Wind gusts are a key driver of aerodynamic loading, especially for tall structures such a bridges and wind turbines. However, gust characteristics in complex terrain are not well understood and common approximations used to describe wind gust behavior may not be appropriate at heights relevant to wind turbines and other structures. Data collected in the Perdigão experiment are analyzed herein to provide a foundation for improved wind gust characterization and process-level understanding of flow intermittency in complex terrain. High-resolution observations from sonic anemometers and vertically pointing Doppler lidars are used to conduct a detailed study of gust characteristics with a specific focus on the parent distributions of nine gust parameters (that describe velocity, time, and length scales), their joint distributions, height variation, and coherence in the vertical and horizontal planes. Best-fit distributional forms for varying gust properties show good agreement with those from previous experiments in moderately complex terrain but generate nonconservative estimates of the gust properties that are of key importance to structural loading. Probability distributions of gust magnitude derived from vertically pointing Doppler lidars exhibit good agreement with estimates from sonic anemometers despite differences arising from volumetric averaging and the terrain complexity. Wind speed coherence functions during gusty periods (which are important to structural wind loading) are similar to less complex sites for small vertical displacements (10 to 40 m), but do not exhibit an exponential form for larger horizontal displacements (800 to 1500 m).

Topographic channeling or enhancement of the near-surface flow can lead to
local increases in wind speed (Wagenbrenner et al., 2016) and hence
enhance the wind resource (Clifton et al., 2014; Barthelmie et al.,
2016; Jubayer and Hangan, 2018). Terrain inhomogeneity also induces complex
flow conditions (Wood, 2000), particularly in the presence of vegetation
(Suomi et al., 2013), that have implications for wind loading on
structures, pollutant dispersion, wildfire propagation, and wind turbine
siting and operation (Sanz Rodrigo et al., 2017; Wagenbrenner et al.,
2016; Butler et al., 2015). Key features of flow in complex terrain include
thermo-topographic flows arising from differential heating (Rucker et
al., 2008; Rotach and Zardi, 2007) and lee-side vortices that develop
parallel to mountain ridges (Grubišić et al., 2008). Regions
with complex topography and land cover heterogeneity also tend to experience
more frequent and stronger wind gusts (herein defined as coherent short-term
wind speed maxima) (Letson et al., 2018; Earl et al., 2017; Sheridan,
2011; Hasager et al., 2003) due in part to

terrain-induced alteration of the structure of mesoscale convective systems and thus the downdrafts and wind gusts generated therefrom (Markowski and Dotzek, 2011).

generation of small-amplitude mountain waves in stably stratified air that can cause strong and gusty downslope winds when the flow becomes supercritical and these waves “break” (see detailed discussion in Durran, 1990, and Hertenstein and Kuettner, 2005).

Herein we address these research needs using data collected during January–July 2017
at a site in eastern Portugal near Perdigão (Fig. 1a).
Two parallel ridges running from the northwest to southeast and separated by 1.4 km
dominate the local topography in the study area. These ridges stand 300
to 350 m above the surrounding terrain and approximately 175 m above the
valley located between them (Fig. 1b). This location was the focus of a
measurement campaign during which over 50 meteorological masts were deployed
over an area of a few square kilometers (Mann et al., 2017). The data
collected in the Perdigão experiment and employed herein to characterize
flow behavior at heights relevant to wind turbine selection, operation, and
micro-siting with a specific focus on wind gusts are high-frequency (18 Hz)
3-D wind measurements from Gill WindMaster Pro sonic anemometers deployed on
the nine tallest of the meteorological masts (that extended to heights (

The objectives of the current study are as follows.

Evaluate the degree to which the best-fit probability distributions to various gust parameters (e.g., intensity, temporal scale, and length scale) as advanced by Hu et al. (2018) are generalizable across terrain types. The resulting parametric descriptions of gust properties are potentially of utility to the engineering community because they permit estimation of extreme values (IEC, 2005; ASCE, 1998) (e.g., using Rice theory; Gomes and Vickery, 1977), facilitate development of joint distributions of gust parameters, allow characterization of gusts that contribute to structural fatigue, and are used with design standards (for example, extreme gusts are modeled in wind turbine design standards based on mean wind speeds and turbulence intensity; IEC, 2005). They are potentially also of use within the meteorological community since they could afford a methodology for downscaling of wind gusts in either weather forecasting (Friederichs and Thorarinsdottir, 2012; Suomi and Vihma, 2018) or climate downscaling contexts (Cheng et al., 2014). Further, fluctuating wind loads on engineering structures requires estimates of multiple components of the flow, including characteristics that have previously received relatively little attention (e.g., the shape of wind gusts) (Mücke et al., 2011; Suomi et al., 2013). Various parametric distributions are evaluated in terms of their goodness of fit to the empirical data and their accuracy at the distribution tails and are used to develop joint probability distributions of different gust properties at a single location and of the same gust property across space (where the latter can be used to develop bivariate extreme value copulas; Bonazzi et al., 2012). Where possible the distributional forms for each gust parameter are compared with previous work in flat or moderately complex terrain (Morgan et al., 2011; Cheng and Bierbooms, 2001; Friederichs and Thorarinsdottir, 2012; Hu et al., 2018).

