, and
Ψm represents the stability correction to the profile and depends on
z/L, where L is the Monin–Obukhov length . Based on
this equation, experimental studies on the wind profile over forested areas
typically present estimates of z0 and d as a pair
e.g.. A
dependence among measurable forest characteristics (height and density) and
z0 and d was suggested by and .
According to , a dense forest should be represented by a
relatively lower z0 and a higher d than a sparser forest with the same
tree heights. For sites without forest density information,
recommended setting z0=0.1h and d=2/3h, where h
is the tree height.
The Wind Atlas Analysis and Application program (WAsP, www.wasp.dk,
last access: 23 November 2017) method
uses a measured wind climate for the prediction of a wind
climate at another location. It is also available as a flow model
in the WindPRO software, which is developed by EMD International A/S
(www.emd.dk/windpro, last access: 12 May 2018). WAsP includes z0 in two different ways: in the absence of nearby
obstacles, the difference between the predicted and observed wind climate is
calculated through a geostrophic roughness model that uses
Eq. () in combination with the geostrophic drag law for
vertical and horizontal extrapolation. Heterogeneity in roughness is modelled
through a roughness change model, which consists of an internal
boundary layer model that is driven by lines of roughness changes on a map
. The speed-up effects due to changes in terrain height
are taken into account by a flow-over-terrain model .
Using data from small beech forests, showed that the
internal boundary layer growth closely resembled the prediction of the WAsP
roughness change model. In a later study, , it was
demonstrated that WAsP could correctly predict the wind climate at the forest
sites from observations at a nearby agricultural area, when the z0 value
was set to the values found in the surface layer studies mentioned above,
which were significantly higher than those that are typically used for forest
studies. However, these studies investigated sites with near-surface wind
observations in an open landscape with small distinct forests, which differ
greatly from the northern European sites that have recently started to be
developed for wind energy. The northern European sites have a landscape that
is dominated by forests with smaller areas of lower-roughness clearings and
lakes, leading to study areas where both the observation and predicted sites
are located in a high-roughness forested area. This study looks to determine
if the roughness map has as much impact at such sites, as was demonstrated
for the sites in .
There is currently no consensus on how to take d in
Eq. () into account in WAsP . Many
siting engineers use terrain height products from the Space Radar Topography
Mission (SRTM) to describe the orography effects, which includes the
vegetation height in the terrain height, meaning that for forested areas, the
displacement height is already included to some extent
. In , a terrain
height map that did not include the forest height was used and the
displacement height was included by adjusting the height of the wind
observations in a post-processing step. However, this post-processing
approach does not work close to forest edges since they cause the flow to
speed up similar to a terrain height escarpment . In
forested sites, measurement masts are often placed in clearings near forest
edges, suggesting that the displacement height is particularly important.
This study includes an investigation into the impact of adding d to terrain
data on model predictions.
The performance of the flow modelling depends greatly on the availability of
accurate maps of terrain height and z0. It is common for siting engineers
to use z0 maps derived from land use classifications, and many siting
tools, such as WindPRO, provide these maps for download directly in the
software. These maps are quite useful in that they can be obtained anywhere
in the world and do not require additional time to locate and implement in
the siting tool. However, because the land use categories were not developed
for wind energy applications, a specific land use class may not correspond to
a unique effect on the wind field. Additionally, neither the forest height
nor forest density are typically part of land use classifications, making it
difficult to apply the relationship suggested by , for
example,
to forested areas. This information may be found either by a site visit or
from the forest owners, but it is difficult to find consistent high-quality
information over the large areas required for wind resource assessment. This
difficulty was one of the starting points for this study and is connected
with aim (1) stated above.
An attractive solution to obtaining high-quality information about forest
characteristics can be found in the raw data from remote-sensing airborne
laser scans (ALSs) for land surface mapping . During the last
decade, ALS technology has seen a rapid expansion and ALS mapping campaigns
have been performed for entire countries e.g..
Simultaneously, the price of ALS studies has decreased, making mapping
campaigns for in-depth studies possible for both research and commercial wind
projects e.g.. The raw data from the scans are
stored in standard format, allowing siting engineers to use the same data
source for land surface description for different sites .
introduced a method that used the raw data from ALS
campaigns in canopy-resolving flow models. Here, we translate the derived
forest height from ALS data to a roughness map for use in a WAsP analysis.
The ALS-based model results are compared with model results based on standard
land use maps. The four land-use-based maps tested in this study had
different resolutions, and included a varying level of detail. To investigate
the importance of resolution, the roughness maps made from the ALS scans were
created at resolutions matching the land use models. In addition to
evaluating model performance, the different resolutions allowed for the
investigation of how WAsP handled the large number of data, with a particular
focus on retaining the speed of WAsP calculations.
