Validation of WAsP Engineering for site-specifi c wind conditions assessment

Mas

ter

Thes

is

Georgios MandrekasMEK-FM-EP 2010-01January 2010

Preface This report is the result of the work carried out by Georgios G. Mandrekas, student at the Technical University of Denmark (DTU), for the fulfillment of the requirements of the M.Sc. programme in Wind Energy. The project has been developed during the period July 2009 to January 2010 in cooperation with the Fluid Mechanics Section of the Mechanical Engineering Department (MEK) at DTU and the Risø National Laboratory for Sustainable Energy. The supervision has been undertaken by the DTU Professor Kurt S. Hansen, the Risø Senior Scientist Morten Nielsen and the Risø Scientist Jacob B. Jørgensen. The author would like to give many thanks to his supervisors for the useful guidance and valuable support which they were always willing to provide through the past six months that the project was carried out.

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Abstract In the present M.Sc. project, it is made a validation of WAsP Engineering 2.0 software with the aim to come up with conclusions on the use of the software tool for site-specific wind conditions assessment. Two different case studies are considered. The first one is made on the Hjardemål site, representing a moderately complex terrain type as it can be described as a 30° escarpment over a generally flat landscape. The second case study is the Bolund island, which represents a complex terrain type as it contains an almost vertical escarpment as well as rapidly changing roughness length. Certain methodology has been used for the measurements processing as well as for each model’s configuration. The flow simulation results are compared with measurements and the resulted errors are reported. Useful conclusions are finally derived in respect to the uncertainty fallible in the evaluation of the wind resources by a linearized model such as WAsP Engineering.

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Contents List of Figures .................................................................................................................................5 List of Tables...................................................................................................................................6 1 Introduction .............................................................................................................................7

1.1 Wind energy ....................................................................................................................7 1.2 Site assessment and related standards .............................................................................7 1.3 Scope of the project.........................................................................................................8

2 Theoretical background.........................................................................................................10 2.1 Mathematical description of wind speed.......................................................................10 2.2 Variation of wind speed by the height ..........................................................................10 2.3 Turbulence.....................................................................................................................11 2.4 Thermal effects on wind conditions ..............................................................................12

3 Introduction to WAsP Engineering .......................................................................................14 3.1 Linearized flow model ..................................................................................................14 3.2 Turbulence model..........................................................................................................15 3.3 Extreme winds model....................................................................................................16 3.4 Inputs-Outputs-Limitations ...........................................................................................16

4 The Hjardemål case study .....................................................................................................17 4.1 Site description and instrumentation .............................................................................17 4.2 Measurement data processing .......................................................................................19 4.3 WEng model..................................................................................................................21

4.3.1 Model configuration..............................................................................................21 Map....................................................................................................................................21 Roughness length ..............................................................................................................21 Resolution..........................................................................................................................22

4.3.2 Results ...................................................................................................................23 Horizontal speed-up ..........................................................................................................24 Vertical wind profiles........................................................................................................26 Turbulence intensity ..........................................................................................................29

5 The Bolund case study ..........................................................................................................31 5.1 Site description and instrumentation .............................................................................31 5.2 Simulation cases............................................................................................................32 5.3 WEng model..................................................................................................................34

5.3.1 Model configuration..............................................................................................34 5.3.2 Results ...................................................................................................................35

Horizontal speed-up ..........................................................................................................36 Flow inclination.................................................................................................................38 Vertical wind profiles........................................................................................................39 Turbulent kinetic energy ...................................................................................................40

6 Conclusions ...........................................................................................................................42 References .....................................................................................................................................44 A1 - Matlab program for the process of Hjardemål measurements ..............................................45

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List of Figures Figure 1: Diagram of cooperation between manufacturer and developer of a W/T project. .........................8 Figure 2: Typical wind speed time series. (Source: ref. [10]) .....................................................................11 Figure 3: Wind profile in stable, neutral and unstable air. (Source: ref. [4]) ..............................................13 Figure 4: Qualitative sketch of the action of a ridge on the turbulence according to the RDT model. The fluctuations in the u-component of the turbulence are attenuated, as seen from the u-spectrum (red curve), the v-fluctuations are not changed much (green curve), while the w-fluctuations are amplified (blue curve). (Source: ref. [6])..............................................................................................................................15 Figure 5: Hjardemål site view (a) (Source: ref. [5]) ....................................................................................17 Figure 6: Hjardemål site view (b) (Source: ref. [5])....................................................................................17 Figure 7: Hjardemål site view (c) (Source: ref. [5]) ....................................................................................17 Figure 8: Met. mast instrumentation. (Source: ref. [5]) ..............................................................................18 Figure 9: Terrain profile (stars indicate the instruments listed in Table 1). (Source: ref. [5]) ....................18 Figure 10: Model domain with the elevation and the sites locations. .........................................................21 Figure 11: Absolute deviation between measured and simulated wind speed values in function with the resolution for masts 7, 8, and 10 at 24m a.g.l..............................................................................................23 Figure 12: Absolute deviation between measured and simulated TI values in function with the resolution for masts 1, 7, 8, and 10 at 24m a.g.l...........................................................................................................23 Figure 13: Speed-up at 24m a.g.l. (forward flow). ......................................................................................25 Figure 14: Speed-up at 10m a.g.l. (forward flow). ......................................................................................25 Figure 15: Speed-up at 10m a.g.l. (backward flow). ...................................................................................26 Figure 16: Vertical wind profile for Mast 1. ...............................................................................................27 Figure 17: Vertical wind profile for Mast 7. ...............................................................................................27 Figure 18: Vertical wind profile for Mast 8. ...............................................................................................28 Figure 19: Vertical wind profile for Mast 10. .............................................................................................28 Figure 20: Turbulence intensities at 24m a.g.l. (forward flow)...................................................................29 Figure 21: Turbulence intensities at 10m a.g.l. (forward flow)...................................................................29 Figure 22: Turbulence intensities at 10m a.g.l. (backward flow)................................................................30 Figure 23: View of Bolund taken from the 125m high measuring mast at Risø DTU (Source: ref. [14]). .31 Figure 24: The Bolund orography and the positions of the ten masts (Source: ref. [14]). ..........................32 Figure 25: View from upstream of the escarpment (Line B, 270°). Source: ref. [14].................................32 Figure 26: View from upstream of the escarpment (Line A, 239°). Source: ref. [14] ................................32 Figure 27: Expanded map in WEng - Roughness grid. ...............................................................................34 Figure 28: Expanded map in WEng– Elevation grid...................................................................................34 Figure 29: WEng map - Site locations. .......................................................................................................35 Figure 30: WEng map - Terrain inclination grid.........................................................................................35 Figure 31: Horizontal speed-up (270° flow case, mast line B). ..................................................................36 Figure 32: Horizontal speed-up (239° flow case, mast line A). ..................................................................37 Figure 33: Horizontal speed-up (90° flow case, mast line B). ....................................................................37 Figure 34: Flow inclination (270° flow case, mast line B)..........................................................................38 Figure 35: Flow inclination (239° flow case, mast line A). ........................................................................38 Figure 36: Flow inclination (90° flow case, mast line B)............................................................................39 Figure 37: Vertical speed-up. 270° flow case. M7 (left), M6 (right). .........................................................39 Figure 38: Vertical speed-up. 270° flow case. M3 (left), M8 (right). .........................................................40 Figure 39: TKE (270° flow case, mast line B). ...........................................................................................40 Figure 40: TKE (239° flow case, mast line A)............................................................................................41 Figure 41: TKE (90° flow case, mast line B). .............................................................................................41

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List of Tables Table 1: Location of different instruments..................................................................................................18 Table 2: Height position of instruments on different ..................................................................................18 Table 3: Measurements runs and respective time lengths ...........................................................................19 Table 4: Runs characteristics (forward flow) ..............................................................................................24 Table 5: Runs characteristics (backward flow) ...........................................................................................24 Table 6: Deviations of horizontal wind speeds at 24m a.g.l. (see Fig. 13). ................................................25 Table 7: Deviations of horizontal wind speeds at 10m a.g.l. (see Fig. 14). ................................................25 Table 8: Deviations of horizontal wind speeds at 10m a.g.l. for the backward flow (see Fig. 15). ............26 Table 9: Deviations of wind speeds at Mast 1 (forward flow, see Figure 16).............................................27 Table 10: Deviations of wind speeds at Mast 7 (forward flow, see Figure 17)...........................................27 Table 11: Deviations of wind speeds at Mast 8 (forward flow, see Figure 18)...........................................28 Table 12: Deviations of wind speeds at Mast 10 (forward flow, see Figure 19).........................................28 Table 13: Deviations of turbulence intensity at 24m a.g.l. (forward flow, see Figure 20)..........................29 Table 14: Deviations of turbulence intensity at 10m a.g.l. (forward flow, see Figure 21)..........................29 Table 15: Deviations of turbulence intensity at 10m a.g.l. (backward flow, see Figure 22).......................30 Table 16: The positions of the masts (Source: ref. [14]). ............................................................................32 Table 17: An overview of the instrumentation. The heights are only approximate. (Source: ref. [14]). ....32 Table 18: Reference wind speeds for the modeling (Source: ref. [14]). The reference wind speeds used in the WEng model are underlined with blue. (s: total wind velocity, u*0: friction velocity at the reference mast, TKE: Turbulent Kinetic Energy) .......................................................................................................33

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1 Introduction

1.1 Wind energy The kinetic energy of the wind derives from the solar radiation and about 2% of the solar energy which falls on the planet is converted to wind energy. The wind power of the whole earth is estimated at about 36109 MW. For instance, the energy demands of U.S.A. are almost only the 10% of the wind energy available there. Hence, it can be seen that the wind is a very powerful energy resource. The power of an air stream is proportional to its density and the cube of its velocity. So, by comparing an air stream with a water stream which have the same velocities and cross-section areas, it seems that the air stream contains almost 800 times less energy than the respective water stream. Thus, the wind energy is a ‘sparse’ or ‘mild’ energy resource, i.e. the energy quantity per time unit which may be captured at a squared meter of a surface hit by the wind is small. For example, a 9.5 m/s wind has a power of 500 W/m2, while a wind turbine, at the best case, can capture the 48% of this power. This causes the need for the construction of units with big dimensions. The modern technology anticipates quite well with this disadvantage by increasing the size of the wind turbines and makes wind energy economically competent against the conventional energy resources. The wind power development the latest years has led to the establishment of a specific wind turbine type in the related wind energy projects. This type is the horizontal axis wind turbine (HAWT) with 3 blades.

1.2 Site assessment and related standards The expression ‘site assessment’ is defined, according to the common use in wind energy context, as acronym for ‘assessment of site specific wind conditions’. These are necessary for the design of a wind turbine project. As shown in Figure 1, a very crucial cooperation between the wind turbine manufacturer and the developer of a W/T project is necessary in order for the project to be approved both by the funding institution (bank etc.) and by the approving energy authority. Guarantees must be given for the expected annual energy production of the wind turbine installation as well as for the structural safety and lifetime of the wind turbines. The developer is responsible to provide the manufacturer with the evaluated wind conditions that the latter will need to use as inputs in the design of the wind turbines.

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Figure 1: Diagram of cooperation between manufacturer

and developer of a W/T project. Widely accepted practices are usually codified by engineering standards. Standards create the framework for business contracts and legal disputes and replace long design reports which might not be read or fully understood by the decision makers. The rules in standards reflect reality, but they are deliberately simplified and often slightly conservative. There are several standards related to wind energy projects. The present study has been based on the recommendations of the following two standards: ‘61400-1’ by IEC [11] The International Electrotechnical Commission (IEC) provides standards for all kinds of electrical equipment. Among these is the IEC 61400-1 standard for wind turbine safety. This standard covers topics like structural integrity, turbine control, electrical safety, and environmental conditions. In this study, however, the wind-related aspects of the standard are of concern. The IEC 61400-1 approach is first to classify turbines and then to verify that the site-specific conditions are within the design limits of the turbine class of the selected turbine. As already mentioned, the turbine classification is the responsibility of the manufacturer, and site assessment is the responsibility of the project developer.

’Evaluation of site specific wind conditions’ by MEASNET [12] The international Measuring Network of Wind Energy Institutes (MEASNET) is a co-operation of institutes which are engaged in the field of wind energy and publish standards and recommendations on methodologies for high quality measurements. Recently, they have published the standard mentioned above which is actually a summary of recommendations for those who perform site assessment. The standard is aligned with the IEC 61400-1 standard. Among its suggestions, it refers to the methods that should be used for the acquisition and process of the meteorological measurements, the computer modeling of the wind conditions, and the method of reporting.

1.3 Scope of the project WAsP and WAsP Engineering are software tools which aim to evaluate the wind resources for a specific wind turbine site. WAsP is used for the calculation of the annual energy production of a wind farm, while WAsP Engineering is used for the estimation of extreme wind conditions, wind shear and turbulence that are necessary as inputs in the structural design of the wind turbine components. The aim of this project is to validate WAsP Engineering (WEng) for site specific wind conditions assessment on different types of terrain. The following questions should have been answered by the end of the project:

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Which meteorological measurements are necessary to obtain for the better evaluation of

the wind conditions at the candidate wind turbine site?

How should the measurements be processed for validation?

Which are the capabilities/limitations of WAsP Engineering?

How the WAsP Engineering model configuration should be done?

Which are the uncertainties of the WAsP Engineering modeling in different terrain types?

Two terrain types representing moderately and complex terrain have been selected for the validation procedure: Hjardemål (30° maximum slope-moderately complex terrain)

Bolund (~90° maximum slope - scaled complex terrain)

The study focuses on the modeling of the mean wind flow and turbulence, rather than the prediction of the extreme wind conditions.

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2 Theoretical background Most of the theory presented in this chapter has been found in reference [1]. The following is only a brief introduction to the basics from wind engineering theory.

