Atmospheric stability has a significant effect on wind shear and turbulence intensity, and these variables, in turn, have a direct impact on wind power production and loads on wind turbines. It is therefore important to know how to characterise atmospheric stability in order to make better energy yield estimation in a wind farm.

Based on the research-grade meteorological mast at Alaiz (CENER's test site in Navarre, Spain) named MP5, this work compares and evaluates different instrument set-ups and methodologies for stability characterisation, namely the Obukhov parameter, measured with a sonic anemometer, and the bulk Richardson number based on two temperature and one wind speed measurement. The methods are examined considering their theoretical background, implementation complexity, instrumentation requirements, and practical use in connection to wind energy applications. The sonic method provides a more precise local measurement of stability while the bulk Richardson is a simpler, robust and cost-effective technique to implement in wind assessment campaigns. Using the sonic method as a benchmark, it is shown that to obtain reliable bulk Richardson measurements in onshore sites it is necessary to install one of the temperature sensors close to the ground where the temperature gradient is stronger.

The vertical wind profile and the turbulence intensity in the atmospheric boundary layer (ABL) are two of the main physics aspects driving wind energy production and turbine loads. The vertical wind profile is especially important since rotors are getting bigger and hub heights are getting higher, making it invaluable to know the wind speed at hub height. The vertical wind profile shape and turbulence intensity can directly influence wind turbine production but also wind turbine loads, affecting the wind turbine's lifetime. Despite the fact that the IEC standard (IEC61400-1 (ED4) 2019, 2019) specifies a power law vertical model independent of atmospheric stability to perform load calculations, the dependence of this and, in turn, the turbulence intensity with atmospheric stability is widely demonstrated (Emeis, 2013; Lange et al., 2004b; Peña and Hahmann, 2012). In addition several studies have demonstrated the impact of atmospheric stability on wind resource assessment (Lange et al., 2004a), wind turbine power curves and annual energy production (AEP) calculations (Martin et al., 2016; Schmidt et al., 2016); wind turbine loads (Kelly et al., 2014; Sathe et al., 2013) and wind turbine wakes (Abkar and Porté-Agel, 2015; Hansen et al., 2010; Machefaux et al., 2016). This is why the wind industry is developing models and methods to include the effect of atmospheric stability in the layout design and energy yield assessment. These methodologies and models require the characterisation of the probability distribution of atmospheric stability at each site. Therefore different methods and parameters are used to describe atmospheric stability without an industry-wide convention about which one is the most appropriate.

According to Monin and Obukhov similarity theory (MOST) (Foken, 2006; Monin and Obukhov, 1954), stability can be estimated in terms of the inverse of Obukhov length that can be calculated with vertical fluxes of heat and momentum obtained with the eddy covariance method. To obtain the necessary high-frequency measurements of wind speed vector components and temperature, sonic anemometers are used, which is why this calculation method is called the “sonic method”.

Another measure for stability is the Richardson number, which as Bardal et al. (2018) explains, according to Stull (1989) has several formulations: the flux Richardson number, gradient Richardson number and bulk Richardson number. The latter is based on one height wind speed measurement and two temperature measurements, one from the air at one height and the other from the ground or water surface.

In the wind energy context some studies have been done about how to measure the stability and their influence in the turbulence intensity and vertical wind profile. However, most of these studies have been carried out in offshore sites (Peña and Hahmann, 2012; Sanz Rodrigo et al., 2015; Sathe et al., 2011), finding relationships (Grachev and Fairall, 1997) between the Obukhov length and the Richardson bulk number that facilitate the characterisation of stability without the need of sonic anemometer. This is convenient, because although the sonic anemometer has many advantages (Cuerva et al., 2006), it adds complexity in terms of use and data management, and it increases the cost of the long-term site assessment campaigns.

For onshore sites there are few studies that analyse how to characterise atmospheric stability, and those that exist are on simple topography in coastal areas (Bardal et al., 2018).

Although the behaviour of wind flow over complex terrain is widely studied, as Finnigan et al. (2020) summarise, and discussed in recent publications about the influence of atmospheric stability in wind farms located in complex terrain (Han et al., 2018; Menke et al., 2019; Radünz et al., 2020, 2021), there are no references that analyse in detail how to characterise atmospheric stability according to different instrumentation requirements.

Measuring atmospheric stability in complex terrain has some challenges (compared to flat terrain): one of them is the fact that the MOST is developed for horizontally homogeneous and flat terrain, and in complex terrain vertical wind speed can be due to stability or sloping terrain. Therefore, vertical fluxes will be “contaminated” by terrain effects. This can be mitigated by using good measurement practices (data quality, coordinate systems and post-processing options) (Stiperski and Rotach, 2015).

This study presents atmospheric stability characterisation from one mountainous site obtained using two methods: the sonic method and the Richardson bulk number. Measurements of different heights have been used to see the influence of this parameter on the results.