This study performs validation and analysis of the model results for the
cross prediction of seven masts located in a predominantly forested area in
central Sweden. At such high latitudes, icing on cup anemometers and wind
vanes is a common problem for wind measurement . There
were periods with frozen cup anemometers and wind vanes: the process for
removal of these periods is described in Sect. . The
processing of the ALS data and their conversion to roughness length and
displacement height is presented in Sect. .
Section also contains descriptions of the land use
classification based datasets. The WAsP flow model and the cross-prediction
method used for the model assessment are then described in
Sect. . Section presents the results of the
comparison among model performance among the different roughness products.
Finally, we discuss uncertainties, opportunities, and possible improvements in
Sect. .
Wind measurements
Site and instrumentation
The site used in this study is situated on two forested ridges in central
Sweden (Fig. , left). It is located approximately 140 km from
the Baltic sea coast, approximately 3∘ below the polar circle. Within
an area of 10 × 10 km, the site had two 59 m and five 100 m tall
meteorological masts, each of which had cup anemometers and wind vanes at
several heights (Table ). The measurement periods were
different from mast to mast, but all masts were operational between
23 February 2009 and 18 February 2010. Three different types of cup
anemometers were used; NRG #40 anemometers, manufactured by NRG Systems,
Inc., were used for the profile measurements on all masts. The two 59 m
masts each had two top-mounted WindSensor (Risø) P2546A anemometers
, and the top-mounted anemometers on the 100 m masts
were Thies First Class anemometers.
Measurement period and instrumentation for each of the seven masts.
Mast no.
Meas. period
Top
Profile
Heights (m)
1
Jan 2008–Mar 2010
Risø P2546A
NRG40
59.0, 59.0, 57.0, 44.5, 31.5
2
Dec 2007–Feb 2010
Risø P2546A
NRG40
59.0, 59.0, 57.3, 44.0, 32.1
3
Nov 2008–Feb 2010
Thies First Class
NRG40
100.7, 100.7, 96.4, 80.7, 57.8
4
Feb 2009–Feb 2010
Thies First Class
NRG40
100.8, 100.8, 96.4, 80.8, 57.7
5
Feb 2009–Nov 2011
Thies First Class
NRG40
100.8, 100.8, 96.4, 80.9, 57.8
6
Feb 2009–Feb 2010
Thies First Class
NRG40
100.8, 100.8, 96.4, 80.7, 57.6
7
Feb 2009–Jun 2011
Thies First Class
NRG40
100.8, 100.8, 96.4, 80.9, 57.8
Treatment of observational wind data
An initial screening of the observed wind data (10 min averages) showed
significant inconsistencies in both wind speed and wind direction. The
erroneous data were prevalent during winter and most likely caused by ice
growth on the instruments. During most of these periods, the wind speed would
have a constant near-zero value, signifying that the cup was completely
frozen. However, there were also times when the wind speed of a particular
anemometer was much lower than expected given other wind measurements,
suggesting that the anemometer was able to turn, but at a lower rate than if
ice free. The following data screening steps were applied to clean the data
of ice-contaminated measurements.
Periods when the cup anemometer was clearly malfunctioning were
removed,
requiring that 0≤U≤50 m s-1 and Iu < 1, where U
is the wind speed and Iu=σu/U is the turbulence intensity, and
σu is the standard deviation of the wind speed.
Periods with constant wind speed were removed, requiring Ui≠Ui±1, where i denotes a 10 min block average.
Ice-affected data were removed by comparing pairs of cup anemometers in each
mast,
requiring the relative difference from at least three other anemometers on the
same mast to be within 3σ of the ice-free mean relative difference,
where the relative difference is defined as RD=(Ui-Uj)/Ui, σ is the standard deviation of RD, and the
ice-free period is defined as May to September.
Data passing these criteria were associated with a quality control (QC) value
of 1. These steps removed between 8 and 26 % of the data.
In addition to the ice-related issues, it was found that the NRG cup
anemometer wind speeds were systematically lower than the top anemometers. We
attribute this difference to both mast shadowing and a systematic small
instrumental error, possibly related to the temperature response of the
instrument. Finally, there was a slight offset between the two top
anemometers related to wind direction. To get an accurate wind profile, both
the NRG offset error and the top wind speed measurement were corrected as
follows.
Which top cup anemometer data to use was determined based on wind direction.