2.1 Mathematical description of wind speed To describe the wind speed mathematically, the use of Cartesian coordinates can be used. Defining that the x-axis is in the direction of the mean wind speed, the y-axis in the lateral direction and the z-axis positive upwards, the velocities at a given time t are given by: in the longitudinal direction ( ) ( , , , )U z u x y z t (Eq. 1) in the lateral direction ( , , , )v x y z t (Eq. 2) in the vertical direction ( , , , )w x y z t (Eq. 3) where the mean wind velocity U(z) depends only on the height z above ground. u, v, w describe the fluctuating part of the wind field and can be treated mathematically as stationary, stochastic processes with a zero mean value.

2.2 Variation of wind speed by the height The problem of expressing the vertical variation of the magnitude of the horizontal wind velocity by a specific law is an issue for many studies. Often the choice between the power and the logarithmic law is made arbitrarily, as there are arguments versus and against both laws. The expressions that are currently used in the bibliography for the wind speed distribution in the surface layer are given below:

Power law a

z

z

U

U

2

1

2

1 (Eq. 4)

Logarithmic law

0*

ln1

z

z

ku

U (Eq. 5)

where U, U1, U2 the horizontal component of the wind velocity at height z, z1, and z2 respectively, u* the friction velocity, a the exponential factor of the power law, k the Von Karman constant, and z0 the roughness length. Usually in meteorological problems, the power law is used, due to its easier mathematical treatment. The value of the exponential factor a is only a function of the roughness length. It has been found that in the first meters of the atmospheric boundary layer, the wind speed distribution follows the power law, while in bigger heights, the logarithmic law gives a more accurate expression of the distribution. Furthermore, the problem of using the logarithmic law is that the exact value of the friction velocity and the Von Karman constant must be known. The

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approximate computation of these values weakens the strength of the precise mathematical expression of the wind speed distribution by the logarithmic law. Hence, this results to an approximation error of equal order of magnitude to that which derives from the use of the power law. Furthermore, the use of the power law has the advantage of speed and flexibility in fitting the vertical distribution into a group of distributions of known surfaces which have been studied before. The logarithmic profile as given by Eq. 5 only applies close to the ground, i.e. 50-100 m above terrain. In the so-called corrected logarithmic profile, the height of the boundary layer is also taken into account. At high wind velocities, i.e. more than 20 m/s, the corrected logarithmic profile gives accurate results up to 300 m above ground.

2.3 Turbulence [1] Wind velocity is described by mean velocity U and turbulence components u, v, and w, as stated in Eqs. 1, 2, 3. In Figure 2, a typical wind speed time series is shown.

Figure 2: Typical wind speed time series. (Source: ref. [10])

There are several means to describe the three turbulence components, such as their standard deviation, time and integral length scales, power spectral density functions that define the frequency distribution and normalized co-spectra that specify the spatial correlation. If it is assumed that the terrain is homogeneous, the flow will be also horizontally homogeneous, and in that way its statistical properties do not change in the horizontal plane. Standard deviations σu, σv, and σw for the turbulence components will therefore only depend on the height z above ground. The three standard deviations are almost zero at geostrophic wind heights, but experimental results, e.g. Davenport (1967), Harris (1970), and Armitt (1976), show that the three standard deviations usually decrease by height very slowly up to the heights of common structures. Armitt (1976) states that the standard deviations are almost constant up to approximately half the height of the internal boundary layer. Up to a height of about 100-200 m above homogeneous terrain, the standard deviations of the three turbulence components are approximately:

*Auu uv 75.0 uw 5.0 (Eq. 6)

where the constant 5.2A if z0=0.05 m and 8.1A if z0=0.3 m. The turbulence intensity uI for the longitudinal turbulence component u is defined as:

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UI u

u

(Eq. 7)

where u is the standard deviation of the turbulence component u and U is the mean wind

velocity. The turbulence intensities for the lateral and the vertical turbulence components can be found similarly. Up to 100-200 m above ground, it is usually reasonable to assume that the turbulence components distribution is normal with a zero mean value and standard deviations as given by Eq. 6. [1]

2.4 Thermal effects on wind conditions [1] In addition to the mechanically generated wind conditions, the thermal state of the atmosphere may significantly influence the actual mean wind velocity and turbulence components. These thermal effects have to be taken into account if the wind speed is less than approximately 10 m/s (Armitt, 1976). At higher wind speeds, the mechanical cause of the generated wind conditions prevails. It is considered for practical purposes that the clean air is transparent to the radiation which is emitted either from the ground or from the sun. Close to the ground, i.e. up to the first 10 meters, there is an effective heat transfer between the air and the ground surface. The clean air may be assumed to be heated or cooled by the ground with convection rather than radiation. This assumption is mentioned here in order to help in the understanding of the three basic thermal regimes that may occur in a homogeneous boundary layer, as described below: Stable

An atmosphere with a constant temperature is stable. If the temperature is increasing by height, it is likewise shown that the atmosphere is even more stable and air mixing is prevented. Stable conditions are typically found in a cloudless sky at night, when the ground surface is cooled down by radiation and therefore also the lower air layers. This phenomenon is called inversion. In stable conditions, strong wind shear and small eddies characterize the wind flow.

Unstable If the temperature decreases significantly by height, wind conditions are unstable. A mass of air which is moved upwards will find itself surrounded by heavier air and will probably move even higher. This phenomenon is called convection and causes significant air mixing. Typically, it occurs when the sun heats the ground surface, increasing the temperature in the lower part of the atmosphere in relation to higher layers. In unstable conditions, the flow is characterized by large turbulent eddies.

Neutral Between the stable and the unstable conditions, there is a neutral state characterized by equilibrium of the mass of air independently its position, though only if there is no heat exchange with the environment. It follows then that the neutral state of the atmosphere corresponds to a moderate decrease of the air temperature with height. The flow can be characterized by the combination of wind shear and no convection. In the neutral boundary layer, the heat flux is almost zero and the wind velocities tend to be very high close to the ground, therefore, these wind conditions are considered as ideal.

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A dry atmosphere is in a neutral state when the temperature decreases upwards at 1° per 100 m. If the decrease rate is quicker, the atmosphere becomes unstable, and if it is slower or even the temperature increases upwards, the atmosphere becomes stable [1]. The influence of the thermal state of the atmosphere on the wind profile may be observed in Figure 3.

Figure 3: Wind profile in stable, neutral and unstable air. (Source: ref. [4])

Ideal atmospheric boundary layer regimes, i.e. stationary neutral, convective (unstable), or stable boundary layers, are difficult to find in the nature. Usually, the atmospheric boundary layer is a mixture of all types of stability conditions. In this study whenever it has been necessary to distinguish the different atmospheric stability conditions, the bulk Richardson number Rib has been used as a measure. It can be obtained from the temperature difference and velocity measurements. This approach is chosen since it seems to be the most robust and reliable. The bulk Richardson number is given by the following equation:

2uT

zzC

gTg

Rip

b

(Eq. 8)

where T is the absolute temperature, g is the acceleration of gravity, g/Cp = 0.0098 K/m is the adiabatic lapse rate, ΔT is the difference of the potential temperatures measured at two heights with height difference Δz, and Δu is the corresponding difference of the wind speeds. Rib is positive for stable stratification, negative for unstable stratification, and zero for neutral stratification.

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3 Introduction to WAsP Engineering In this chapter, it is given a brief description of the models behind WAsP Engineering, the assumptions that have been made, the applications and the limitations of the program. A more detailed and analytical description of the software can be found in references [6], [7], [8], and [9]. [6] WAsP Engineering is a software tool for estimating extreme winds, shears, flow angles, wind profiles, and turbulence over moderately complex terrain. WAsP Engineering has its focus on aspects of the wind that generate loads on wind turbines. It complements the WAsP program (Wind Atlas Analysis and Application Program), which has its primary focus on estimating the wind energy resource. Both programs have been developed at Risø National Laboratory of Denmark. The wind properties that are treated in WAsP Engineering are:

1. Wind shears and wind profiles. Strong mean wind shears (large differences of the mean wind speed over the rotor) give large fluctuating loads and consequently fatigue on wind turbine blades, because the blades move through areas of varying wind speed.

2. Turbulence. Turbulence (gusts of all sizes and shapes) causes dynamic loads on various

civil engineering structures, including wind turbines. The strength of the turbulence varies from place to place. Over land the turbulence is more intense than over the sea. Also the hills affect the structure of turbulence.

3. Extreme wind speeds, e.g. the 50 year wind. If a wind turbine is well situated on a hill the

mean wind speed and thereby the energy production can be increased significantly compared to that over flat terrain. Unfortunately, the 50 year wind will increase correspondingly, maybe calling for increased strength of the wings or other parts of the turbine.

3.1 Linearized flow model “Within the concept of linearized flow models originally introduced by Jackson and Hunt (1975), Troen and de Baas (1986) developed a relatively simple model for neutrally stable flow over hilly terrain. The model was later named LINCOM, an acronym for LINearized COMputation. The base of this version of the code, giving the influence of the topography on the flow of a neutrally stratified atmosphere, was later extended with a model for the influence of varying surface roughness also over water (Astrup et al. 1997, Astrup and Larsen 1999, Astrup, Larsen, Rathmann and Madsen 1999). Finally, the model has also been extended to calculate spatial derivatives of the mean wind field, such as the vertical shear zU , which is used in the turbulence modeling. LINCOM is based on an analytical solution in Fourier space to a set of linear equations derived from the normal nonlinear mass and momentum equations for incompressible fluid flows. The

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linear equations describe the perturbations in velocity and pressure which the real terrain induces in an equilibrium flow corresponding to a flat terrain with uniform surface roughness. The perturbations caused by horizontal gradients in ground elevation and surface roughness are determined separately and added as a first order approximation to the combined perturbation.”

3.2 Turbulence model “The modeling of the turbulence structure is divided into two parts: Orography and roughness variations. For the former rapid distortion theory (RDT) is used. Effects of both on the turbulence are treated as perturbations to the flat and homogeneous terrain turbulence model of Mann (1994), which encompasses many well known properties of atmospheric surface layer turbulence. To simplify the RDT equations various approximations are applied (Mann 2000), and although the results have been tested against the Askervein data, the limit of applicability in terms of the complexity of the landscape remains to be fully understood. An illustration of the modification of the turbulence spectra is shown in Figure 4.

Figure 4: Qualitative sketch of the action of a ridge on the turbulence according to the RDT model. The fluctuations in the u-component of the turbulence are attenuated, as seen from the u-spectrum (red curve), the v-fluctuations are not changed much (green curve), while the w-fluctuations are amplified (blue curve). (Source: ref. [6])

The modeling of turbulence changes due to roughness variations is not limited to the outer layer and should apply all the way down to the roughness sub-layer which is very close to the ground. The flow disturbances produced by roughness changes are by nature viscous and thus much “slower” than those due to RDT. It is used and modified the idea that eddies respond to roughness changes in the order of “the eddy turn-over time scale” (Panofsky, Larko, Lipschutz, Stone, Bradley, Bowen and Højstrup 1982, Højstrup 1981). A consequence of this is that the low frequency end of the spectrum responds very slowly to roughness changes while small eddies quickly get in equilibrium with the underlying surface. The basic model result is the so-called spectral tensor (Mann 1994). From this mathematical quantity more familiar statistics, such as spectra, cross-spectra, variances, turbulence intensities and coherences, can be derived. The calculation does not use information about the landscape directly, but indirectly through the mean flow field calculated by LINCOM.”[6]

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3.3 Extreme winds model WAsP Engineering operates with: Observed extreme-wind climates Predicted extreme-wind climates at turbine sites Regional extreme-wind climates for standard terrain

The calculations are supported by the combination of the flow model, Gumbel statistics, and the geostrophic drag law, also used by WAsP. Local extreme-wind data are preferred, but when these are unavailable, users have free access to a database of regional extreme-wind climates by NCEP/NCAR reanalysis data.

3.4 Inputs-Outputs-Limitations The user must firstly introduce the map of the area under assessment with the specified orography, roughness length, and resolution. Then the site locations and respective heights have to defined. Three types of input winds may be given: Measured

Measured wind speed magnitude and direction angle is given in this case together with the measurement location and height.

Geostrophic The geostrophic wind is the wind high above the ground where orography has no influence. The geostrophic wind is uniform over large areas (many kilometers) and results from a balance between the pressure gradient and the Coriolis force-parallel to isobars.

Reduced geostrophic The reduced geostrophic wind is the wind over ideally flat and homogeneous landscape. The ideal landscape has a roughness length specified by the user and the wind speed is given at a user-defined height. This may be used to ‘translate’ winds from nearby (ideally flat) airport measurements to winds in a complex terrain.

The outputs from WAsP Engineering as already mentioned consist of results on the mean wind flow (magnitude of wind speed components, direction and tilt angles), as well as turbulence (standard deviation of wind speed components, spectra) and extreme winds. All outputs are also given in the context of the IEC requirements for site assessment. The main limitation of the model comes from the fact that neutral state of the atmosphere is assumed. This can be an important constraint in cases of moderate wind velocities over the sea, where stable stratification can suppress turbulence. Also at low wind speeds both stable and unstable atmospheric stratification may change both the mean flow and the turbulence and hence the structural loads in a big extent. A characteristic example of this is a steel chimney, which may experience the largest dynamic loads at light stably stratified (turbulence free) winds, where vortex shedding occurs. Furthermore, the model assumes that the flow is always parallel to the surface (does not account for flow separation). Therefore, it is limited to moderately complex terrain, with surface inclination angles up to 20°.

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4 The Hjardemål case study The Hjardemål site is the one of the two case studies of the present project and it is a good representative of the category of moderately complex terrain sites.

4.1 Site description and instrumentation The site and the instrumentation are described in detail in the official data report [5]. The Hjardemål experiment was conducted in September and October 1989 at a site near Hjardemål in Northern Jutland, Denmark. The site is generally flat rural terrain. An escarpment crosses the landscape with the shape of a 30° ramp raising about 16 m from the old, flat sea floor to a wide plateau, which is almost flat. At the place where the experiment took place the escarpment is almost linear running approximately from NW to SE (332°).