Quantify the dependence of different descriptors of wind gusts on
measurement height (

Characterize power spectra of wind speeds from sonic anemometers and ZephIR
lidars at different heights. These power spectra are used to determine how
the presence of wind gusts affects their shape (Hu et al., 2018)
and to derive first-order estimates of the so-called reverse height (i.e., height
above ground at which surface-driven processes cease to dominate
scales of variability) using the amount of variance expressed at the diurnal
timescale (Larsén et al., 2018; Troen and Lundtang Petersen,
1989). In the near-surface levels surface-driven processes produce the
diurnal peak in the power spectrum of wind speeds, while aloft it is
primarily the product of pressure perturbations deriving from the
atmospheric tide (Larsén et al., 2018). At intermediate heights
there is a relative minimum in the amount of variance expressed at periods

Quantify the dependence of wind gust parameters on atmospheric conditions; specifically stability, wind direction, and turbulence intensity (Barthelmie et al., 2016; Hu et al., 2018). Previous work has shown that GFs are strongly and directly related to turbulence intensities (Ashcroft, 1994; Greenway, 1979; Hu et al., 2018) and that turbulent kinetic energy (and hence the potential for gusts) is enhanced downstream of obstacles (Jubayer and Hangan, 2018). Thus, wind gust properties at the nine towers are conditionally sampled by wind direction, stability class, and by turbulence intensity.

Quantify spatial coherence in flow properties, particularly wind gusts. The physical scales of wind gusts are critically important to loading on structures (Solari, 1987; Hui et al., 2009; Bos et al., 2016), and the potential for gusts to remain coherent as they propagate through a wind farm has implications for power quality and grid management (Sørensen et al., 2002; Vigueras-Rodríguez et al., 2012). The frequency characteristics of longitudinal wind speed are investigated using spectral analysis of output from individual sonic anemometers and coherence functions among pairs of sonic anemometers during gusty periods. Horizontal coherence functions between sonic anemometers on different masts and thus displaced by distance of hundreds of meters are used to describe the degree to which wind gust variations are coherent in the complex terrain of the study area, and comparisons are made to coherences from previous work.

The primary data set analyzed herein comprises 18 Hz, wind
components, and sonic virtual temperature as measured by Gill WindMaster Pro
sonic anemometers deployed on these meteorological masts (Table 1 and Fig. 1)
at heights above the surrounding vegetation. The three tallest towers have
seven measurement heights (

Locations and measurement heights of each meteorological mast (tower) and each ZephIR lidar. Measurement heights referred to in this paper as “60 m” are shown in bold. Reference tower (Tower 29) is emphasized by italics. Tower base elevations are given in meters above sea level (a.s.l.) and mean vegetation height is calculated from aerial laser scans in a 50 m square cell surrounding each tower or ZephIR lidar. Definitions used to conditionally sample the towers as valley or ridge are also shown along with a parenthetical statement of their location on the northeast (NE) or southwest (SW) ridge. Valley towers are those with elevations below 400 m a.s.l.

Tower 29, the 100 m tower on the northeast ridge (Fig. 1),
is used herein as a reference tower to represent pseudo free-stream flow and
characterize the prevailing atmospheric stability because of the prevalence
of northeasterly flow during the field experiment (Fig. 2). Measurements from
this meteorological mast indicate a high frequency of flow perpendicular to
the ridges. Wind directions between 30 and 60

Overview of wind conditions at Perdigão.