The expected top wind speed was calculated from the profile cups by linear
extrapolation from the two highest profile cups.
A correction factor was defined as the ratio between the actual top cup
measured wind speed and the profile estimated value for each 10 min period.
The correction factor was applied to all wind speeds in the profile.
The final data cleaning step required that all cup anemometers had
simultaneous values of QC=1 to ensure that the wind
distributions used in the cross predictions were generated from the same
period across all anemometers. After applying the filtering steps, 8764 10 min mean wind speeds were available at each height and mast, which
corresponds to approximately 1.5 months of data. The effect of the data
filtering is shown in Sect. .
After cleaning the data, an “observed wind climate” was created for use in
WAsP. The observed wind climate is a histogram of wind speeds for
different wind direction sectors, i.e. the frequency of the wind for each
wind speed and direction bin. For this study, a data discretization of
1 m s-1 for wind speed and 30∘ for wind direction were used.
WAsP set-up
WAsP version 11.6 was used in this study to simulate the wind resource at the
different masts. In WAsP, the effect of changes in roughness length on the
wind speed around the site are modelled using the internal boundary layer
zooming-grid model , while the speed-up
effects from terrain elevation are simulated using the spectral model
described in and . As input, WAsP requires
an observed wind climate and vector maps of elevation and roughness.
WAsP uses the following modelling chain to simulate the wind climate at one
position, horizontal and vertical, from an observed wind climate at another
position. This modelling chain is extensively described in
and Eqs. 13–15. Here we briefly summarize the steps.
Fit a Weibull distribution to the observed wind climate for each sector,
preserving the third moment of wind speed and the probability to exceed the mean wind speed.
Calculate the background wind profile using the geostrophic roughness and the
observed wind speed, from which the effects of the roughness changes, terrain
height, and atmospheric stability at the observational site have been removed.
Calculate the wind speed (generalized wind climate) for predefined heights
and roughness lengths using the geostrophic drag law in combination with the
background wind profile.
Apply the effects of geostrophic roughness, terrain height, roughness
changes, and stability using this generalized wind climate for the predicted
site.
The predicted wind climate can be quite sensitive to the choice of the standard
heights and roughness lengths used in step 3.
For this study, the predefined heights were set to 3, 10, 30, 60, and
120 m above the surface here, and the roughness lengths were set to 0.0, 0.1,
0.4, 1.0, 3.0 m, which covers all possible roughness length values that
occur in the maps. In the WAsP model, large water bodies are required to have
a roughness length of 0.0 m, which is then internally converted to a value
of z0=0.0002 m.
The impact of varying topography, roughness changes, and orography is modelled
as correction factors that are applied to the scale parameter (A) of the
Weibull distribution of the wind climate in steps 1 and 4 of the model chain.
For computational efficiency, WAsP filters the roughness changes to include
only those that have the most significant impact on the wind speed. This is
carried out by creating a distance-weighted roughness length (lnz0w), which
is found by multiplying log-transformed roughness values with the
exponentially weighted distance from the mast to the roughness changes
xk,
xk^=xd[1-exp(-xkxd)],
where xd is a decay length, which is currently set to 10 km.
Then the n items in the array with all transformed roughnesses and
distances are found by fitting a step function that stops when either the
maximum number of allowed steps nmax is reached or the residual
variance RMSmax is below a specified threshold. More
details about the algorithm can be found in Sect. 8.3 in .
The default values for nmax and RMSmax
are 10 and 0.3, respectively. From this filtered set of roughness change
lines, the internal boundary layer equations described in
and are applied to the reduced
arrays to compute a speed-up factor in each sector.
To calculate the geostrophic wind, WAsP uses a corrected logarithmic wind
profile, for which the correction factors for internal boundary layer and
orographic effects have been removed, in combination with the geostrophic
drag law. The roughness length that is used in these relations is the
so-called geostrophic roughness length z0G, which is computed
sector-wise from the mean of ln(z0) and with a distance weight similar
to Eq. ():
lnz0G=ln(z01)1-exp-x1xd+∑k=2N-1ln(z0k)exp-xk-1xd-exp-xkxd+ln(z0N)exp-xNxd,
where z01 is the roughness length at the mast, k=2, …, N-1
denotes the kth roughness change from the mast location, and N is the last
roughness change on the map.
In addition to the standard inputs, WAsP uses the long-term distribution of
heat fluxes at the site to model the effect of atmospheric stability. Since
no heat flux observations were taken at the site, the default heat flux
distribution, with mean and the standard deviation of -40 and
100 W m-2, respectively, was used over land. Over water, these values
were set to -8 and 30 W m-2.