Figure 5: Hjardemål site view (a)

(Source: ref. [5])

Figure 6: Hjardemål site view (b)

(Source: ref. [5])

Figure 7: Hjardemål site view (c) (Source: ref. [5])

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Figure 8: Met. mast instrumentation. (Source: ref. [5])

Figure 9: Terrain profile (stars indicate the instruments listed in Table 1). (Source: ref. [5])

Table 1: Location of different

instruments (see Figure 9). (Source: ref. [5])

Table 2: Height position of

instruments on different masts. (Source: ref. [5])

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“The experiment was conducted shortly after the fields had been harvested, but not yet ploughed; hence the soil was mostly bare. Hedges on the low side of the escarpment running along 236°, divide the landscape into long strips of fields for different use. The mast array was placed midway between two of these hedges with 40 m distance to either of the hedges. Thus the array was orientated along 236°, which is close to being perpendicular to the escarpment (242°).”[4] A mast line of 700 m was constructed with the furthest upstream mast at 400 m from the escarpment. Eleven measuring masts were erected as shown in Figure 8. In Table 1 and Table 2, the x-locations of the masts as well as the height of the placed instruments are cited.

4.2 Measurement data processing The data provided included 21 runs with 1-min averaged records. The time length of each run varies from 30 min to 604 min. The original sampling rate was 10 Hz for sonic anemometer channels and 2 Hz for the cup anemometer and wind vanes signals. In Table 3, a list of the runs provided and the respective time lengths is given.

Run ID Length (min) Run ID Length (min) 14 63 29 105 16 30 30 215 17 127 31 560 18 333 36 78 20 300 37 161 21 224 38 180 22 88 40 225 23 155 41 222 26 100 42 150 27 160 46 124 28 604

Table 3: Measurements runs and respective time lengths It must be noticed that many data were erroneous and some of them were missing for specific masts. In particular, data from Masts 9, 10, and 11 for Run 17 and Run 46 are missing. Furthermore, it has been found that cup anemometer measurements at 24 m at Mast 1 for Run 18, 21, and 22 are erroneous. A program in Matlab was made to facilitate the data browsing. Using the program, periods of stationary meteorological conditions, favorable wind directions and neutral stability can be selected. In particular, the user defines the following parameters in the program: Required number of continuous measurements (equivalent to recording time in minutes) Desired wind direction ± certain deviation angle Required standard deviation of the wind direction of the set Required standard deviation of the wind speed of the set Bin size for wind speeds categorization

The program browse all different Runs and finds all sets of continuous measurements with the required wind direction and respective deviation (sector) that fulfill the requirements for the standard deviations. For the selected sets, the mean wind speed and direction are given in order to be used as reference inputs in WAsP Engineering. Since, in some cases, many such reference

20

inputs derive, the wind speeds are categorized in bins and only one bin-representative value is selected. The bulk Richardson number which gives information about the atmospheric stability (as given by Eq. 8) is also given in the program results. The proper definition of the aforementioned parameters must be made in order to get measurements that can actually be used for comparison with the simulation results in WAsP Engineering. Given that the distance between the furthest upstream mast and the furthest downstream mast is 700 m, it is assumed that the selection of at minimum 15 continuous records (15 minutes) is sufficient. A maximum of 3.5° is defined for the standard deviation of the wind direction of the set, and a respective maximum of 0.5 m/s for the wind speed standard deviation. Hence, stationary meteorological conditions are ensured to count for the steady-state assumption of WAsP Engineering. Since the mean and the standard deviation values for each ω min period are actually derived from pre-processed data sets, they have to be calculated according to the following equations [13]:

min1

1 kN

kk

X XN (Eq. 9)

2 2min min

1

11

1

kN

S k k Sk S

N X X NN N

(Eq. 10)

where Nk is the number of pre-processed data sets within a ω min period Xk is the parameter averaged over pre-processing time period Xωmin is the parameter averaged over ω min Ns is the number of data samples of pre-processed data sets σk is the standard deviation of pre-processed parameter σωmin is the standard deviation of pre-processed parameter averaged over ω min In the present case the period ω is equal to 15 minutes. The number of data samples Ns of pre-processed data sets is found by using the known sampling rate (2 Hz for cup anemometers and wind vanes and 10 Hz for the sonic anemometers) and the known averaging period Ts (60 sec). Hence, 2 60 120S S SN f T for the cup anemometers and the wind vanes and

10 60 600S S SN f T for the sonic anemometers.

For the calculation of the mean and the standard deviation of the wind direction angles, Equations 13 and 14 have been used:

(cos( ))c mean X (Eq. 11) (sin( ))s mean X (Eq. 12)

1tans

X meanc

(Eq. 13)

2 21X s c (Eq. 14)

where

21

X is a vector of direction angles X is the mean value of X

X is the standard deviation of X

Finally, it must be noticed that the wind directions have been given uncorrected (aligned to an arbitrary object in the landscape). Therefore, in order to get the correct meteorological directions, 33° have been subtracted from the readings.

4.3 WEng model

4.3.1 Model configuration

Map

The map contains 252 contour lines with heights varying from 0.3 to 22.7 m. The domain extends from -800 to 800 m in x- direction and from -500 to 500 m in y-direction. Met.Mast 7 is positioned at (0, 0). Considering that 242° is the direction which is perpendicular to the escarpment, 28° (270-242) must be added to the wind direction value before this is inserted in the WAsP Engineering model.

Figure 10: Model domain with the elevation and the sites locations.

Roughness length

The condition of the farms is briefly described in section 4.1 (which is found in the experiment’s report [4]). It is reported that ‘the experiment was conducted shortly after the fields had been harvested, but not yet ploughed and the soil was mostly bare’. This also confirmed by photographs of the site. However, a detailed description of the surface roughness at the area giving any particular variations of the roughness and the exact positions of the hedges and obstacles was not available. Therefore, the roughness length is only given a uniform value in the map for the whole domain.

22

In order to come up with a uniform value for the roughness, the measurements of the furthest upstream meteorological mast (M1) have been used. The measured vertical wind profile can be used to fit in a logarithmic profile and extract the corresponding roughness length, as given by Eq.5. Various wind directions were selected; however, few could give reliable results. Some of them are giving high or negative values of the bulk Richardson number implying no-neutral atmospheric conditions. Other wind directions give bad logarithmic fits (big norms of residuals) which is caused by the presence of hedges and the influence of the escarpment (for wind directions vertical to the escarpment line). Clean results are obtained for Run 14, for a wind direction equal to 315° which is almost parallel to the escarpment and gives the minimum value for the norm of the residuals deriving from the logarithmic fit and the atmospheric conditions show neutral stratification. The logarithmic fit gives a roughness length z0 = 0.0562. This value has been used for the model configuration.

Resolution

Another important parameter that has to be defined during the model configuration is the resolution. When selecting the resolution in WEng, a compromise must be made between the domain’s extent, the resolution and the computer’s available memory. For the extent of the domain, a rule of thumb is proposed which suggests that the domain’s boundary should be at a distance of at least 100 times the height for which a wind prediction is demanded from the site location. This derives from the fact that the model applies periodic boundary conditions. However, the number 100 cannot always be kept and actually it is unnecessarily too big (i.e. in cases of flat terrain with uniform roughness). A very big domain is ideal, but then the grid points get so many that the computer memory of a typical working computer is not enough to carry out the simulation. The same happens if the resolution is increased (i.e. if the number which defines the distance between the grid points is decreased). In the Hjardemål case study, the specific domain extent (as given in a previous paragraph) is considered to be sufficiently big and is not changed. Hence, the resolution is left to be defined by taking into account the computer’s memory restriction. The actual computer’s memory capacity has not permitted to use a resolution higher than 1m. By trying different resolutions in the range of 5 to 1m, the simulation results can be compared with the measurements and the respective deviation can be derived. This has been carried out for Met. Masts 1, 7, 8, and 10 at 24m a.g.l.. Measurements are taken from Run 36 (244.6°) with stationary meteorological conditions and neutral stratification as these have been defined in section 4.2. The results for the horizontal wind speed are shown in Figure 11 and the results for the turbulence intensity are shown in Figure 12.

23

1 1.5 2 2.5 3 3.5 4 4.5 50

1

2

3

4

5

624m a.g.l.

Resolution [m]

Abs

olut

e de

viat

ion

betw

een

mea

sure

dan

d si

mul

ated

win

d sp

eed

valu

es [

%]

Mast7

Mast8Mast10

Figure 11: Absolute deviation between measured and

simulated wind speed values in function with the resolution for masts 7, 8, and 10 at 24m a.g.l.

1 1.5 2 2.5 3 3.5 4 4.5 50

0.5

1

1.5

2

2.5

3

3.5

4

4.5

524m a.g.l.

Resolution [m]

Abs

olut

e de

viat

ion

betw

een

mea

sure

d an

d

sim

ulat

ed t

urbu

lenc

e in

tens

ity v

alue

s [%

]

Mast1

Mast7Mast8

Mast10

Figure 12: Absolute deviation between measured and simulated TI values in function with the resolution for

masts 1, 7, 8, and 10 at 24m a.g.l. First of all, it can be observed in both figures that the deviation decreases by the increase of the resolution. It seems that there is a convergence at 2m; however this could be better proved if resolution values smaller than 1m could also be included in the sensitivity check. Furthermore, it is seen that all curves (for the different masts) follow the same behavior. Hence, the resolution of 2m is chosen for the simulations which results into a mesh of 796 x 498 grid points.

4.3.2 Results As already mentioned, the mast array stands at 236°. Two wind directions are selected to be shown here. The first case is for winds running at 242°, i.e. in the line which is perpendicular to the escarpment, and the second case concerns winds coming from the exact opposite direction, i.e. 62° (backwards flow). The direction perpendicular to the escarpment is selected so that the maximum terrain inclination is obtained and hence the prediction accuracy of WEng may be tested in a steep escarpment of 30°.

24

As derived from the model configuration, the roughness length used in the simulations is 0.0562, and the resolution is kept at 2m. The following results stand for 15 min winds, for which the standard deviation of the direction is not higher than 3.5° and the standard deviation of the speed is not higher than 0.5 m/s. These stationary meteorological conditions were only found by the program in specific Runs (Table 4 and 5), given that the wind direction is within the range of ±10° of the desired one (242° for the forward flow and 62° for the backward flow). By trying different reference heights, it has been proved that the use of the wind speed from the biggest height available gave results more close to the measurements. This is possibly because in that way ‘undisturbed’ wind conditions are better captured.

Run Rib Wind direction

at 24m a.g.l. (M1) Wind direction

at 10m a.g.l. (M2) 18 6.0E-3 232.3 229.5 18 4.0E-3 250.0 246.3 21 1.8E-3 251.9 249.0 22 1.6E-3 241.1 237.1 36 1.7E-6 244.6 241.1 40 6.3E-6 251.3 245.9 42 -0.9E-6 251.4 248.9 46 -5.1E-6 239.8 236.9

Table 4: Runs characteristics (forward flow)

Run Rib Wind direction

at 10m a.g.l. (M10) 26 685E-3 66.9 27 21.3E-3 58.9 27 22.8E-3 59.1 28 245E-3 62.7 28 26.4E-3 54.6 29 30710E-3 57.5 29 403E-3 58.7

Table 5: Runs characteristics (backward flow) Among the Runs listed in Table 4, the set of records which has a wind direction closest to the desired of 242° is one from Run 36, and it also has the smallest bulk Richardson number which ensures neutral conditions. For the backward flow case (Table 5), the second set of records from Run 27 is giving the smallest bulk Richardson number and it is closest to the desired wind direction (62°). Therefore, the aforementioned sets (grey shading in the Tables) are selected for the simulations.

Horizontal speed-up

For the forward flow, two types of results are presented below. The one is the horizontal speed-up at 24m a.g.l. for Masts 1, 7, 8 and 10, and the other is the horizontal speed-up at 10m a.g.l. for all Masts. It must be noticed here that measurements of the wind direction at 10m a.g.l. from Mast 1 were missing. Therefore, Mast 2 has been used as the reference mast in WAsP Engineering for the simulations of the wind flow at 10m, while Mast 1 is the reference mast for the 24m flow. The reference wind speed for the 24m flow is V=4.01 m/sec and for the 10m flow V=3.29 m/sec. The reference wind directions are shown in Table 4.

25

-400 -300 -200 -100 0 100 2000

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2Run 36 Speed-up at M1, M7, M8, M10 at 24m a.g.l. 244.6 (forward flow)

x [m]

U/U

ref

Measured

WEng

Figure 13: Speed-up at 24m a.g.l. (forward flow).

Mast 1 7 8 10

%100Measured

MeasuredWEng Ref. 1.2 0.1 5.3 Table 6: Deviations of horizontal wind speeds at 24m

a.g.l. (see Fig. 13).

-400 -300 -200 -100 0 100 200 3000

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2Run 36 Speed-up at all Masts at 10m a.g.l. 241.081 (forward flow)

x [m]

U/U

ref

Measured

WEng

Figure 14: Speed-up at 10m a.g.l. (forward flow).

Mast 1 2 3 4 5 6 7 8 9 10 11

%100Measured

MeasuredWEng -2.2 Ref. 1.1 -1.1 2.1 4.2 8.3 2.1 -4.1 -2.9 -9.1 Table 7: Deviations of horizontal wind speeds at 10m a.g.l. (see Fig. 14).

In the 10m flow (Figure 14), more measured points are available than in the 24m case and hence it is possible to get a better overview of how well WEng has performed. In general, the wind prediction is quite close to the measured values with small deviations. Typically wind turbines are erected on the tops of escarpments to take advantage of the speed-up effect; therefore, it is crucial that the model will give accurate results at this position. However, high deviation is reported at Mast 7 which stands on the top of the escarpment.