Lidars used in atmospheric applications can employ either light emitted in
continuous-wave or pulsed forms (Held and Mann, 2018; Vasiljević et al.,
2017). Measurements from two ZephIR continuous-wave Doppler lidars (referred
to here as “lidars” and by their unit numbers, z447 and z423) are used to
extend the analysis of gust parameters to heights above 100 m a.g.l. One
ZephIR lidar was deployed in the central valley 311 m from meteorological
mast 25 and one to the west of the SW ridge (Fig. 1b; locations in Table 1).
The ZephIR 300 series is a continuous-wave coherent monostatic lidar that has
a wavelength of 1.575

High-precision estimates of the terrain elevation and canopy height were
derived from aerial laser scans performed by helicopter. The

Section 3.1 provides definitions used herein and outlines methods used in the conditional sampling, while Sect. 3.2 briefly describes the methods used in the spectral and coherence analyses.

The following definitions are used herein:

wind direction (

gust magnitude (

gust amplitude (

peak factor (

GF, ratio between the 3 s gust magnitude and the
10 min mean wind speed:

Rise time (

Lapse time (

Gust duration, (

Gust length scale (

Turbulence intensity (TI) is standard deviation (

Stability class includes five classes denoting atmospheric stability based
on Monin–Obukhov length (

In numerical weather prediction (NWP) models, wind gusts are generally
sub-grid scale and thus are estimated using parameterizations. In the
simplest case, the peak factor (

Following Hu et al. (2018) four two-parameter probability distribution types
are fitted to the gust parameters (1 and 3–10, above) as derived from time
series from sonic anemometers on all meteorological masts, for all 10 min
periods when

Weibull

log-logistic

lognormal

gamma

Distributions are fitted to each gust parameter using maximum likelihood estimation (MLE), and best-fit distribution types are determined using negative-log-likelihood (NLL) values (Hogg et al., 2005). Since two or more distributional forms may exhibit relatively good fits to the empirical distributions, we also note results wherein a second distribution type exhibits equivalent NLL values (i.e., those within 0.1 % of the best fit). The tails of probability distributions are typically of the greatest importance to wind loading (e.g., turbine design and control systems; IEC, 2005) and are not always well described by distributional forms that best represent the body of the distributions (Friederichs and Thorarinsdottir, 2012). Thus, the effectiveness of each distribution type in representing the 99th percentile gust magnitude and gust amplitude and the first percentile rise time are evaluated by comparing the parametric estimate derived from the fitted distribution to the empirically derived percentile value.

Once distributional forms for individual gust properties have been derived
they are used to construct joint mass distributions of gust parameters using
a general method that converts gust parameters following any type of
distribution to the standard Gaussian domain and generates the joint
distribution of the transformed gust parameters. For gust parameters
following Weibull distribution with the probability density function (PDF,
Eq. 2), the transformation to a Gaussian form is realized using the
following explicit equation:

After the gust parameters are transformed to standard normal variables, 2-D
elliptical contours are computed that enclose a specified percent of
transformed data using the fact that the sum of squared Gaussian random
variables follows a chi-square distribution. The orientation angle

Conditional sampling is used to explore the functional dependencies of gust
properties. Gust periods (as defined by the gust criteria in Sect. 3.1)
are treated separately in several of the analyses below. The presence or
absence of wind gusts is always determined locally (at a given sonic
anemometer). The samples of

Distributions of gust parameters at each of the nine towers (using data
collected at 60 m a.g.l.) for 10 min periods with

Power spectral densities (PSDs) of wind speeds from the sonic anemometers and
the ZephIR lidars are calculated using Welch's method (Welch, 1967). For
the sonic anemometer data this method is applied to 2 h time series of
18 Hz longitudinal wind speed measurements that meet the gust criteria and
(separately) those that do not. Spectra are plotted in nondimensionalized
form wherein the power at each frequency is multiplied by the frequency and
divided by the variance computed from the 18 Hz time series, and the
frequency is multiplied by a measurement height (

Spatial relationships of longitudinal wind speeds from the sonic anemometers
(and ZephIR lidars) are characterized in the frequency domain using
coherence functions,

Characterization of the height at which the surface characteristics cease to
dominate scales of flow in the atmosphere has applications to microscale
model verification and validation and is accomplished herein through
investigation of the height dependence of the spectral peak associated with
the diurnal timescale (

Calculate the PSD using Welch's method and the longest complete data period.

Perform log-smoothing (35 points per decade) of these PSDs by piecewise cubic interpolation.