The performance of the different topographic maps was evaluated using cross
predictions. A cross prediction is defined as the prediction of the flow from
one observed wind climate, a specific mast and height, to another observed
position, either another height on the same mast or an observed height on
another mast. Cross predictions were made from all four heights at six of the
seven masts, but at mast 6 the 80.7 m height was excluded due to the limited
number of data with QC = 1. After excluding self-predictions, i.e.
predictions and inputs at the same mast and height, there were a total of 702
different combinations. The relative errors for each cross prediction were
computed as a percentage from the observed (obs) and modelled data (mod) as
δ=100(mod-obs)/obs for both wind speed
(δU) and power density (δP). It is important to include power
density in the evaluation since the production of wind turbines is
determined by the available power. The total power density is calculated by
summation of the frequency-weighted third moment of the Weibull distribution
from each sector of the total number of sectors D,
P=∑l=1D0.5ρflAl3Γ(1+3/kl),
where ρ is a reference air density (here 1.225 kg m-3), f is
the frequency of occurrence, and k is the shape parameter of the Weibull
distribution.
Results
The results are presented in three subsections. First, the ORA roughness
lengths will be compared with the roughness lengths from the land-use-based
datasets. Second, the results of the wind data filtering algorithms will be
shown. Finally, the results from the WAsP cross predictions are shown.
Roughness maps
Roughness maps from land use datasets, and from ORA at 100 and
500 m resolutions, coloured by roughness values. Open circles show mast
locations.
Figure shows the roughness lengths of the four
different land-use-based datasets and two resolutions of the ORA data. It can
be seen that the small lakes in the eastern part of the domain are not well
represented at resolutions of 300 m or more. In addition to the different
roughness length values, the forest edges and clearings are positioned
differently across the different datasets.
In the ORA maps the average roughness of the map varies between 1.42 and
1.46 m. The logarithmic average roughness value over these maps changed from
1.02 m (20 × 20 m) to 1.39 m (1000 × 1000 m)
resolution. The impact of resolution is discussed further in
Sect. .
It is clear from Fig. that the roughness lengths
from the ORA maps are larger than from the land-use-based maps. Additionally,
the ORA data, in part due to the higher roughness values, have significantly
more roughness changes. For example, CORINE only has two forest roughness
lengths, 0.4 and 0.5 m, while the ORA data represent forest roughness
lengths in six different bins from 0.5 to 3.0 m.
These features can be seen more clearly in the histograms of the roughness
lengths for each map (Fig. ). For example, the
roughness lengths of the grid cells in the ORA maps are higher on average and
are spread over more bins than the satellite-based maps. The GLCC dataset is
dominated by a single land use class with z0=0.5 m. The MODIS data have
slightly more detail and grid cells with z0=0.3 m are most frequent.
The CORINE data have the highest resolution of the land-use-based products
and have most grid cells with z0=0.5 m. Note that the CORINE and ORA20 maps
include more variation in the roughness, which causes the geometric mean to
be smaller than the arithmetic mean.
Histogram of roughness for different datasets over the same domain
as shown in Fig. . The header of each graph also
contains the arithmetic and geometric means of roughness for the region.
Wind distributions and profiles
To demonstrate the impact of the quality control that was described in
Sect. , three distributions of wind speeds at different
stages of the quality control process are shown for the cup anemometer
located at mast 1, 59 m (Fig. ). Due to the
confidentiality of the data, a normalized wind speed U^ was computed
by dividing each 10 min measurement by the mean wind speed of the filtered
data. The distribution before any QC filtering (Fig. a)
shows a high frequency of measurements with very low wind speeds (< 0.2)
as well as an increase in wind speed occurrences between 0.2 and 1.0, when
compared to the distribution in Fig. b that includes
only data with QC = 1. These differences likely reflect the icing of the
cup anemometers. Because of the large number of near-zero wind speeds, the
Weibull distribution from the WAsP method in Fig. a
gives a rather poor fit. The fit was improved for the distributions including
only data with QC = 1 (Fig. b), which include
59 % of the original dataset, and requiring that QC = 1 for all cup
anemometers simultaneously (Fig. c), which retains only
16 % of the original dataset. The mean wind speed for the three
distributions were 0.85, 0.97, and 1, highlighting that although there was a
large change in dataset size when requiring QC = 1 for all cups
simultaneously, there was a small change in mean wind speed compared to
QC = 1 for a single location. This relationship was found for all masts
and heights. All 27 anemometers showed an increase between 1 and 6 % when
demanding that QC = 1 for all cup anemometers simultaneously, which shows
that the wind climate in the final dataset used for the validation is
representative for the site.