26

In the case of the backward flow, only the horizontal speed-up at 10m a.g.l. for all Masts is presented. The reference mast for WEng is Mast 11. The reference wind speed is V=7.59 m/sec. The reference wind direction is shown in Table 5. The backward flow results (Figure 15) are interesting because, usually over a generally more complex terrain, there are many cases where the terrain has steep slopes which face backwards for common wind directions. As in the forward flow case, WEng overestimates the speed-up on the top of the escarpment, but, furthermore here, the wind speed is overestimated at the bottom of the escarpment and further until Mast 1. Hence, it can be seen in Table 8, that the simulated wind speed at Mast 5, which lies at the bottom of the escarpment, is 149.6 % of the measured value. This is caused by the fact that WEng does not account for the separation of the flow which actually occurs immediately after it passes Mast 7.

-400 -300 -200 -100 0 100 200 3000

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2Run 27 Speed-up at all Masts at 10m a.g.l. 59.1274 (backward flow)

x [m]

U/U

ref

Measured

WEng

Figure 15: Speed-up at 10m a.g.l. (backward flow).

Mast 1 2 3 4 5 6 7 8 9 10 11

%100Measured

MeasuredWEng -1.6 13.3 38.6 77.8 149.6 3.6 12.7 4.6 0.3 0.7 Ref. Table 8: Deviations of horizontal wind speeds at 10m a.g.l. for the backward flow (see Fig. 15).

Vertical wind profiles

The results on the vertical wind profiles for Mast 1, 7, 8, and 10 for the forward flow are presented below. At the reference Mast 1 (Figure 16), the wind speed seems to be underestimated at all heights, with a maximum deviation of -7.2% at 5 m a.g.l.

27

2 2.5 3 3.5 4

5

10

15

20

25Run 36 Horizontal wind speed versus height for M1 244.6 (forward flow)

U [m/s]

z [m

]

Measured

WEng

Figure 16: Vertical wind profile for Mast 1.

Height [m] 2 5 10 24

%100Measured

MeasuredWEng -3.4 -7.2 -1.6 Ref.Table 9: Deviations of wind speeds at Mast 1

(forward flow, see Figure 16).

3.5 4 4.5 5 5.50

5

10

15

20

25

30Run 36 Horizontal wind speed versus height for M7 244.6 (forward flow)

U [m/s]

z [m

]

Measured

WEng

Figure 17: Vertical wind profile for Mast 7.

Height [m] 2 5 10 24

%100Measured

MeasuredWEng 7.2 8.4 8.7 -1.2 Table 10: Deviations of wind speeds at Mast 7

(forward flow, see Figure 17). At the top of the escarpment, Mast 7 (Figure 17), the wind speed is not well predicted at low heights but it gets closer to the measured value at the highest point (24m). Furthermore, it is obvious that he negative shear is not predicted by WEng.

28

3 3.5 4 4.5 50

5

10

15

20

25Run 36 Horizontal wind speed versus height for M8 244.6 (forward flow)

U [m/s]

z [m

]

Measured

WEng

Figure 18: Vertical wind profile for Mast 8.

Height [m] 2 5 10 24

%100Measured

MeasuredWEng 0.6 -5.6 2.6 -0.1 Table 11: Deviations of wind speeds at Mast 8

(forward flow, see Figure 18).

3 3.5 4 4.5 5

5

10

15

20

25Run 36 Horizontal wind speed versus height for M10 244.6 (forward flow)

U [m/s]

z [m

]

Measured

WEng

Figure 19: Vertical wind profile for Mast 10.

Height [m] 2 5 10 24

%100Measured

MeasuredWEng -16.7 -6.4 -2.5 -5.3 Table 12: Deviations of wind speeds at Mast 10

(forward flow, see Figure 19).

29

Turbulence intensity

The turbulence intensity results which are presented below count for the horizontal component of the wind speed standard deviation. For the forward flow case, predictions seem to be better for at 24m a.g.l. (Figure 20) than at 10m a.g.l. (Figure 21). The deviation levels are even higher for the backward flow case (Figure 22).

-400 -300 -200 -100 0 100 2000

2

4

6

8

10

12

14

16

18

20Run 36 Turbulence Intensity for M1, M7, M8, M10 at 24m a.g.l. 244.6 (forward flow)

x [m]

TI

[%]

Measured

WEng

Figure 20: Turbulence intensities at 24m a.g.l. (forward flow).

Mast 1 7 8 10

%100Measured

MeasuredWEng -5.2 1.5 -1.1 -1.1 Table 13: Deviations of turbulence intensity at 24m

a.g.l. (forward flow, see Figure 20).

-400 -300 -200 -100 0 100 2000

2

4

6

8

10

12

14

16

18

20Run 36 Turbulence Intensity for M1, M7, M8, M10 at 10m a.g.l. 241.081 (forward flow)

x [m]

TI

[%]

Measured

WEng

Figure 21: Turbulence intensities at 10m a.g.l. (forward flow).

Mast 1 7 8 10

%100Measured

MeasuredWEng -1.7 -18.3 -11.1 -11.4 Table 14: Deviations of turbulence intensity at 10m a.g.l.

(forward flow, see Figure 21).

30

-400 -300 -200 -100 0 100 2000

2

4

6

8

10

12

14

16

18

20Run 27 Turbulence Intensity for M1, M7, M8, M10 at 10m a.g.l. 59.1274 (backward flow)

x [m]

TI

[%]

Measured

WEng

Figure 22: Turbulence intensities at 10m a.g.l. (backward flow).

Mast 1 7 8 10

%100Measured

MeasuredWEng -4.9 -26.5 -16.4 -5.8 Table 15: Deviations of turbulence intensity at 10m a.g.l.

(backward flow, see Figure 22).

31

5 The Bolund case study The geometry of the Bolund hill contains a vertical crest that makes the site a challenging case study for flow simulations, but the big change in surface roughness also contributes to the complexity. Furthermore, even though Bolund is a small hill, it resembles the physical properties of a larger hill. In that way, there is the possibility of scaling up the geometry and getting useful conclusions about flow modelling in complex terrain. The Bolund experiment is a field campaign that provides a new dataset for validating models of flow in complex terrain. A first blind comparison of various flow models has already taken place and the results were presented and discussed at a workshop held at Risø on the 3rd and 4th of December 2009. Thus, the case study of the present chapter was partly the contribution of the author in the aforementioned blind comparison and has already been presented at the workshop.

5.1 Site description and instrumentation A detailed description of the Bolund experiment can be found in reference [14]. The experiment was performed during a three month period in 2007 and 2008. Bolund is a 12m high coastal hill located just north of Risø DTU (see Figure 23).

Figure 23: View of Bolund taken from the 125m high measuring mast at Risø DTU (Source: ref. [14]).

Figure 24 gives an overview of the Bolund orography and the positions of the ten masts that supported the instrumentation. 35 anemometers (23 sonics and 12 cups) were installed in total on all masts. The ‘undisturbed’ wind was measured at mast M0 and M9. The remaining masts were located along two lines (line A and B) with a 239° and 270° direction respectively. The positions of the masts are given in Table 16. The masts were instrumented with a combination of sonic (S), cup (C), and lidar (L) anemometers. Table 17 gives an overview of the instrumentation.

32

Figure 24: The Bolund orography and the positions of the ten masts (Source: ref. [14]).

Table 16: The positions of the masts

(Source: ref. [14]).

Table 17: An overview of the instrumentation. The heights are only approximate. (Source: ref. [14]).

Figure 25: View from upstream of the

escarpment (Line B, 270°). Source: ref. [14]

Figure 26: View from upstream of the escarpment

(Line A, 239°). Source: ref. [14]

5.2 Simulation cases As already mentioned, at mast M0 and mast M9 the ‘undisturbed’ wind conditions were measured for westerly and easterly winds respectively. Measurements have been sorted upon temperature stratification and those data which are to be used for comparison with the simulations refer to only neutrally stratified conditions (|1/L|<0.004). Furthermore, concerning the selection of the wind data sets, 10min time series have been selected with an allowable margin of ±8° for the wind directions.

33

Four simulation cases are considered. The three first cases (Case 1, 2, 3) are westerly wind directions (270°, 255°, and 239°). The fourth case (Case 4) is with the wind coming from the east (90°). For each simulation case, the reference wind speeds are given in Table 18.

Table 18: Reference wind speeds for the modeling (Source: ref. [14]). The reference wind speeds used in the WEng model are underlined with blue. (s: total wind velocity, u*0: friction velocity at the reference mast, TKE:

Turbulent Kinetic Energy) The reference wind data used in the WEng model are shown underlined with blue in Table 18. Given that time restriction did not allow the test of different reference heights, only one had to be selected. This was the biggest height that was available in each simulation case, as its use proved (in the Hjardemal case study) to be the best practice. The reference wind velocity to use in the WEng model is found by multiplying the quantity s/u*0 (Table 18) by the respective friction velocity u*0, which is equal to 0.4, except for the 90 dir case, where it is equal to 0.5.

34

5.3 WEng model

5.3.1 Model configuration The map has been provided by the team organizing the blind comparison [ref.14]. It was a very detailed map of the island with a 25cm resolution. It contained 200 contour lines and 1 roughness line. However, the map only covered the island it self and it was necessary to expand the map at least to include the reference masts M0 and M9. The roughness length that would be used in the models was already specified and all modelers should use the same values. Bolund is covered by grass with an estimated roughness length of 0.015m. The surrounding water is characterized by a roughness length of 0.0003m. In reality, the water roughness changes with wind speed, however, in order to unify the blind comparison, the aforementioned value should be used. Another guidance said that, when expanding the map, the terrain height/water height of 75cm should be kept and that the eastern region (x>327m) should be given a roughness length of 0.015m. The expansion of the map resulted into a domain with a length of 800m and a width of 600m. In Figure 27 and 28 below, the roughness and elevation grids of the expanded map in WEng are shown.

Figure 27: Expanded map in WEng - Roughness grid. Figure 28: Expanded map in WEng– Elevation grid.

The size of the domain did not allow for a resolution bigger than 5m, given the available memory of the computer used. Hence, the grid contains 160x120 points. The demand for the blind comparison was to extract the model results in 600 points (different x-y positions and heights z). This was a problem for WAsP Engineering, since all of them could not be implemented into one project. Hence, 12 different projects were created with 50 site locations each. Another problem that had to be faced was the finding of a means to extract the results from WEng. For each site location the following quantities had to be specified: s, u, v, w,

TKE, ''uu , ''vv , ''ww , u*. (where s: total wind velocity [m/s], u: east/west component of the velocity [m/s], v: north/south component of the velocity [m/s], w: vertical component of the velocity [m/s], TKE: Turbulent kinetic energy [m2/s2], ''uu : east/west component of TKE

[m2/s2], ''vv : north/south component of TKE [m2/s2], ''ww : vertical component of TKE [m2/s2], u*: local friction velocity [m/s]). The default reports in WEng do not give all the aforementioned

35

quantities. Therefore, the internal script in Visual Basic had to be edited in order to obtain a report with all demanded results. Figure 29 below shows the map with the sites across the mast lines A and B defined previously. Figure 30 shows the terrain inclination grid in the map. It can be observed that the current resolution gives a maximum terrain inclination of 52.25°, while in reality the maximum slope is approximately 90° at the edge of the crest.

Figure 29: WEng map - Site locations.

Figure 30: WEng map - Terrain inclination grid.

5.3.2 Results The results presented in the following refer to the three simulation cases with wind directions from 270°, 239°, and 90°. It is all that has been provided from the blind comparison organizing team. Results in tabular format have not been provided yet to participants as this is expected after the publication of the official report on the results from the blind comparison. However, the following figures may give a lot of information of how well WEng has performed against measurements as well as other types of models. The participating models included in total: 3 models using experimental methods (wind tunnel, flow channel) 9 linearized flow models (WAsP like, WEng)

36

37 non-linear CFD models (LES, hybrid RANS-LES, RANS 1-Eq., RANS 2-Eq.) In all Figures below, the author’s WEng model is indicated by a thick pink line to separate it by the rest, while the measurements are indicated by the black boxes.

Horizontal speed-up

The terrain inclination across the 270° and 239° directions reaches almost 90°, and therefore there are no high expectations for WEng predictions. The separation of the flow is not taken account by WEng, and hence, in all Figures below, the error between the simulated data and the measurements is quite big. The results of the speed-up for the 90° flow case (Figure 33) seem to be better than the other cases as well as in general the 5m predictions are better compared to those at 2m a.g.l.. Furthermore, it can be seen that the peak of the speed-up at the edge of the crest cannot be captured by WEng, while it is only captured by some of the non-linear CFD models.

Figure 31: Horizontal speed-up (270° flow case, mast line B).

According to the blind comparison organizing committee, the averaged error for all models in wind velocity for mast line A and B are found as 35% for 2m height measurements, and 17% for 5m height measurements. Hence, the mean error is equal to 26%. The error results in respect to different types of models are given below: All models: 26% Linearized models: 35% LES models: 26% RANS 1-eqn models: 25% RANS 2-eqn models: 20%

37

Figure 32: Horizontal speed-up (239° flow case, mast line A).

Figure 33: Horizontal speed-up (90° flow case, mast line B).

38

Flow inclination

The flow inclination (Figures 34-36), seems to be better predicted by WEng in the 270° flow case than in the 239° flow case. In the 90° flow case, it is quite well predicted for all masts except for Mast 7 standing at the bottom back of the crest.

Figure 34: Flow inclination (270° flow case, mast line B).

Figure 35: Flow inclination (239° flow case, mast line A).

39

Figure 36: Flow inclination (90° flow case, mast line B).

Vertical wind profiles

In Figures 37 and 38, the vertical wind speed-ups for the 270° flow case are presented.

Figure 37: Vertical speed-up. 270° flow case. M7 (left), M6 (right).