The place used in this study meets the characteristics of a typical complex
terrain site for wind energy deployment. The 118

Special focus is given to explaining the post-processing methodologies to derive stability from raw data considering a fast-response sonic anemometer in a complex terrain.

Monin and Obukhov (M–O) (Monin and Obukhov, 1954) introduced
the Obukhov length

Table 1 shows the (Sorbjan and Grachev, 2010) stability classification,
proposing four regimes in stable conditions. This classification is also
followed by Sanz Rodrigo et al. (2015) assuming a symmetric classification in
the unstable range. Sanz Rodrigo et al. (2015) shift the
“extremely unstable and stable” regime limit to

Classification of atmospheric stability adapted from Sorbjan and Grachev (2010).

Using sonic anemometers and the eddy covariance technique, the Obukhov length can
be obtained. In this way, stability is evaluated locally based on turbulent
fluxes averaged over periods from 10

A sonic anemometer can be used in complex terrain to derive the local Obukhov length. Following the planar fit method of Wilczak et al. (2001), momentum fluxes should be calculated in the mean streamline plane and heat fluxes in the true vertical coordinate system. If the streamline plane can be known a priori, from a wind direction sector with uniform slope, the planar fit method can be used to infer the mounting tilt angle and correct for it to reduce the uncertainty on the vertical fluxes.

The bulk Richardson number

As Bardal et al. (2018) propose, the general empirical relations from
Businger et al. (1971) slightly modified by Dyer (1974) have been
used to relate

Alternatively

Classification of atmospheric stability (Mohan, 1998).

The MP5 mast is located (42

Alaiz elevation map, close-up of the test site and view from the upstream ridge to the north.

Besides the MP5 meteorological mast there are four other reference met masts (MP0,
MP1, MP3 and MP6), all of them 118

The test site started operating in 2009 with the site calibration
procedures. The first wind turbines were installed in the summer of 2011. The
standard configuration of each mast is designed for multi-megawatt wind
turbine testing and includes sonic and cup anemometer, wind vanes and
temperature–humidity measurements. Replicated cup anemometers are situated
2

The MP5 is a permanent 118

The instrumental set-up is compliant with IEC 61400-12-1 (IEC61400-12-1 (ED1) 2005-12, 2005), with MEASNET cup anemometer calibration (Measnet, 2009) and with ENAC accreditation according to UNE-EN ISO/IEC 17025.

The data acquisition system consists of a real-time controller CompactRIO from National Instruments with 128 MB DRAM and 2 GB storage embedded in a chassis in connection with eight modules of digital and analogical data acquisition, all connected to an Ethernet network.

The rate sample is 5

Wind rose of 10

Figure 2 shows the wind rose at the MP5 site, from the period between
July 2014 and June 2015. It presents a bidirectional wind climate, with
prevailing winds from the north-northwest sector (330–360, 32

In the present work, a 1-year period (1 July 2014 to 30 June 2015) is
analysed. Flux measurements from the sonic anemometer at 115.5, 75.5 and
39.5

Before calculating the stability parameter, all data are checked for data quality.

Data from conventional sensors (wind direction, relative humidity, air
pressure and temperature) have been processed following Brower (2012). This consists in checking the completeness of the collected data and
applying several tests (range, relational and trend). After filtering for
quality-control purposes, the conventional sensors provide horizontal wind
speed, direction, relative humidity, pressure and temperature
availabilities greater than 85

For sonic anemometer there are a lot of procedures (Aubinet et al., 2012) and test criteria for quality control of turbulent time series and studies about the impact of these procedures on the results (Stiperski and Rotach, 2015).

High-frequency raw data often contain impulse noise, that is, spikes, dropouts, constant values and noise. Spikes in raw data can be caused by instrumental problems, such as imprecise adjustment of the transducers of ultrasonic anemometer, insufficient electric power supply and electronic noise, as well as water contamination of the transducers, bird droppings, cobwebs, or rain drops and snowflakes in the path of the sonic anemometer.

Several spikes in wind speed have been detected in the raw sonic anemometer
data. Therefore, a de-spiking filter is applied based on the change in wind
speed from each data point to the next and taking into account the physical
limits according to sensor specifications. Data points are removed if they are
preceded and followed by changes exceeding the lowest 99

The operating principles of the sonic anemometer are described by different authors (Aubinet et al., 2012; Cuerva et al., 2003; Kaimal and Businger, 1963; Kaimal and Finnigan, 1994; Schotanus et al., 1983). The sonic anemometer output provides three wind components in an orthogonal axis system and sonic temperature. The relation between sonic temperature and absolute real temperature is given by Kaimal and Gaynor (1991).