Histogram of the observed all-sector normalized wind speed U^
(see text) at mast 1 at 59 m a.g.l. without any filtering (a),
after selecting data with QC = 1 with 59 % of the data (b),
and during the times when all masts simultaneously had QC = 1 with 16 %
of the data (c). The red line denotes the Weibull distribution that
WAsP fits for this histogram.
The all-sector modelled mean wind profile (lines) and the
observations (points) at the seven masts. All the profiles were obtained by
using the observed wind climate from mast 1 at 59.0 m and have been
normalized by the mean wind speed observed there.
Figure shows the vertical profiles of mean wind speed for
all anemometer positions using the observed wind climate from mast 1 at
59 m. The data have been normalized with the mean wind speed from the
observed position. In addition to the land-use-based simulations, the ORA
runs include the highest-resolution maps both with displacement heights
included (ORA20D) and without (ORA20). The impact of introducing a
displacement height can be observed near the canopy, where the wind speed is
much lower than when a displacement height is not included. At masts 1, 3,
and 7 the ORA20D simulations are closer to the observations than without
displacement, while they are comparable at the other masts. At higher
heights, the differences in mean wind speed among different tests are
smaller. The worst predictions occur at mast 6; however, this site is at a
higher hill than the other masts, so this difference could be due to
orographic speed-ups.
WAsP sensitivity to different roughness maps
The first test performed was to investigate the sensitivity of the ORA method
to different tree height to roughness length conversions in
Eq. (). In this sensitivity test, simulations were
performed using maps where z0=H/5, z0=H/10, and z0=H/20 with
and without applying a displacement length. For each pair of observed
histograms, the histogram at the source location was used to predict the wind
distribution at the target location and compared to the observed histogram at
the target location (see Sect. ). The resulting mean absolute
error from all 702 cross predictions, |δU|‾, is shown in
Fig. , for these tests as well as a sensitivity test of
the CORINE land-use-based roughness.
For the roughness maps without a displacement height, it can be seen that
increased roughness lengths result in lower errors, i.e. H/20 has the
highest error and H/5, which corresponds to a mean roughness length of more
than 2 m, has the lowest. When a displacement height is applied, better
representing the location, the H/5 test has the largest errors, while the tests
using H/10 and H/20 maps have very similar |δU‾|. When
looking at power density, it was found that the ORA100D simulations with
H/10 and H/20 had a |δP‾| of 9.48 and 10.74 %,
respectively. This study shows that z0=H/10 is a reasonable modelling
choice.
After finding that higher roughness lengths lead to better results, and
noting that the roughness maps based on land use classes (GLCC1000, MODIS500,
CORINE100, and GLOB300) are characterized by much lower roughness lengths than
the ORA maps (Fig. ), one could hypothesize that
increasing z0 in the satellite-based products to a more realistic value
would improve the results. The CORINE100 data were chosen for this since it
could be seen that the CORINE100 map had a realistic representation of the
land use around the site (Fig. ).
To test this, the roughness length of the forest classes (i.e. areas with
z0=0.4 m and z0=0.5 m) in the CORINE100 map were increased by a
factor of 3 to 1.2 and 1.5 m, respectively, which is approximately the
roughness length observed in maps using the ORA approach (see
Fig. ). The simulation using this roughness map is
labelled with “high z0” and had an error of |δU|‾=3.5 %, which is closer to the ORA100 test's error of
|δU|‾=3.4 % than the standard CORINE100 test with an
error of |δU|‾=3.8 %. Therefore, the performance of the
land-use-based maps could potentially be improved for this site by increasing
the roughness length. However, the factor of 3 was chosen based on
knowledge of the roughness length from the ORA maps; thus in the absence of
tree height measurements it could be difficult to set the correct value.
The next sensitivity test was designed to investigate the effect of the data
filtering on the roughness change model. This was achieved by changing the
limit of RMSmax to ≈0 and varying
nmax from 0 to 10, which causes the model to include only
nmax roughness changes after filtering. Note that using 0
roughness changes disables the internal boundary layer model, which means
that all observed differences are due to a different z0G (see
Sect. ). To isolate the impact of taking more roughness changes
into account, all simulations were normalized by the |δU‾|
from simulations with 0 roughness changes.