40

Figure 38: Vertical speed-up. 270° flow case. M3 (left), M8 (right).

Turbulent kinetic energy

The TKE results are the proof of the inability of WEng to simulate such complex terrains, since there is almost no agreement with measured values for the 270° and 239° flow cases (Figure 39, 40). In the 90° flow case (Figure 41), where the terrain slope is lower, the turbulent kinetic energy is better evaluated both for 2m and 5m height a.g.l.

Figure 39: TKE (270° flow case, mast line B).

41

Figure 40: TKE (239° flow case, mast line A).

Figure 41: TKE (90° flow case, mast line B).

42

6 Conclusions From the flow simulation on the two different sites (Hjardemal and Bolund) by the use of WAsP Engineering 2.0 some useful conclusions are derived. These conclusions are synopsized below: The maximum absolute deviation between measured and simulation values (error) found at the Hjardemal case study in respect to the horizontal wind speed is: Forward flow: 24m → 5.3% 10m → 9.1%

Backward flow: 10m → 149.6%

The error in the backward flow case is very big, however, it is found at the bottom of the escarpment, where it is known that flow separation is not taken into account by WEng. Of course, this error has to be mentioned in terms of validating a model. But, in practice, such a location could not be a wind turbine site. In a hypothesis that the simulation is carried out in order to evaluate the wind conditions for a candidate wind turbine erection site and defining that this site would be the location on the top of the escarpment (M7), the following errors would apply: Forward flow: 24m → 1.2% 10m → 8.3%

Backward flow: 10m → 12.7%

These errors are still quite big if we consider the recommendations of international institutions such as the TPWind (European Technology Platform for Wind Energy) for instance which allows a 3% error in wind resources evaluations for wind energy projects. Furthermore, the uncertainty on evaluating the site-specific wind conditions will increase when real atmospheric conditions, different than neutral, are to be considered. The simulated vertical wind profiles are used to extract the wind shear factor by fitting the profile to the well-known power law. Hence, the error that will derive from a simulation of the wind speed vertical profile will also apply to the wind shear factor that is going to be used for the structural design of the wind turbine. The maximum absolute error reported in the forward flow case, is equal to 16.7 % and refers to Mast 10 which is the furthest downstream mast. At Mast 7, the same error is equal to 8.7%. The turbulence intensity maximum error levels were higher than those of the wind speeds. These were found as 18.3% for the forward flow case at Mast 7 and 26.5% for the backward flow case at Mast 7 again. In the more complex Bolund case study, the errors were found even bigger, and it has been shown that the linearized WEng model is inappropriate to be used even to get a rough idea (for

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example in respect to the turbulent kinetic energy which corresponds to the turbulence intensity that is required in the IEC standards). The error in respect of the horizontal wind velocity reached the level of 35% for the WEng model. However, in the Bolund case, even the most advanced non-linear models gave an average error of 20%. From the WEng simulations in both sites but also specifically from the big diversion in the results of the different models participated in the blind comparison, it is concluded that the appropriate model configuration is an important factor affecting the result. The experience of the modeler as well as the quality of the map and the available computing power are crucial. Concerning the WEng modelling, the following conclusions can be made: Sensitivity checks should be carried out in order to find the appropriate resolution which is not necessarily the highest one. The results must be independent of the mesh refinement. The rule of thumb that says that domain should extend at least 100 times the hub height from the site to the boundary is not always applicable due to the computer memory restrictions. This becomes a bigger problem when a buffer zone has to be added so that the periodic boundary conditions will not lead to a wrong flow evaluation. Thus, eventually a compromise between the domain size, the resolution, and the available computer memory must be made. Finally, the measurements used in any simulation must be processed carefully in order to come up with valid results. Concerning the WEng modelling, stationary meteorological conditions have to be extracted from the measurements from all different wind directions that it is possible. Furthermore, there is no point in including wind data referring to non-neutral atmospheric stratification, as the model is not designed to work for such cases. The sensitivity on the change of the reference height should be checked when measurements are available and hence it can be found the reference height which gives the smallest errors. These checks in the Hjardemål case study showed that the biggest the reference height is, the smaller is the error.

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References [1] ‘Wind Loads on Structures’, Dyrbye and Hansen, John Wiley & Sons, 1997. [2] ‘Sensing the wind profile’, Alfredo Peña, Risø-PhD-45 (EN), 2009.

[3] ‘Atmospheric Boundary Layer Flows’, Kaimal and Finnigan, Oxford University Press, 1994.

[4] ‘Computational methods in wind power meteorology’, Jorgensen, Ott, Mann, Badger, Risø-R-1560 (EN), 2006.

[5] ‘Hjardemål Experiment Data Report’, Emeis, Courtney, Hojstrup, Jensen, Risø-M-2289 (EN), 1993.

[6] ‘WAsP Engineering DK’, Mann, Astrup, Kristensen, Rathmann, Madsen, Heathfield, Risø-R-1179 (EN), 2000.

[7] ‘WAsP Engineering User's Guide’, Jorgensen, Heathfield, Mann, Nielsen, Mortensen, Risø-I-2391 (EN), 2005.

[8] ‘WAsP Engineering 2000’, Mann, Ott, Jorgensen, Frank, Risø-R-1356 (EN), 2002.

[9] ‘WAsP Engineering flow model for wind over land and sea’, Astrup, Larsen, Risø-R-1107 (EN), 1999.

[10] ‘Course Notes-WAsP Engineering’, Risø National Laboratory, Denmark, October 2009.

[11] ‘International Standard IEC 61400-1’, Wind turbines- Part 1: Design requirements, Edition 2005.

[12] ‘Evaluation of site-specific wind conditions’, Version 1, MEASNET, November 2009.

[13] ‘International Standard IEC 61400-12’, Wind turbines- Part 12: Power performance measurements of electricity producing wind turbines, Edition 1998.

[14] ‘The Bolund experiment: Overview and background. Technical Report’, Risø-R-1658 (EN), 2009.

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A1 - Matlab program for the process of Hjardemål measurements

The program process all available measured data from the Hjardemål experiment. The user defines all necessary parameters to extract stationary meteorological conditions and demanded wind directions. If the wind direction is equal to 242° or 62°, the program returns tabular results and plots of both the measured and simulation results in WEng. For any other direction angle, the only measurements are returned in tabular format and in plots. The following scripts and functions should be copied into a separate Matlab directory. The program is executed by the script hj.m. hj.m clear;close all;clc; global iRUN props_cor nm props0_1 props0_2 std_V_lim std_D_lim rl global iD md dmd binsize pr nruns typres pr_ props0_3 props0_4 back props_temp load allruns.mat % Parameters--------------------------------------------------------------- nm=15; %number of measurements std_V_lim=0.5; std_D_lim=3.5; md=242;dmd=10; binsize=1; plotmode=1; rl=0.03; %-------------------------------------------------------------------------- run initial k=1;res_exist=0; for iRUN=1:nruns run run_case if back==0 [res_V,res_D,res_V_weng,res_D_weng,res_TI,res_Ri]=filtering(RUN); s=size(res_V,1); if s~=0 res_exist=1; y=k+s-1; RES_V(k:y,:)=[ones(s,1)*runnames(iRUN) res_V]; RES_D(k:y,:)=[ones(s,1)*runnames(iRUN) res_D]; RES_V_weng(k:y,:)=[ones(s,1)*runnames(iRUN) res_V_weng]; RES_D_weng(k:y,:)=[ones(s,1)*runnames(iRUN) res_D_weng]; RES_TI(k:y,:)=[ones(s,1)*runnames(iRUN) res_TI]; RES_Ri(k:y,:)=[ones(s,1)*runnames(iRUN) res_Ri]; k=y+1; end elseif back==1 if iRUN==3 disp(' ');

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elseif iRUN==nruns disp(' '); elseif iRUN==2 disp(' '); else [res_V,res_D,res_V_weng,res_D_weng,res_TI,res_Ri]=filtering(RUN); s=size(res_V,1); if s~=0 res_exist=1; y=k+s-1; RES_V(k:y,:)=[ones(s,1)*runnames(iRUN) res_V]; RES_D(k:y,:)=[ones(s,1)*runnames(iRUN) res_D]; RES_V_weng(k:y,:)=[ones(s,1)*runnames(iRUN) res_V_weng]; RES_D_weng(k:y,:)=[ones(s,1)*runnames(iRUN) res_D_weng]; RES_TI(k:y,:)=[ones(s,1)*runnames(iRUN) res_TI]; RES_Ri(k:y,:)=[ones(s,1)*runnames(iRUN) res_Ri]; k=y+1; end end end end if res_exist==1 RES_V RES_VD_weng=[RES_V_weng RES_D_weng(:,2)] RES_TI RES_Ri else RES_V=[] RES_VD_weng=[] RES_TI=[]; RES_Ri=[]; end run postproc initial.m %Table and plot results---------------------------------------------------- disp('P A R A M E T E R S'); disp(['Accepted Min number of measurements: ' sprintf('%g',nm)]); disp(['Accepted stdev(ws) for averaging: ' sprintf('%g',std_V_lim) ' [m/s]']); disp(['Accepted stdev(dir) for averaging: ' sprintf('%g',std_D_lim) ' [deg]']); disp(['Wind direction range presented: ' sprintf('%g',md-dmd) '~' sprintf('%g',md+dmd) ' [deg]']); if md==242-180 && dmd==10 back=1; else back=0; end if back==0 disp(' '); run props disp('R E S U L T S');

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disp('1. Horizontal wind speed for Masts 1,7,8,10 at 24m a.g.l.'); disp('2. Horizontal wind speed for all Masts at 10m a.g.l.'); disp('3. Horizontal wind speed versus height for Mast 1'); disp('4. Horizontal wind speed versus height for Mast 7'); disp('5. Horizontal wind speed versus height for Mast 8'); disp('6. Horizontal wind speed versus height for Mast 10'); typres=input('Enter:'); if typres==1 pr=props1;iD=1; pr_=props1_std; elseif typres==2 pr=props2;iD=2; pr_=props2_std; elseif typres==3 pr=props3;iD=1; pr_=props3_std; elseif typres==4 pr=props4;iD=1; pr_=props4_std; elseif typres==5 pr=props5;iD=1; pr_=props5_std; elseif typres==6 pr=props6;iD=1; pr_=props6_std; else disp('n/a'); return; end elseif back==1 typres=2; run props pr=props2;iD=2; pr_=props2_std; end filtering.m function [res_V,res_D,res_V_weng,res_D_weng,res_TI,res_Ri]=filtering(RUN) global iRUN props_cor nm props0_1 props0_2 std_V_lim std_D_lim global iD md dmd binsize pr nruns typres pr_ props0_3 props0_4 back props_temp %33 deg correction--------------------------------------------------------- RUN(:,props_cor(iRUN,:))=RUN(:,props_cor(iRUN,:))-33; %-------------------------------------------------------------------------- lnm=size(RUN,1); nds=lnm-nm+1; for i=1:nds if back==0 std_VD(i,1)=std(RUN(i:i+nm-1,props0_1(iRUN,1))); %#ok<AGROW> std_VD(i,2)=std_dir(RUN(i:i+nm-1,props0_2(iRUN,1))); %#ok<AGROW> %std_VD=[std_V std_D] elseif back==1 std_VD(i,1)=std(RUN(i:i+nm-1,props0_3(iRUN,1))); %#ok<AGROW>

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std_VD(i,2)=std_dir(RUN(i:i+nm-1,props0_4(iRUN,1))); %#ok<AGROW> %std_VD=[std_V std_D] end end filtered1=find(std_VD(:,1)<=std_V_lim & std_VD(:,2)<=std_D_lim); if isempty(filtered1)==1 res_V=[]; res_D=[]; res_V_weng=[]; res_D_weng=[]; res_TI=[]; res_Ri=[]; % disp('Filter 1 not passed (standard deviation limits)'); else for i=1:size(filtered1,1) n=filtered1(i); X_k=RUN(n:n+nm-1,pr(iRUN,:)); std_k=RUN(n:n+nm-1,pr_(iRUN,:)); res_STD_V(i,:)=std_of_a_set(X_k,std_k,0); %#ok<AGROW> U2=RUN(n:n+nm-1,4); U24=RUN(n:n+nm-1,7); dU=U24-U2; T2=RUN(n:n+nm-1,props_temp(iRUN,1)); T24=RUN(n:n+nm-1,props_temp(iRUN,2)); T=mean([T2 T24],2)+273.15; dT=RUN(n:n+nm-1,props_temp(iRUN,3)); g_Cp=0.0098;dz=20;g=9.81; dTHETA=dT+dz*g_Cp; Ri=dTHETA*g*dz./T./dU.^2; res_Ri(i,:)=mean(Ri,1); %#ok<AGROW> if back==0 res_V(i,:)=mean(RUN(n:n+nm-1,[props0_1(iRUN,1) props0_1(iRUN,2) pr(iRUN,:)])); %#ok<AGROW> res_D(i,1)=mean_dir(RUN(n:n+nm-1,props0_2(iRUN,1))); %#ok<AGROW> res_D(i,2)=mean_dir(RUN(n:n+nm-1,props0_2(iRUN,2))); %#ok<AGROW> res_TI(i,:)=res_STD_V(i,:)./mean(X_k,1); %#ok<AGROW> elseif back==1 res_V(i,:)=mean(RUN(n:n+nm-1,[props0_3(iRUN,1) props0_3(iRUN,1) pr(iRUN,:)])); %#ok<AGROW> res_D(i,1)=mean_dir(RUN(n:n+nm-1,props0_4(iRUN,1))); %#ok<AGROW> res_D(i,2)=mean_dir(RUN(n:n+nm-1,props0_4(iRUN,1))); %#ok<AGROW> res_TI(i,:)=res_STD_V(i,:)./mean(X_k,1); %#ok<AGROW> end end if md-dmd>=0 && md+dmd<=360 filtered2=find(res_D(:,1)>=md-dmd & res_D(:,1)<=md+dmd); elseif md-dmd<0 filtered2=find(res_D(:,1)>=360+md-dmd | res_D(:,1)<=md+dmd); elseif md-dmd>=0 && md+dmd>360 filtered2=find(res_D(:,1)>=md-dmd | res_D(:,1)<=md+dmd-360); end if isempty(filtered2)==1 res_V=[]; res_D=[];