High-frequency data from sonic anemometer have been processed to obtain
10

The main requirements for instruments and data acquisition systems used for
eddy covariance data are their response time to solve fluctuations up to
10

The transformation of high-frequency signals into means, variances and
covariances requires different steps (Aubinet et al., 2012; Stiperski and
Rotach, 2015); in this study the next steps have been proposed.

Quality control of raw data is explained in Sect. 4.1.

Coordinate rotation is the transformation of coordinate systems from the original axes based on the anemometer output to the streamline terrain-following system, based on the planar fit method (PFT) (Richiardone et al., 2008; Wilczak et al., 2001). Momentum fluxes and heat fluxes have been calculated with respect to the streamline terrain-following coordinate system. Figure 3 shows the steps to rotate the axes from mounting coordinates to streamline coordinates.

Variance and covariance computation applies the eddy covariance technique for
calculation of vertical turbulent fluxes (heat and momentum). It corresponds
to the calculation of the covariance of the fluctuations of the vertical
velocity with the quantity

Schematic description for the rotation process.

The MP5's sonic anemometers, at 115.5, 75.5 and 39.5

The 10

The MP5's sonic anemometers allow evaluation of stability based on the local Obukhov length at different heights. This will be the benchmark method since it is directly obtained from the measurements without introducing any assumptions or empirical relationships. The bulk Richardson number is evaluated as an alternative methodology since it follows easier instrumentation set-up and post-processing; for offshore sites it has presented good results (Sanz Rodrigo, 2011; Sanz Rodrigo et al., 2015) and for complex terrain sites it also gives meaningful results (Menke et al., 2019).

To obtain the stability parameter

In complex terrain, the hypothesis of a homogeneously horizontal surface layer is not fulfilled, so the applicability of Monin and Obukhov similarity theory (MOST) to complex terrain conditions is not obvious. This signifies that for the complex sites such as Alaiz the theory is not completely valid because the topography creates local variations in wind flow near the ground (Kaimal and Finnigan, 1994).

As was explained before, sonic anemometry is not routinely used in wind
energy, and bulk Richardson number

In the

With Eq. (3) the obtained

The study is divided into two parts: statistics of atmospheric stability with both methods (the Obukhov length and Richardson bulk) and comparison between both methods.

Atmospheric boundary layer (ABL) models used in wind farm design tools are
typically based on Monin–Obukhov theory. In stable conditions this
surface-layer theory is extended to the entire ABL by assuming local scaling
of turbulence characteristics through the stability parameter

In the study case, as was explained before, from the high-frequency
(20

In Fig. 4 the stability parameter

Probability distribution of

Figure 5 shows the distribution of atmospheric stability against wind speed at the MP5 measurement heights. The nine stability classes proposed in Table 1 are reduced to five, combining weakly unstable and stable classes with unstable and stable classes and very unstable and stable with extremely unstable and stable. Table 3 shows the classification used. For the three heights, the stable situations are slightly higher than the unstable ones, and there is an increase in neutral and stable conditions with increasing wind speeds; this is in accordance with the general knowledge that for strong wind speeds the atmosphere becomes neutrally stratified.

Distribution of atmospheric stability with wind speed based on

In accordance with Table 1, the five reduced stability classes are shown.

As mentioned before, a significant dependence of stability
distributions on height is observed. At higher levels, the stability distributions are
broader, and there are more frequent cases with very large and extreme
stability. This dependency of the stability distribution with height is
because

The diurnal cycle (see Fig. 6) presents unstable conditions developing from 09:00 to 15:00 UTC. The rest of the day is dominated by stable conditions, resulting in low turbulence intensities.

Distribution of atmospheric stability with hour based on

Figure 7 shows the evolution of stability throughout
the year. The stable side dominates during winter months, with unstable
conditions peaking between April and August where they take a

Monthly distribution of stability based on

The variation in atmospheric stability with wind direction is shown in
Fig. 8. Stable situations dominate in most of the directions except for the
northwest direction (330–350

Distribution of atmospheric stability with wind direction based on

Following the stability classification defined in Table 3, Figs. 9 and 10
present the dependency of wind shear (calculated as the wind speed ratio
between 118 and 40

Wind shear and turbulence intensity vs. sonic stability in
the MP5 337.5–22.5

Wind shear and turbulence intensity vs. sonic stability in
the MP5 157.5–202.5

For the three heights it is observed that, as is explained by Emeis (2013), in unstable situations the ground surface is warmer than the air above so there is a positive heat flux that causes more turbulence. This results in a convective well-mixed surface layer with small vertical gradients. On the other hand, lower turbulence and high shear wind profiles are associated with stable situations where turbulence is reduced due to a negative vertical heat flux.