Figure shows the normalized |δU‾| for
different numbers of roughness changes. It can be seen that for most
roughness maps, the model errors generally decrease from 0 to 2
nmax, and for larger nmax the ratio is more
constant. This indicates that in this case only two roughness changes
contribute significantly to WAsP modelling at each mast. This is consistent
with the best practice for hand digitizing roughness maps, which states that
only the most important roughness changes need to be digitized
. It should be noted that nmax is likely
site specific and that using nmax>2 could still give
significant improvements at other sites.
(a) Mean absolute error in wind speed (%) and
(b) power density for all simulations using a land use description
with a resolution of 100 m.
By comparing the different ORA resolutions, the impact of resolution on the
roughness change model can be examined. It was found that the simulation
using the ORA20 map had the largest reduction and |δU‾|/|δU0‾|≈0.86, while the coarser-resolution
ORA1000 map did not have as large of a reduction in error ratio,
|δU‾|/|δU0‾|≈0.94 using >2
roughness changes. This shows that resolution is important for roughness
change modelling, which was expected since the higher-resolution maps can
better resolve the precise location of a roughness change. Interestingly, the
GLOB300 simulations have |δU‾|/|δU0‾|>1,
indicating that the map with nmax=0 performs best. This means
that the model results can lead to larger errors when including roughness
changes that do not represent the modelling area well.
Ratio between the mean absolute error in wind speed and the mean
absolute error without taking into account any roughness changes
(|δU‾|/|δU0‾|) as a function of the
number of significant roughness changes n.
To further illustrate the effect of using different maps, we can plot the
|δU‾| as a function of z0G‾
(Fig. ), where z0G‾ is the all-sector
geostrophic roughness length, which was calculated as the geometric mean of
z0G from each sector. Since there are no displacement heights available
for the land-use-based maps, the displacement height was not used in this
comparison. As expected, the satellite-based products have a much lower
z0G‾ than the ORA maps. There is also a relationship between
the model error and z0G‾, in that the MODIS500 map has the
highest |δU‾| of ≈4.4 %, with the lowest
z0G‾, whereas the ORA1000 map has the highest
z0G‾ and the lowest |δU‾| of
≈3.4 %.
The effect of including a displacement height for the ORA maps at different
resolutions is shown in Fig. . The roughness change model
is used with the default settings (see Sect. ); thus these
results are impacted by both the roughness changes and the different values
of z0G. The ORA20D and ORA100D have a |δU‾| that is
≈0.2 % lower than the ORA20 and ORA100, respectively; they
therefore
benefit from including a displacement height.
At coarser resolutions, adding the displacement height increases
|δU‾| by ≈0.5 %. The displacement height at all
masts using the ORA1000 map is significantly higher than for the ORA20 map
(Table ). This suggests that the displacement height
for the coarser resolutions is likely too high, because the forest clearing
around the mast is not resolved. Therefore, it is recommended that the
displacement height correction should only be performed when the resolution
of the map is sufficient to represent the effect of forest clearings near the
mast.
Mean absolute error in wind speed as a function of the geostrophic
roughness length when using the default WAsP settings but with the roughness
change model switched off.
Summary of using different roughness maps
In this section, the overall performance of WAsP simulations using satellite-based maps and the proposed ORA approach is summarized. Thus far, only
|δU‾| was used for comparing the model results since the
comparisons were largely investigations of the model behaviour. However, for
an annual energy production estimation, it is more relevant to quantify
map-related errors on |δP‾| (Eq. ) to
assess the potential performance of the wind turbine. Therefore, to evaluate
the overall performance of the modelling with different maps, both
|δU‾| and |δP‾| will be used.
Figure shows the distribution of |δP| for each of
the cross predictions, binned in three categories for all four land-use-based
maps and the highest-resolution ORA map with a displacement height. For this
analysis, the cross predictions are broken into two types. Horizontal
predictions (Fig. a) are those for which the observed wind
climate and the predicted wind climate are from different masts, while the
vertical cross predictions are those for which they come from the same mast
(Fig. b).
The mean absolute error of the simulations with the ORA maps with
and without applying a displacement height for different map
resolutions.
Summary of the error metrics using all model runs (702 cross
predictions). Defining y as the modelled and x as the observed variable with a
line denoting a mean, the mean absolute error is defined as
100|(yi-xi)/xi|‾, the mean bias as
100(yi-xi)/xi‾, and the root-mean-square error (RMSE) in
percent of the wind speed U and the power P as
(100(yi-xi)/xi)2‾. The lowest value of an
error metric is denoted in bold.