49

res_V_weng=[]; res_D_weng=[]; res_TI=[]; res_Ri=[]; % disp('Filter 2 not passed (main direction wanted)'); else res_V=res_V(filtered2,:); res_D=res_D(filtered2,:); res_TI=res_TI(filtered2,:); res_Ri=res_Ri(filtered2,:); filtered3=wsbins(res_V(:,1),binsize); for i=1:size(filtered3,1) i_filtered3(i)=find(res_V(:,1)==filtered3(i)); %#ok<AGROW> end res_V=res_V(i_filtered3,:); res_D=res_D(i_filtered3,:); res_V_weng=res_V(:,iD); res_V=res_V(:,3:end); res_D_weng=res_D(:,iD)+28; res_TI=res_TI(i_filtered3,:); res_Ri=res_Ri(i_filtered3,:); end end run_case.m if iRUN==1 RUN=run14; elseif iRUN==2 RUN=run16; elseif iRUN==3 RUN=run17; elseif iRUN==4 RUN=run18; elseif iRUN==5 RUN=run20; elseif iRUN==6 RUN=run21; elseif iRUN==7 RUN=run22; elseif iRUN==8 RUN=run23; elseif iRUN==9 RUN=run26; elseif iRUN==10 RUN=run27; elseif iRUN==11 RUN=run28; elseif iRUN==12 RUN=run29; elseif iRUN==13 RUN=run30; elseif iRUN==14 RUN=run31; elseif iRUN==15 RUN=run36;

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elseif iRUN==16 RUN=run37; elseif iRUN==17 RUN=run38; elseif iRUN==18 RUN=run40; elseif iRUN==19 RUN=run41; elseif iRUN==20 RUN=run42; elseif iRUN==21 RUN=run46; end std_of_a_set.m function [std_set]=std_of_a_set(X_k,std_k,angles) Nk=size(X_k,1); %Number of 1min records Ns=120; %Number of records within 1min (given that f=2Hz) if angles==1 X_set=mean_dir(X_k,1); %Case with angles else X_set=mean(X_k,1); end for j=1:size(X_k,2) summa=0; for i=1:Nk summa=summa+(Ns*(X_set(j)-X_k(i,j))^2+std_k(i,j)^2*(Ns-1)); end std_set(1,j)=sqrt((1/(Nk*Ns-1))*summa); %#ok<AGROW> end mean_dir.m function [m]=mean_dir(x) x=deg2rad(x); c=mean(cos(x)); s=mean(sin(x)); m=rad2deg(mean((atan2(s,c)))); if m<0 m=360+m; end std_dir.m function [sd]=std_dir(x) x=deg2rad(x); c=mean(cos(x)); s=mean(sin(x));

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%%mean % m=rad2deg(mean((atan2(s,c)))); % if m<0 % m=360+mean_x; % end var_x=1-s^2-c^2; sd=rad2deg(sqrt(var_x)); %%Yamartino % e=sqrt(var_x); % sd=asin(e)*(1+((2/sqrt(3))-1)*e^3); % sd=rad2deg(sd); wsbins.m function [data_]=wsbins(data,binsize) bins=[0.5:binsize:20.5]'; m=0; for n=1:length(bins)-1 cv(n)=bins(n)+(bins(n+1)-bins(n))/2; index=find(data>=bins(n) & data<bins(n+1)); nf(n)=length(index); if nf(n)~=0 m=m+1; [yy,ii]=min(abs(data(index)-cv(n))); data_(m,:)=data(index(ii),:); end end props.m props0_1=[7 21 7 20 7 20 7 20 7 20 7 20 7 20 7 20 7 20 7 20 7 20 7 20 7 21 7 21 7 21 7 21 7 21 7 21 7 21 7 21 7 21]-2;%V1_24 V2_10 props0_3=[75 73 3

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73 73 73 73 73 73 73 73 73 74 74 74 74 74 74 74 74 3 ]-2;%V11_10 props0_2=[11 38 10 37 10 37 10 37 10 37 10 37 10 37 10 37 10 37 10 37 10 37 10 37 11 38 11 38 11 38 11 38 11 38 11 38 11 38 11 38 11 38]-2;%D1_24 D2_10 props0_4=[78 76 3 76 76 76 76 76 76 76 76 76 77 77 77 77 77 77 77

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77 3 ]-2;%D11_10 props1=[7 31 36 74 7 30 35 72 7 30 35 3 7 30 35 72 7 30 35 72 7 30 35 72 7 30 35 72 7 30 35 72 7 30 35 72 7 30 35 72 7 30 35 72 7 30 35 72 7 31 36 73 7 31 36 73 7 31 36 73 7 31 36 73 7 31 36 73 7 31 36 73 7 31 36 73 7 31 36 73 7 31 36 3]-2; props2=[6 21 22 23 24 25 28 34 68 71 75 6 20 21 22 23 24 27 33 66 69 73 6 20 21 22 23 24 27 33 3 3 3 6 20 21 22 23 24 27 33 66 69 73 6 20 21 22 23 24 27 33 66 69 73 6 20 21 22 23 24 27 33 66 69 73 6 20 21 22 23 24 27 33 66 69 73 6 20 21 22 23 24 27 33 66 69 73 6 20 21 22 23 24 27 33 66 69 73 6 20 21 22 23 24 27 33 66 69 73 6 20 21 22 23 24 27 33 66 69 73 6 20 21 22 23 24 27 33 66 69 73 6 21 22 23 24 25 28 34 67 70 74 6 21 22 23 24 25 28 34 67 70 74 6 21 22 23 24 25 28 34 67 70 74 6 21 22 23 24 25 28 34 67 70 74 6 21 22 23 24 25 28 34 67 70 74 6 21 22 23 24 25 28 34 67 70 74 6 21 22 23 24 25 28 34 67 70 74 6 21 22 23 24 25 28 34 67 70 74 6 21 22 23 24 25 28 34 3 3 3]-2; props3=[4 5 6 7 4 5 6 7 4 5 6 7 4 5 6 7 4 5 6 7 4 5 6 7 4 5 6 7 4 5 6 7 4 5 6 7 4 5 6 7 4 5 6 7 4 5 6 7 4 5 6 7

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4 5 6 7 4 5 6 7 4 5 6 7 4 5 6 7 4 5 6 7 4 5 6 7 4 5 6 7 4 5 6 7 ]-2; props4=[26 27 28 31 25 26 27 30 25 26 27 30 25 26 27 30 25 26 27 30 25 26 27 30 25 26 27 30 25 26 27 30 25 26 27 30 25 26 27 30 25 26 27 30 25 26 27 30 26 27 28 31 26 27 28 31 26 27 28 31 26 27 28 31 26 27 28 31 26 27 28 31 26 27 28 31 26 27 28 31 26 27 28 31]-2; props5=[32 33 34 36 31 32 33 35 31 32 33 35 31 32 33 35 31 32 33 35 31 32 33 35 31 32 33 35 31 32 33 35 31 32 33 35 31 32 33 35 31 32 33 35 31 32 33 35 32 33 34 36 32 33 34 36 32 33 34 36 32 33 34 36 32 33 34 36 32 33 34 36 32 33 34 36 32 33 34 36 32 33 34 36]-2; props6=[69 70 71 74 67 68 69 72 3 3 3 3 67 68 69 72 67 68 69 72 67 68 69 72 67 68 69 72 67 68 69 72

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67 68 69 72 67 68 69 72 67 68 69 72 67 68 69 72 68 69 70 73 68 69 70 73 68 69 70 73 68 69 70 73 68 69 70 73 68 69 70 73 68 69 70 73 68 69 70 73 3 3 3 3]-2; props_cor=[9 11 38 40 42 44 46 76 78 8 10 37 39 41 43 45 74 76 8 10 37 39 41 43 45 8 8 8 10 37 39 41 43 45 74 76 8 10 37 39 41 43 45 74 76 8 10 37 39 41 43 45 74 76 8 10 37 39 41 43 45 74 76 8 10 37 39 41 43 45 74 76 8 10 37 39 41 43 45 74 76 8 10 37 39 41 43 45 74 76 8 10 37 39 41 43 45 74 76 8 10 37 39 41 43 45 74 76 9 11 38 40 42 44 46 75 77 9 11 38 40 42 44 46 75 77 9 11 38 40 42 44 46 75 77 9 11 38 40 42 44 46 75 77 9 11 38 40 42 44 46 75 77 9 11 38 40 42 44 46 75 77 9 11 38 40 42 44 46 75 77 9 11 38 40 42 44 46 75 77 9 11 38 40 42 44 46 9 9 ]-2; props_dir=props_cor+2; props_weng=[7 11 21 38 7 10 20 37 7 10 20 37 7 10 20 37 7 10 20 37 7 10 20 37 7 10 20 37 7 10 20 37 7 10 20 37 7 10 20 37 7 10 20 37 7 10 20 37 7 11 21 38 7 11 21 38 7 11 21 38 7 11 21 38 7 11 21 38 7 11 21 38 7 11 21 38 7 11 21 38 7 11 21 38 ];

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props1_std=[86 110 115 153 85 108 113 151 67 90 95 1 88 111 116 153 88 111 116 153 88 111 116 153 88 111 116 153 88 111 116 153 88 111 116 153 88 111 116 153 88 111 116 153 88 111 116 153 89 113 118 155 89 113 118 155 89 113 118 155 89 113 118 155 89 113 118 155 89 113 118 155 89 113 118 155 89 113 118 155 68 92 97 1 ]; props2_std=[85 100 101 102 103 104 107 113 147 150 154 84 98 99 100 101 102 105 111 145 148 152 66 80 81 82 83 84 87 93 1 1 1 87 101 102 103 104 105 108 114 147 150 154 87 101 102 103 104 105 108 114 147 150 154 87 101 102 103 104 105 108 114 147 150 154 87 101 102 103 104 105 108 114 147 150 154 87 101 102 103 104 105 108 114 147 150 154 87 101 102 103 104 105 108 114 147 150 154 87 101 102 103 104 105 108 114 147 150 154 87 101 102 103 104 105 108 114 147 150 154 87 101 102 103 104 105 108 114 147 150 154 88 103 104 105 106 107 110 116 149 152 156 88 103 104 105 106 107 110 116 149 152 156 88 103 104 105 106 107 110 116 149 152 156 88 103 104 105 106 107 110 116 149 152 156 88 103 104 105 106 107 110 116 149 152 156 88 103 104 105 106 107 110 116 149 152 156 88 103 104 105 106 107 110 116 149 152 156 88 103 104 105 106 107 110 116 149 152 156 67 82 83 84 85 86 89 95 1 1 1 ]; props3_std=[83 84 85 86 82 83 84 85 64 65 66 67 85 86 87 88 85 86 87 88 85 86 87 88 85 86 87 88 85 86 87 88 85 86 87 88 85 86 87 88 85 86 87 88 85 86 87 88 86 87 88 89 86 87 88 89 86 87 88 89 86 87 88 89 86 87 88 89 86 87 88 89 86 87 88 89

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86 87 88 89 65 66 67 68 ]; props4_std=[105 106 107 110 103 104 105 108 85 86 87 90 106 107 108 111 106 107 108 111 106 107 108 111 106 107 108 111 106 107 108 111 106 107 108 111 106 107 108 111 106 107 108 111 106 107 108 111 108 109 110 113 108 109 110 113 108 109 110 113 108 109 110 113 108 109 110 113 108 109 110 113 108 109 110 113 108 109 110 113 87 88 89 92 ]; props5_std=[111 112 113 115 109 110 111 113 91 92 93 95 112 113 114 116 112 113 114 116 112 113 114 116 112 113 114 116 112 113 114 116 112 113 114 116 112 113 114 116 112 113 114 116 112 113 114 116 114 115 116 118 114 115 116 118 114 115 116 118 114 115 116 118 114 115 116 118 114 115 116 118 114 115 116 118 114 115 116 118 93 94 95 97 ]; props6_std=[148 149 150 153 146 147 148 151 1 1 1 1 148 149 150 153 148 149 150 153 148 149 150 153 148 149 150 153 148 149 150 153 148 149 150 153 148 149 150 153 148 149 150 153 148 149 150 153 150 151 152 155 150 151 152 155 150 151 152 155 150 151 152 155

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150 151 152 155 150 151 152 155 150 151 152 155 150 151 152 155 1 1 1 1 ]; props_temp=[11 12 13 10 11 12 10 11 12 10 11 12 10 11 12 10 11 12 10 11 12 10 11 12 10 11 12 10 11 12 10 11 12 10 11 12 11 12 13 11 12 13 11 12 13 11 12 13 11 12 13 11 12 13 11 12 13 11 12 13 11 12 13 ]; postproc.m if nm==15 && std_V_lim==0.5 && std_D_lim==3.5 && md==242 && dmd==10 && back==0 && rl==0.03 run weng_hjp1_res run dev run plot_all elseif nm==15 && std_V_lim==0.5 && std_D_lim==3.5 && md==242-180 && dmd==10 && back==0 && rl==0.03 run weng_hjp2_res run dev run plot_all elseif nm==15 && std_V_lim==0.5 && std_D_lim==3.5 && md==242-180 && dmd==10 && back==1 && rl==0.03 run weng_hjp3_res run dev run plot_all elseif nm==15 && std_V_lim==0.5 && std_D_lim==3.5 && md==242 && dmd==10 && back==0 && rl==0.06 run weng_hjp5_res run dev run plot_all elseif nm==15 && std_V_lim==0.5 && std_D_lim==3.5 && md==242 && dmd==10 && back==0 && rl==0.04 run weng_hjp6_res run dev run plot_all