Fit a linear function to each PSD (log

Calculate three parameters:

(

Mean sustained (10 min) wind speeds (

In accordance with a priori expectations, gust amplitudes
(

Although gust magnitude and amplitude are useful for determining the loading
force exerted by wind gusts, GFs (i.e., the ratio of the 3–5 s
gust magnitude to the sustained wind speed) are frequently used in the
meteorological community as a nondimensional intensity index
(Krayer and Marshall, 1992) and are sometimes used for assessment of
wind hazards (Deaves, 1993). GFs are generally higher in the valley
than on the ridge (median GF at valley towers is 27 % higher than those
from the ridge towers; Fig. 3c), consistent with the lower

Best-fit distribution types for each gust property (in each 10 min
period when

Gust rise time values are similar at ridge and valley towers, median
(

The results from analyses of data collected in the complex terrain of
Perdigão are thus internally consistent across towers in terms of the
distributional form that best describes the gust samples and are also
generally consistent with analyses of sonic anemometer data at 65 m a.g.l.
collected in moderate-complexity terrain (Hu et al., 2018). To the
extent distribution types are uniform across the site, and consistent with
previous work (as they are for

Joint distributions of

Joint distributions of gust length scale at different heights (

Joint distributions of gust magnitudes (

Joint distributions of

Consistent with previous research, the probability of a wind gust varies
systematically with dynamic stability and is higher under near-neutral and
unstable conditions (Hart and Forbes, 1999), although gust probability at the
valley towers is most similar to the ridge towers during times of very high
(

Median gust parameters during gusty conditions
(

In Fig. 7, data are conditionally sampled to select only periods when wind
gusts occurred (i.e.,

Median values of the gust parameters, by height, at each of the nine
towers for 10 min periods that meet the gust criteria:

Although the ZephIR lidar measurements are disjunct (at approx. 2 s) for
each height and are subject to volumetric averaging (over the volume of the
annulus swept out by the lidar beam, in a cone 30

Gust peak factor (

Box plot of gust peak factor (

The mean marginal gust probability (the average of unconditional gust
probability at all sensors) at 60 m a.g.l. across all nine towers is
2.7 % (range of 1.8 % to 5.1 %, Fig. 10a). Thus, on average in
any 10 min period at any tower there is a 2.7 % chance that

At Towers 25 and 29 (two 100 m towers representing valley and ridge conditions, respectively), the mean intra-tower gust co-occurrence probabilities (computed across heights on the same tower) are 60 % and 55 %, respectively. It is noteworthy that the two ridge-top towers have higher gust probabilities (both conditional and marginal) at their lowest measurement heights, 10 and 20 m, and these probabilities decrease strongly with height (Fig. 10c). Conversely, marginal wind gust probabilities are highest at 80 and 100 m in data from Tower 25 (in the valley) and there is some evidence of a decoupling of data from this tower between heights above and below 80 m as manifested in high joint probabilities of gusts in data from 80 and 100 m and among sonic anemometers at 30, 40, and 60 m a.g.l., but low conditional probabilities between data collected at 80 m and, for example, 40 m.

Co-occurrence of wind gusts in individual 10 min periods
among sonic anemometers deployed on different towers

Normalized power spectra of longitudinal wind speeds from the sonic
anemometers during gust periods differ in three primary ways from the mean
spectra derived as the composite of all 2 h non-gust periods. Firstly,
during gusty periods the spectral peak is shifted to the left (to lower
normalized frequencies), secondly, the spectral peak is more distinct, and
lastly, the spectra exhibit lower variance at higher frequencies (normalized
frequency

Power spectra of wind speeds during gusty conditions
(

Power spectra of horizontal wind speed computed for all 10 ZephIR lidar
measurement heights and from sonic anemometers deployed on the 100 m
meteorological masts indicate relatively wide variability in the magnitude
of the diurnal peak,

Coherence functions of longitudinal wind speed from horizontally separated
sonic anemometer pairs do not conform to an exponential form and instead
exhibit a marked concave-down section at reduced frequencies below 0.7
(Fig. 13a). Nevertheless, functional values are substantially higher for
ridge towers (excluding 10) than for valley towers, indicating greater
coherence across the top of the valley than within the valley. Fitted

Mean coherence in longitudinal wind speeds as measured by sonic
anemometers based on 2 h time series.

The experiment conducted at Perdigão provides an unprecedented data set for studying flow characteristics in complex terrain. Herein we focus on wind gust characteristics as described using 6 months of data recorded at 18 Hz from 51 3-D sonic anemometers deployed on nine tall meteorological masts at heights of 10 to 100 m and two vertically pointing Doppler lidars. Consistent with previous research, analyses presented herein illustrate substantial spatial heterogeneity in the magnitude, scale, and occurrence of wind gusts over an area of approximately 3 km by 3 km (Fig. 1) and reemphasize the complex effects of terrain forcing on near-surface flow.