Mean bias U (%)
Mean abs. error U (%)
Mean abs. error P (%)
RMS error U (%)
RMS error P (%)
CORINE100
0.30
3.82
13.19
5.02
17.09
GLOB300
0.31
4.27
14.41
5.48
18.49
GLCC1000
0.51
3.61
13.14
4.91
17.05
MODIS500
0.22
4.10
13.60
5.21
17.35
ORA20
0.50
3.35
11.15
4.27
14.10
ORA100
0.34
3.43
11.39
4.36
14.24
ORA500
0.17
3.58
11.57
4.51
14.39
ORA1000
0.06
3.42
10.61
4.27
13.16
ORA20D
0.49
3.22
10.03
4.07
12.40
ORA100D
0.36
3.26
9.48
4.03
11.70
ORA500D
0.23
3.98
11.67
4.98
14.48
ORA1000D
0.10
3.79
11.12
4.72
13.73
Absolute percent errors of the power density for 702 cross
predictions using simulations with different maps.
Ideally, we want as many cross predictions with |δP|<12.5 % as
possible. For the horizontal cross predictions, there are ≈20 %
more predictions in this category for the ORA20D run than for the land-use-based maps. Conversely, the number of very high errors, |δP|>25 %, is greatly decreased for the horizontal cross predictions
when using the ORA20D map, from ≈100 when using the CORINE100 and
GLCC1000 map to ≈20 when using the ORA20D map.
For the vertical cross predictions (Fig. b), the errors are
much smaller than for horizontal extrapolations because there are the same
topographic errors for the input and the predicted anemometers. However, as
in the horizontal cross predictions, the ORA20D run has fewer high-error
predictions than the land-use-based roughness map; the ORA20D simulation had only
1 error >12.5 %, whereas for all other land use products they occurred
at least 11 times.
Even when comparing maps with the same resolution (not shown), i.e. the
CORINE100 with the ORA100 simulation, the number of cross predictions with
errors larger than 25 % decreases from 75 to 44, a 41 % decrease.
Using the ORA300 compared to the GLOB300 simulation decreases these errors by
51 % and using the ORA500 compared to the MODIS500 decreased them by
40 %.
Table provides summary error statistics of the
results from the 702 cross predictions for all land use, ORA, and ORA-with-displacement simulations. In addition to the mean absolute error of δU and δP, which has been shown previously, the mean bias and root-mean-square error (RMSE) have been included. The RMSE penalizes high errors
more than the mean absolute error, and therefore identifies simulations that
have a narrow error distribution.
All ORA-based simulations have lower |δP|‾ than any of the
simulations using land-use-based maps. The same is true for the RMSE of
δP, where the improvement of the simulations with the ORA roughness
maps is even larger due to the reduced number of large errors as seen in
Fig. .
Furthermore, it was found that the ORA100D simulation has the lowest
|δP|‾, RMS of δU, and RMS of δP, whereas
the ORA20D has the lowest errors in |δU|. The ORA20D map results in
lower errors due to a more accurate roughness change description
(Fig. ), and due to the application of a displacement
height (Fig. ). However, the z0G was lower than that
used for better-performing maps in the no-roughness change tests
(Fig. ). From these results it is clear that the ORA maps
provide better results, due to the higher z0G and because of the
increased detail of the forest structure. For this site, a best-performing
map could likely be created by using the 20 m resolution map with a slightly
higher z0.
The land-use-based land cover simulations perform similarly despite different
resolutions and different descriptions of the land use. For example, the
GLOB300 and CORINE100 simulations both have a rather high RMSE for both U
and P, despite having a high resolution. This highlights that resolution is
not a panacea but only improves performance when the surface is accurately
represented. For example, the GLCC1000 simulation has almost no roughness
changes (see Fig. ), but has the lowest RMSE in U
and P out of the satellite-based products. Also, we noted that the CORINE100
with a high z0 (see Sect. ) reduced
|δP|‾ to 12.63 % and the RMSE of δP to
15.76 % (not shown); however, both are still significantly higher than
all of the ORA runs. This shows that tweaking z0 of certain land use
classes in existing satellite-based maps will only partially reduce the model
errors.
In Table , the mean bias of U is very close to zero
for all model runs. The ORA1000 simulation has the lowest mean bias of U.
One would expect a difference between runs with a very low and very high
roughness, for example the CORINE100 and ORA100 runs. However, it can be seen
that for both of these runs, the bias is close to zero. This is likely
because the cross prediction includes both upwards and downwards predictions.
This results in errors that will cancel each other out; e.g. a too low
prescribed roughness results in an over-prediction for an upward
extrapolation but an under-prediction for a downward extrapolation.