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else run plot_measur end plot_all.m if plotmode==1 w=0.3;nw=20;xw=w*nw; if md==242 tt='(forward flow)'; elseif md==242-180 tt='(backward flow)'; else tt=''; end if back==0 if typres==1 weng=M1_24; %Met.Mast x-Distances x_dist=[-397.685 0 30.826 199.195]; %Horizontal wind speed - 24 m for i=1:size(RES_V,1) if RES_V(i,1)==17 || RES_V(i,1)==46 disp(['Data records at M10 from Run ' ... sprintf('%g',RES_V(i,1)) ' are not available']); figure; plot(x_dist(1,1:3),[RES_V(i,2)/RES_V(i,2) RES_V(i,3)/RES_V(i,2)... RES_V(i,4)/RES_V(i,2)],'x-',x_dist(1,1:3),weng([1 7 8],4,i)/weng(1,4,i),'.-'); title(['Run ' num2str(RES_V(i,1))... ' \bullet Speed-up at M1, M7, M8 at 24m a.g.l. \bullet ' ... sprintf('%g',RES_D(i,iD+1)) '\circ ' sprintf('%s',tt)]); xlabel('x [m]'); ylabel('U/Uref'); grid; axis([-400 200 0 2]); legend('Measured','WEng'); else figure; plot(x_dist,[RES_V(i,2)/RES_V(i,2) RES_V(i,3)/RES_V(i,2)... RES_V(i,4)/RES_V(i,2) RES_V(i,5)/RES_V(i,2)],'x-',x_dist,weng([1 7 8 10],4,i)/weng(1,4,i),'.-'); title(['Run ' num2str(RES_V(i,1))... ' \bullet Speed-up at M1, M7, M8, M10 at 24m a.g.l. \bullet ' ... sprintf('%g',RES_D(i,iD+1)) '\circ ' sprintf('%s',tt)]); xlabel('x [m]'); ylabel('U/Uref'); grid; axis([-400 200 0 2]); legend('Measured','WEng'); end end %TI plot M1 M7 M8 M10 - 24 m------------------------------------------------------------------------------------------

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for i=1:size(RES_TI,1) if RES_TI(i,1)==17 || RES_TI(i,1)==46 disp(['Data records at M10 from Run ' ... sprintf('%g',RES_TI(i,1)) ' are not available']); figure; hold on; bar(x_dist(1,1:3)-xw,100*[RES_TI(i,2) RES_TI(i,3)... RES_TI(i,4)],w,'b'); bar(x_dist(1,1:3)+xw,100*weng_TI(1:3,2),w,'g'); title(['Run ' num2str(RES_TI(i,1))... ' \bullet Turbulence Intensity for M1, M7, M8 at 24m a.g.l. \bullet ' ... sprintf('%g',RES_D(i,iD+1)) '\circ ' sprintf('%s',tt)]); xlabel('x [m]'); ylabel('TI [%]'); grid; axis([-400-nw 200+nw 0 20]); legend('Measured','WEng'); hold off; else figure; hold on; bar(x_dist-xw,100*[RES_TI(i,2) RES_TI(i,3)... RES_TI(i,4) RES_TI(i,5)],w,'b'); bar(x_dist+xw,100*weng_TI(:,2),w,'g'); title(['Run ' num2str(RES_TI(i,1))... ' \bullet Turbulence Intensity for M1, M7, M8, M10 at 24m a.g.l. \bullet ' ... sprintf('%g',RES_D(i,iD+1)) '\circ ' sprintf('%s',tt)]); xlabel('x [m]'); ylabel('TI [%]'); grid; axis([-400-nw 200+nw 0 20]); legend('Measured','WEng'); hold off; end end elseif typres==2 weng=M2_10; %Met.Mast x-Distances x_dist=[-397.685 -198.06 -98.513 -48.223... -25.031 -12.993 0 30.826 99.029 199.195 300.411]; %Horizontal wind speed - 10 m for i=1:size(RES_V,1) if RES_V(i,1)==17 || RES_V(i,1)==46 disp(['Data records at M9,10,11 from Run ' ... sprintf('%g',RES_V(i,1)) ' are not available']); figure; plot(x_dist(1,1:8),[RES_V(i,2)/RES_V(i,2)... RES_V(i,3)/RES_V(i,2) RES_V(i,4)/RES_V(i,2)... RES_V(i,5)/RES_V(i,2) RES_V(i,6)/RES_V(i,2)... RES_V(i,7)/RES_V(i,2) RES_V(i,8)/RES_V(i,2)... RES_V(i,9)/RES_V(i,2)],'x-',... x_dist(1,1:8),weng(1:8,3,i)/weng(1,3,i),'.-'); title(['Run ' num2str(RES_V(i,1))... ' \bullet Speed-up at all Masts (except for M9,10,11) at 10m a.g.l. \bullet ' ... sprintf('%g',RES_D(i,iD+1)) '\circ ' sprintf('%s',tt)]); xlabel('x [m]'); ylabel('U/Uref');

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grid; axis([-400 310 0 2]); legend('Measured','WEng'); else figure; plot(x_dist,[RES_V(i,2)/RES_V(i,2)... RES_V(i,3)/RES_V(i,2) RES_V(i,4)/RES_V(i,2)... RES_V(i,5)/RES_V(i,2) RES_V(i,6)/RES_V(i,2)... RES_V(i,7)/RES_V(i,2) RES_V(i,8)/RES_V(i,2)... RES_V(i,9)/RES_V(i,2) RES_V(i,10)/RES_V(i,2)... RES_V(i,11)/RES_V(i,2) RES_V(i,12)/RES_V(i,2)],... 'x-',x_dist,weng(:,3,i)/weng(1,3,i),'.-'); title(['Run ' num2str(RES_V(i,1))... ' \bullet Speed-up at all Masts at 10m a.g.l. \bullet ' ... sprintf('%g',RES_D(i,iD+1)) '\circ ' sprintf('%s',tt)]); xlabel('x [m]'); ylabel('U/Uref'); grid; axis([-400 310 0 2]); legend('Measured','WEng'); end end %TI plot M1 M7 M8 M10 - 10 m------------------------------------------------------------------------------------------- for i=1:size(RES_TI,1) if RES_TI(i,1)==17 || RES_TI(i,1)==46 disp(['Data records at M10 from Run ' ... sprintf('%g',RES_TI(i,1)) ' are not available']); figure; hold on; bar(x_dist(1,[1 7 8])-xw,100*[RES_TI(i,2) RES_TI(i,8)... RES_TI(i,9)],w,'b'); bar(x_dist(1,[1 7 8])+xw,100*weng_TI(1:3,1),w,'g'); title(['Run ' num2str(RES_TI(i,1))... ' \bullet Turbulence Intensity for M1, M7, M8 at 10m a.g.l. \bullet ' ... sprintf('%g',RES_D(i,iD+1)) '\circ ' sprintf('%s',tt)]); xlabel('x [m]'); ylabel('TI [%]'); grid; axis([-400-nw 200+nw 0 20]); legend('Measured','WEng'); hold off; else figure; hold on; bar(x_dist(1,[1 7 8 10])-xw,100*[RES_TI(i,2) RES_TI(i,8)... RES_TI(i,9) RES_TI(i,11)],w,'b'); bar(x_dist(1,[1 7 8 10])+xw,100*weng_TI(:,1),w,'g'); title(['Run ' num2str(RES_TI(i,1))... ' \bullet Turbulence Intensity for M1, M7, M8, M10 at 10m a.g.l. \bullet ' ... sprintf('%g',RES_D(i,iD+1)) '\circ ' sprintf('%s',tt)]); xlabel('x [m]'); ylabel('TI [%]'); grid; axis([-400-nw 200+nw 0 20]); legend('Measured','WEng');

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hold off; end end elseif typres==3 weng=M1_24; %Height z z=[2 5 10 24]; %Horizontal wind speed versus z for M1 for i=1:size(RES_V,1) figure; plot([RES_V(i,2) RES_V(i,3)... RES_V(i,4) RES_V(i,5)],z,'x-',weng(1,:,i),z,'.-'); title(['Run ' num2str(RES_V(i,1))... ' \bullet Horizontal wind speed versus height for M1 \bullet ' ... sprintf('%g',RES_D(i,iD+1)) '\circ ' sprintf('%s',tt)]); xlabel('U [m/s]'); ylabel('z [m]'); grid; axis([0 20 0 30]); legend('Measured','WEng'); end elseif typres==4 weng=M1_24; %Height z z=[2 5 10 24]; %Horizontal wind speed versus z for M7 for i=1:size(RES_V,1) figure; plot([RES_V(i,2) RES_V(i,3)... RES_V(i,4) RES_V(i,5)],z,'x-',weng(7,:,i),z,'.-'); title(['Run ' num2str(RES_V(i,1))... ' \bullet Horizontal wind speed versus height for M7 \bullet ' ... sprintf('%g',RES_D(i,iD+1)) '\circ ' sprintf('%s',tt)]); xlabel('U [m/s]'); ylabel('z [m]'); grid; axis([0 20 0 30]); legend('Measured','WEng'); end elseif typres==5 weng=M1_24; %Height z z=[2 5 10 24]; %Horizontal wind speed versus z for M8 for i=1:size(RES_V,1) figure; plot([RES_V(i,2) RES_V(i,3)... RES_V(i,4) RES_V(i,5)],z,'x-',weng(8,:,i),z,'.-'); title(['Run ' num2str(RES_V(i,1))... ' \bullet Horizontal wind speed versus height for M8 \bullet ' ... sprintf('%g',RES_D(i,iD+1)) '\circ ' sprintf('%s',tt)]); xlabel('U [m/s]'); ylabel('z [m]'); grid; axis([0 20 0 30]); legend('Measured','WEng'); end elseif typres==6 weng=M1_24; %Height z

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z=[2 5 10 24]; %Horizontal wind speed versus z for M10 for i=1:size(RES_V,1) if RES_V(i,1)==17 || RES_V(i,1)==46 disp(['Data records at M10 from Run ' ... sprintf('%g',RES_V(i,1)) ' are not available']); else figure; plot([RES_V(i,2) RES_V(i,3)... RES_V(i,4) RES_V(i,5)],z,'x-',weng(10,:,i),z,'.-'); title(['Run ' num2str(RES_V(i,1))... ' \bullet Horizontal wind speed versus height for M10 \bullet ' ... sprintf('%g',RES_D(i,iD+1)) '\circ ' sprintf('%s',tt)]); xlabel('U [m/s]'); ylabel('z [m]'); grid; axis([0 20 0 30]); legend('Measured','WEng'); end end else disp('n/a'); return; end elseif back==1 weng=M11_10; %Met.Mast x-Distances x_dist=[-397.685 -198.06 -98.513 -48.223... -25.031 -12.993 0 30.826 99.029 199.195 300.411]; %Horizontal wind speed - 10 m for i=1:size(RES_V,1) if RES_V(i,1)==17 || RES_V(i,1)==46 disp(['Data records at M9,10,11 from Run ' ... sprintf('%g',RES_V(i,1)) ' are not available']); figure; plot(x_dist(1,1:8),[RES_V(i,2) RES_V(i,3) RES_V(i,4) RES_V(i,5)... RES_V(i,6) RES_V(i,7) RES_V(i,8)... RES_V(i,9)],'x-',x_dist(1,1:8),weng(i,:),'.-'); title(['Run ' num2str(RES_V(i,1))... ' \bullet A K Y R O Speed-up at all Masts (except for M9,10,11) at 10m a.g.l. \bullet ' ... sprintf('%g',RES_D(i,iD+1)) '\circ ' sprintf('%s',tt)]); xlabel('x [m]'); ylabel('U/Uref'); grid; axis([-400 310 0 20]); legend('Measured','WEng'); else figure; plot(x_dist,[RES_V(i,2)/RES_V(i,12)... RES_V(i,3)/RES_V(i,12) RES_V(i,4)/RES_V(i,12)... RES_V(i,5)/RES_V(i,12) RES_V(i,6)/RES_V(i,12)... RES_V(i,7)/RES_V(i,12) RES_V(i,8)/RES_V(i,12)... RES_V(i,9)/RES_V(i,12) RES_V(i,10)/RES_V(i,12)... RES_V(i,11)/RES_V(i,12) RES_V(i,12)/RES_V(i,12)],... 'x-',x_dist,weng(i,:)/weng(i,11),'.-'); title(['Run ' num2str(RES_V(i,1))... ' \bullet Speed-up at all Masts at 10m a.g.l. \bullet ' ... sprintf('%g',RES_D(i,iD+1)) '\circ ' sprintf('%s',tt)]);

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xlabel('x [m]'); ylabel('U/Uref'); grid; axis([-400 310 0 2]); legend('Measured','WEng'); end end %TI plot M1 M7 M8 M10 - 10 m-------------------------------------------------------------------------------------------------- for i=1:size(RES_TI,1) if RES_TI(i,1)==17 || RES_TI(i,1)==46 disp(['Data records at M10 from Run ' ... sprintf('%g',RES_TI(i,1)) ' are not available']); figure; hold on; bar(x_dist(1,[1 7 8])-xw,100*[RES_TI(i,2) RES_TI(i,8)... RES_TI(i,9)],w,'b'); bar(x_dist(1,[1 7 8])+xw,100*weng_TI(1:3,1),w,'g'); title(['Run ' num2str(RES_TI(i,1))... ' \bullet Turbulence Intensity for M1, M7, M8 at 10m a.g.l. \bullet ' ... sprintf('%g',RES_D(i,iD+1)) '\circ ' sprintf('%s',tt)]); xlabel('x [m]'); ylabel('TI [%]'); grid; axis([-400-nw 200+nw 0 20]); legend('Measured','WEng'); hold off; else figure; hold on; bar(x_dist(1,[1 7 8 10])-xw,100*[RES_TI(i,2) RES_TI(i,8)... RES_TI(i,9) RES_TI(i,11)],w,'b'); bar(x_dist(1,[1 7 8 10])+xw,100*weng_TI(:,1),w,'g'); title(['Run ' num2str(RES_TI(i,1))... ' \bullet Turbulence Intensity for M1, M7, M8, M10 at 10m a.g.l. \bullet ' ... sprintf('%g',RES_D(i,iD+1)) '\circ ' sprintf('%s',tt)]); xlabel('x [m]'); ylabel('TI [%]'); grid; axis([-400-nw 200+nw 0 20]); legend('Measured','WEng'); hold off; end end end end plot_measur.m if plotmode==1 if md==242 tt='(forward flow)'; elseif md==242-180 tt='(backward flow)'; else tt=''; end if typres==1 %Met.Mast x-Distances