Since sonic anemometers are not commonly used in wind resource assessment, an
alternative method to estimate the atmospheric stability is bulk Richardson
number. It is based on mean wind speed at height

The calculation of the bulk Richardson number is, in the present study, not
straightforward because of the lack of reliable sensors at the surface. The
lower air temperature is measured at 2

The MP5 mast has no measurements of surface temperature or near the ground.
Some authors in these circumstances either extrapolate the values to the
surface (

The values of the bulk Richardson number have been obtained over a period of
10

Figure 11 shows the distribution for the bulk Richardson number method. The
lower measurement level is varied between 2 and 38

Probability distribution of

The selection of temperature measurement heights has a great effect on the bulk Richardson number method, both in the exactitude and in the applicability of the method. To reduce uncertainties, the measurements should be made either with differential temperature sensors or with calibrated sensors and a sufficient vertical separation in order to reduce the influence of inaccuracies in the temperature measurements (Baker and Bowen, 1989; Brower, 2012).

Figure 12 shows the distribution of atmospheric stability against wind
speed. On the left side atmospheric stability is directly classified with the

Distribution of atmospheric stability with wind speed

In accordance with Table 2 the five reduced stability classes are shown.

Both distributions show a differentiated behaviour with fewer “very” unstable
and stable situations and a greater number of neutral observations in the case
of the classification with

Comparing the distribution of atmospheric stability against wind speed based
on the sonic method (Fig. 5) with the results obtained based on the

Table 5 presents a frequency of occurrence of stability classes with
concurrent data using different methods. This quantitative comparison shows
that taking the sonic method as a benchmark, it is observed that the bulk method,
when the Businger and Dyer functions are used to estimate the stability
parameter

Frequency of occurrence of stability classes.

Wind shear and turbulence intensity in each of the stability
classes. On the left is based on

Besides these methodological reasons, there are some physical causes of the differences found. One of these is that the Richardson bulk number represents a bulk average stability value instead a local measurement like the sonic method.

As is shown in Table 5, the stability description obtained with the bulk Richardson number does not match the sonic one. The ultimate goal of the stability characterisation is to provide good predictive power of turbulence intensity and shear at hub height. Thus in order to analyse it, Table 6 shows these values in each of the stability classes with both methods in the two main wind direction sectors in MP5. In comparison with the sonic method, the stability characterisation with the bulk Richardson number underestimates the wind shear (overestimating the turbulence intensity) for unstable situations in both sectors. For neutral and stable situations it depends on the wind sector.

In this work, a detailed data analysis focuses on how to estimate atmospheric
stability at a site with complex terrain. The Obukhov parameter

It is shown that the resulting stability depends on which method is chosen. The sonic method is taken as a benchmark because it is the only way of measuring local stability without the use of empirical functions or theoretical assumptions. However, this method requires working with accurate high-frequency data, rotating the measurements to align the coordinate system to the mean wind vector, which is reported to require special attention in complex terrain to guarantee that the mean streamline plane will be parallel to the terrain surface, to finally obtain turbulent fluxes using the eddy covariance technique.

According to the stability parameter

The seasonal and diurnal cycle is identified: in the winter and during the
hours between 17:00 and 8:00 UTC the stable side dominates, while between April and
August and between 9:00 and 15:00 UTC unstable conditions are found to be more
frequent. Winds from the predominant northwest direction (330–350

For the three heights, and in the two predominant sectors, it is observed that in unstable situations the ground surface is warmer than the air above, so there is a positive heat flux that causes more turbulence. This results in a convective well-mixed surface layer with small vertical gradients. On the other hand, lower turbulence and high-shear wind profiles are associated with stable situations where turbulence is reduced due to a negative vertical heat flux.

As an alternative to characterise stability, the bulk Richardson number is
explored, which requires a minimum level of instrumentation, mean wind speed at
height

On the MP5 there is not a surface temperature sensor, so the 2

In summary the sonic method is more costly and complex, but, in this study, it
shows results in accordance with the general atmospheric boundary layer
knowledge, so we recommend it as a first option to obtain a local measurement of
atmospheric stability that can be associated with a certain height above the
ground and in consequence provide good predictive power of turbulence
intensity and wind shear at hub height. For the bulk Richardson number, based
in the references read, there is not a standard methodology for characterising
atmospheric stability using this method, and there are many different
approximations. Furthermore, empirical relations to relate

Data belong to CENER, and they can be obtained from the author upon request.

EC is the principal investigator of the project and coordinated the activities and the preparation of the paper. DP aided in the formulation of the scope of the work, FB assisted in the measurement post-processing and the methodology was devised by EC, JS and DP. The stability analysis and visualisation was performed by EC. EC wrote the original draft, AG helped with the composition of the paper and EC, JSR, FB, DP and AG contributed, reviewed and edited the final paper.

The contact author has declared that neither they nor their co-authors have any competing interests.

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

The authors are grateful to CENER for sharing the MP5 database with us during the course of this research.

This paper was edited by Jakob Mann and reviewed by Llorenç Lledó and one anonymous referee.