Discussion
The presented results for the mean prediction error in
Table show a complex interdependency of roughness
magnitude (Figs. and ), imprecision of
roughness lines due to either limited map resolution or a coarse land use
classification (Fig. ), and inclusion (or not) of
displacement height (Figs. and ).
Nevertheless, the ORA approach showed consistently improved results relative
to the roughness maps based on land use classification for the studied site.
This demonstrated robustness of the ORA approach should make it attractive to
use for turbine siting. Given the relatively small processing time needed to
make the maps, and the fact that all maps could be loaded into WAsP and
predictions finalized within a few minutes, the approach is promising. At
this site, it turned out to be better to use a land use map with hardly any
roughness change lines than to use products with more detailed, but
incorrect,
information (e.g. GLCC1000 versus GLOB300) when comparing only the
commercially available maps (Table ).
Ideas for further improvements
As argued by and , forest density and
forest height are likely to influence the optimal ratios of z0/H and
d/H. Since forest density in terms of plant area index can also be
estimated from airborne lidar data , it would be
interesting to investigate a more refined roughness classification based on
this parameter. It was also demonstrated that raising the roughness value in
the CORINE data reduced the mean prediction error compared to the original
roughness conversion (Fig. ), indicating that this
potential “quick fix” could result in significantly reduced errors. Without
access to forest height information, it will however be hard to justify the
exact level to which the roughness should be adjusted. Since imprecise
roughness change lines can lead to an increase in prediction error, as seen
when using GLOB300 data (Fig. ), a simpler way of reducing
the error could be to smooth the map and increase the geostrophic roughness
in order to achieve lower error, as demonstrated for the ORA maps in
Fig. . The results in Fig. reinforce
the recommendation to use high values of roughness length for forested areas,
even for landscapes where all mast observations are affected by the forest.
When downgrading the resolution of the ORA maps, the arithmetic average of
the roughness remained nearly identical because the starting point for all
the ORA maps was the tree height, whereas the presence of clearings in the
high-resolution ORA maps reduced the geostrophic roughness
(Fig. ) since the WAsP method uses the geometric average
see, e.g.for a motivation and more background. In
forested areas, the use of geometric averaging could be particularly
problematic since – in reality – the presence of clearings, which have low
roughness lengths, tend to increase the overall turbulence levels and
increase the aggregated roughness of the landscape . It
should also be noted that the log-space averaging approach has limitations
for low vegetation since it omits the significant non-equilibrium effects of
roughness aggregation .
Because of the log-averaged aggregated geostrophic roughness, it would be of
interest to systematically investigate the roughness value chosen for the
clearings. The value of z0=0.1 m, used in this study, was assessed to
be low for a newly cleared forest area but reasonable to high for
low-vegetation wetland. If a larger roughness length was used for the
clearings, it would be expected that z0G would also be increased, which
would reduce the error associated with the geostrophic roughness closer to
the level of the ORA1000 map. There is, however, a risk that increasing the
value could affect the filtering of significant roughness changes, which
could thereby increase the related error.
Does a better map make a significant difference?
The reduction in mean prediction error for both the mean wind speed
and power density is only a few percent. However, as demonstrated in
Fig. , this reduction reflects changes over a wide
distribution of cross-prediction errors. We see the demonstrated reduction of
the large errors as one of the main advantages of the ORA method since such
large errors in the predicted wind climate could result in significant costs
when estimating the performance of a wind turbine throughout its lifetime.
Whereas large errors could result in higher lifetime costs of turbine
operation at any site, revealed that wind turbines
located in forested areas are more prone to experience fatigue loads,
vibration errors, and lower annual energy productions than other sites.
Therefore, an improved wind climate prediction could be of high consequence
for the forested landscape.
With this in mind, it is recommended that effort is put into finding accurate
and updated information on forest height and structure when evaluating an
optimal location for wind energy exploitation in forested areas. For the
reasons stated above, we also recommend investigating the sensitivity of the
observed wind climate to the relationship between z0 and H since the
ratio used here may not be optimal for other forests.
Availability of tree height information data
To the authors' knowledge, databases of freely accessible ALS data already
exist for Denmark, Finland, and England. In other countries, such as Sweden,
data are accessible at reduced cost (compared to a new campaign) for
international researchers and companies, whereas they are freely accessible
for national researchers.
The processing of lidar data to tree heights is relatively simple, and can be
performed on a normal desktop computer for small areas. In addition, future
drone-mounted lidars and satellite-derived products have
the potential to provide high-accuracy tree height or land cover information
for relatively low cost. This will enable better access to such data and
provide for the ability to assess changes over time.