Nine properties of wind gusts (intensity measures of magnitude, amplitude,
peak factor, and GF and scale metrics of rise and lapse time,
duration, and length scales) exhibit parent probability distributions similar
to those derived from measurements in moderately complex terrain
(Hu et al., 2018), indicating that these distributional forms may
be generalizable. However, the best-fit distributional forms (selected using
negative log-likelihood) underestimate the magnitude and amplitude of
intense gusts (i.e., the 99th percentile values). Although the wind gust
parameters (including probability of gust occurrence) exhibit similar
distributional forms across the site, they differ greatly in terms of the
shape and scale parameters of the distributions as applied to data from
locations in the valley compared to the ridge tops. Joint probability
distributions of the gust parameters indicate high aspect ratios for gust
intensity (e.g., gust magnitude;

GFs measured at Perdigão are larger than those measured in less
complex terrain (Fig. 8c; Suomi, 2015) but decrease with height (

Wind speed spectra during gusty periods (when

Gust parameters, and their spatial heterogeneity, are found to vary with
atmospheric conditions including wind direction, stability, and turbulence
intensity. Differences in observed gust parameters between ridge and valley
towers are less pronounced when the flow is parallel to the ridge
orientation. Unstable and very unstable conditions (as well as high
turbulence intensity) are associated with less ridge–valley differentiation
in

Gust co-occurrences and coherence statistics indicate the presence of
large-scale gust phenomena that are simultaneously manifested at the ridge
towers but not the valley towers. Gust occurrence across the Perdigão
site is significantly influenced by the terrain, resulting in a much lower
average gust co-occurrence probability (of 27 %) across towers than those
observed in flat terrain (Branlard, 2009). The decay of coherence
functions for vertical displacements is in the range found in flat terrain
(Solari, 1987; Vigueras-Rodríguez et al., 2012). However, coherences
for the large horizontal displacements (

There are clear commonalities in gust properties across the site and among
estimates derived using data from sonic anemometers and vertically scanning
Doppler lidar. Additionally, co-occurrence probabilities of wind gusts
across the site illustrate the very high complexity of flow over what is
superficially a simple two-dimensional valley enclosed by two parallel
ridges (Fig. 1). These results further indicate that terrain features (and
the vegetation canopy) may have a more profound impact on the dimensions of
wind gusts than their magnitude. The reverse height (approximately 60 m
above the ridge tops) is consistent with a decoupling of flow derived from
the coherence functions estimated from the vertically scanning Doppler
lidars (as indicated by the step change in

Data collected during the Perdigão experiment and analyses presented herein provide a foundation for improved wind gust characterization in complex terrain. These data also provide an unprecedented opportunity for detailed validation and verification of numerical wind flow models (Butler et al., 2015; Suomi and Vihma, 2018).

All data analyzed herein are available for download from
the New European Wind Atlas data portal (Gomes et al., 2018) hosted by the
University of Porto and accessible at

The supplement related to this article is available online at:

All four authors participated in extensive discussion about the rationale and methods for this paper. FL had primary responsibility for performing analysis and writing the paper. RJB performed principle lidar data processing. WH took the lead in the analysis for joint distributions. SCP performed principle sonic anemometer data processing and made major contributions to the text and organization of the paper. RJB and SCP acquired the funding to make this research possible and, along with many members of the Perdigão research team, performed the field measurements.

The authors declare that they have no conflict of interest.

This article is part of the special issue “Flow in complex terrain: the Perdigão campaigns (ACP/WES/AMT inter-journal SI)”. It is not associated with a conference.

We thank the Perdigão research team, especially the scientists and technicians of the Technical University of Denmark (DTU), INEGI, University of Porto, and the National Center for Atmospheric Research (NCAR) for their excellent work and logistical support during the Perdigão measurement campaign. We particularly acknowledge the leadership of Jakob Mann and Ebba Dellwik of DTU for provision of the tree height data. We gratefully acknowledge funding support from the U.S. National Science Foundation (1565505), and U.S. Department of Energy (DE-SC001643). We are grateful to the municipality of Vila Velha de Ródão, landowners who authorized installation of scientific equipment in their properties, the residents of Vale do Cobrão, Foz do Cobrão, and Alvaiade, Chão das Servas, and local businesses who kindly contributed to the success of the campaign. The space for the operational center was generously provided by Centro Sócio-Cultural e Recreativo de Alvaiade in Vila Velha de Rodão. We also greatly appreciate the thoughtful contributions of the two anonymous reviewers and would like to thank Etienne Cheynet for recommendations in estimating wind speed coherences. Edited by: Jose Laginha Palma Reviewed by: two anonymous referees