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x_dist=[-397.685 0 30.826 199.195]; %Horizontal wind speed - 24 m for i=1:size(RES_V,1) if RES_V(i,1)==17 || RES_V(i,1)==46 disp(['Data records at M10 from Run ' ... sprintf('%g',RES_V(i,1)) ' are not available']); figure; plot(x_dist(1,1:3),[RES_V(i,2) RES_V(i,3)... RES_V(i,4)],'x-'); title(['Run ' num2str(RES_V(i,1))... ' \bullet Horizontal wind speed for M1, M7, M8 at 24m a.g.l. \bullet ' ... sprintf('%g',RES_D(i,iD+1)) '\circ ' sprintf('%s',tt)]); xlabel('x [m]'); ylabel('U [m/s]'); grid; axis([-400 200 0 20]); else figure; plot(x_dist,[RES_V(i,2) RES_V(i,3)... RES_V(i,4) RES_V(i,5)],'x-'); title(['Run ' num2str(RES_V(i,1))... ' \bullet Horizontal wind speed for M1, M7, M8, M10 at 24m a.g.l. \bullet ' ... sprintf('%g',RES_D(i,iD+1)) '\circ ' sprintf('%s',tt)]); xlabel('x [m]'); ylabel('U [m/s]'); grid; axis([-400 200 0 20]); end end elseif typres==2 %Met.Mast x-Distances x_dist=[-397.685 -198.06 -98.513 -48.223... -25.031 -12.993 0 30.826 99.029 199.195 300.411]; %Horizontal wind speed - 10 m for i=1:size(RES_V,1) if RES_V(i,1)==17 || RES_V(i,1)==46 disp(['Data records at M9,10,11 from Run ' ... sprintf('%g',RES_V(i,1)) ' are not available']); figure; plot(x_dist(1,1:8),[RES_V(i,2) RES_V(i,3) RES_V(i,4) RES_V(i,5)... RES_V(i,6) RES_V(i,7) RES_V(i,8)... RES_V(i,9)],'x-'); title(['Run ' num2str(RES_V(i,1))... ' \bullet Horizontal wind speed for all Masts (except for M9,10,11) at 10m a.g.l. \bullet ' ... sprintf('%g',RES_D(i,iD+1)) '\circ ' sprintf('%s',tt)]); xlabel('x [m]'); ylabel('U [m/s]'); grid; axis([-400 310 0 20]); else figure; plot(x_dist,[RES_V(i,2) RES_V(i,3) RES_V(i,4)... RES_V(i,5) RES_V(i,6) RES_V(i,7) RES_V(i,8)... RES_V(i,9) RES_V(i,10) RES_V(i,11)... RES_V(i,12)],'x-'); title(['Run ' num2str(RES_V(i,1))... ' \bullet Horizontal wind speed for all Masts at 10m a.g.l. \bullet ' ...

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sprintf('%g',RES_D(i,iD+1)) '\circ ' sprintf('%s',tt)]); xlabel('x [m]'); ylabel('U [m/s]'); grid; axis([-400 310 0 20]); end end elseif typres==3 %Height z z=[2 5 10 24]; %Horizontal wind speed versus z for M1 for i=1:size(RES_V,1) figure; plot([RES_V(i,2) RES_V(i,3)... RES_V(i,4) RES_V(i,5)],z,'x-'); title(['Run ' num2str(RES_V(i,1))... ' \bullet Horizontal wind speed versus height for M1 \bullet ' ... sprintf('%g',RES_D(i,iD+1)) '\circ ' sprintf('%s',tt)]); xlabel('U [m/s]'); ylabel('z [m]'); grid; axis([0 20 0 30]); end elseif typres==4 %Height z z=[2 5 10 24]; %Horizontal wind speed versus z for M7 for i=1:size(RES_V,1) figure; plot([RES_V(i,2) RES_V(i,3)... RES_V(i,4) RES_V(i,5)],z,'x-'); title(['Run ' num2str(RES_V(i,1))... ' \bullet Horizontal wind speed versus height for M7 \bullet ' ... sprintf('%g',RES_D(i,iD+1)) '\circ ' sprintf('%s',tt)]); xlabel('U [m/s]'); ylabel('z [m]'); grid; axis([0 20 0 30]); end elseif typres==5 %Height z z=[2 5 10 24]; %Horizontal wind speed versus z for M8 for i=1:size(RES_V,1) figure; plot([RES_V(i,2) RES_V(i,3)... RES_V(i,4) RES_V(i,5)],z,'x-'); title(['Run ' num2str(RES_V(i,1))... ' \bullet Horizontal wind speed versus height for M8 \bullet ' ... sprintf('%g',RES_D(i,iD+1)) '\circ ' sprintf('%s',tt)]); xlabel('U [m/s]'); ylabel('z [m]'); grid;

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axis([0 20 0 30]); end elseif typres==6 %Height z z=[2 5 10 24]; %Horizontal wind speed versus z for M10 for i=1:size(RES_V,1) if RES_V(i,1)==17 || RES_V(i,1)==46 disp(['Data records at M10 from Run ' ... sprintf('%g',RES_V(i,1)) ' are not available']); else figure; plot([RES_V(i,2) RES_V(i,3)... RES_V(i,4) RES_V(i,5)],z,'x-'); title(['Run ' num2str(RES_V(i,1))... ' \bullet Horizontal wind speed versus height for M10 \bullet ' ... sprintf('%g',RES_D(i,iD+1)) '\circ ' sprintf('%s',tt)]); xlabel('U [m/s]'); ylabel('z [m]'); grid; axis([0 20 0 30]); end end else disp('n/a'); return; end end dev.m % deviations if back==0 if typres==1 weng=M1_24; for i=1:size(RES_V,1) if RES_V(i,1)==17 || RES_V(i,1)==46 dev_V(i,1)=RES_V(i,1); dev_V(i,2)=0; dev_V(i,3)=(-RES_V(i,3)+weng(7,4,i))/RES_V(i,3)*100; dev_V(i,4)=(-RES_V(i,4)+weng(8,4,i))/RES_V(i,4)*100; dev_V(i,5)=0; else dev_V(i,1)=RES_V(i,1); dev_V(i,2)=0; dev_V(i,3)=(-RES_V(i,3)+weng(7,4,i))/RES_V(i,3)*100; dev_V(i,4)=(-RES_V(i,4)+weng(8,4,i))/RES_V(i,4)*100; dev_V(i,5)=(-RES_V(i,5)+weng(10,4,i))/RES_V(i,5)*100; end end for i=1:size(RES_TI,1) if RES_TI(i,1)==17 || RES_TI(i,1)==46 dev_TI(i,1)=RES_TI(i,1); dev_TI(i,2)=(-RES_TI(i,2)+weng_TI(1,2))/RES_TI(i,2)*100;

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dev_TI(i,3)=(-RES_TI(i,3)+weng_TI(2,2))/RES_TI(i,3)*100; dev_TI(i,4)=(-RES_TI(i,4)+weng_TI(3,2))/RES_TI(i,4)*100; dev_TI(i,5)=0; else dev_TI(i,1)=RES_TI(i,1); dev_TI(i,2)=(-RES_TI(i,2)+weng_TI(1,2))/RES_TI(i,2)*100; dev_TI(i,3)=(-RES_TI(i,3)+weng_TI(2,2))/RES_TI(i,3)*100; dev_TI(i,4)=(-RES_TI(i,4)+weng_TI(3,2))/RES_TI(i,4)*100; dev_TI(i,5)=(-RES_TI(i,5)+weng_TI(4,2))/RES_TI(i,5)*100; end end elseif typres==2 weng=M2_10; for i=1:size(RES_V,1) if RES_V(i,1)==17 || RES_V(i,1)==46 dev_V(i,1)=RES_V(i,1); dev_V(i,2)=(-RES_V(i,2)+weng(1,3,i))/RES_V(i,2)*100; dev_V(i,3)=0; dev_V(i,4)=(-RES_V(i,4)+weng(3,3,i))/RES_V(i,4)*100; dev_V(i,5)=(-RES_V(i,5)+weng(4,3,i))/RES_V(i,5)*100; dev_V(i,6)=(-RES_V(i,6)+weng(5,3,i))/RES_V(i,6)*100; dev_V(i,7)=(-RES_V(i,7)+weng(6,3,i))/RES_V(i,7)*100; dev_V(i,8)=(-RES_V(i,8)+weng(7,3,i))/RES_V(i,8)*100; dev_V(i,9)=(-RES_V(i,9)+weng(8,3,i))/RES_V(i,9)*100; else dev_V(i,1)=RES_V(i,1); dev_V(i,2)=(-RES_V(i,2)+weng(1,3,i))/RES_V(i,2)*100; dev_V(i,3)=0; dev_V(i,4)=(-RES_V(i,4)+weng(3,3,i))/RES_V(i,4)*100; dev_V(i,5)=(-RES_V(i,5)+weng(4,3,i))/RES_V(i,5)*100; dev_V(i,6)=(-RES_V(i,6)+weng(5,3,i))/RES_V(i,6)*100; dev_V(i,7)=(-RES_V(i,7)+weng(6,3,i))/RES_V(i,7)*100; dev_V(i,8)=(-RES_V(i,8)+weng(7,3,i))/RES_V(i,8)*100; dev_V(i,9)=(-RES_V(i,9)+weng(8,3,i))/RES_V(i,9)*100; dev_V(i,10)=(-RES_V(i,10)+weng(9,3,i))/RES_V(i,10)*100; dev_V(i,11)=(-RES_V(i,11)+weng(10,3,i))/RES_V(i,11)*100; dev_V(i,12)=(-RES_V(i,12)+weng(11,3,i))/RES_V(i,12)*100; end end for i=1:size(RES_TI,1) if RES_TI(i,1)==17 || RES_TI(i,1)==46 dev_TI(i,1)=RES_TI(i,1); dev_TI(i,2)=(-RES_TI(i,2)+weng_TI(1,1))/RES_TI(i,2)*100; dev_TI(i,3)=(-RES_TI(i,8)+weng_TI(2,1))/RES_TI(i,8)*100; dev_TI(i,4)=(-RES_TI(i,9)+weng_TI(3,1))/RES_TI(i,9)*100; dev_TI(i,5)=0; else dev_TI(i,1)=RES_TI(i,1); dev_TI(i,2)=(-RES_TI(i,2)+weng_TI(1,1))/RES_TI(i,2)*100; dev_TI(i,3)=(-RES_TI(i,8)+weng_TI(2,1))/RES_TI(i,8)*100; dev_TI(i,4)=(-RES_TI(i,9)+weng_TI(3,1))/RES_TI(i,9)*100; dev_TI(i,5)=(-RES_TI(i,11)+weng_TI(4,1))/RES_TI(i,11)*100; end end elseif typres==3 weng=M1_24; for i=1:size(RES_V,1) dev_V(i,1)=RES_V(i,1); dev_V(i,2)=(-RES_V(i,2)+weng(1,1,i))/RES_V(i,2)*100; dev_V(i,3)=(-RES_V(i,3)+weng(1,2,i))/RES_V(i,3)*100; dev_V(i,4)=(-RES_V(i,4)+weng(1,3,i))/RES_V(i,4)*100; dev_V(i,5)=0; end

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dev_TI=[]; elseif typres==4 weng=M1_24; for i=1:size(RES_V,1) dev_V(i,1)=RES_V(i,1); dev_V(i,2)=(-RES_V(i,2)+weng(7,1,i))/RES_V(i,2)*100; dev_V(i,3)=(-RES_V(i,3)+weng(7,2,i))/RES_V(i,3)*100; dev_V(i,4)=(-RES_V(i,4)+weng(7,3,i))/RES_V(i,4)*100; dev_V(i,5)=(-RES_V(i,5)+weng(7,4,i))/RES_V(i,5)*100; end dev_TI=[]; elseif typres==5 weng=M1_24; for i=1:size(RES_V,1) dev_V(i,1)=RES_V(i,1); dev_V(i,2)=(-RES_V(i,2)+weng(8,1,i))/RES_V(i,2)*100; dev_V(i,3)=(-RES_V(i,3)+weng(8,2,i))/RES_V(i,3)*100; dev_V(i,4)=(-RES_V(i,4)+weng(8,3,i))/RES_V(i,4)*100; dev_V(i,5)=(-RES_V(i,5)+weng(8,4,i))/RES_V(i,5)*100; end dev_TI=[]; elseif typres==6 weng=M1_24; for i=1:size(RES_V,1) weng=M1_24; if RES_V(i,1)==17 || RES_V(i,1)==46 disp(['dev_V for Run ' ... sprintf('%g',RES_V(i,1)) ' are not available']); else dev_V(i,1)=RES_V(i,1); dev_V(i,2)=(-RES_V(i,2)+weng(10,1,i))/RES_V(i,2)*100; dev_V(i,3)=(-RES_V(i,3)+weng(10,2,i))/RES_V(i,3)*100; dev_V(i,4)=(-RES_V(i,4)+weng(10,3,i))/RES_V(i,4)*100; dev_V(i,5)=(-RES_V(i,5)+weng(10,4,i))/RES_V(i,5)*100; end end dev_TI=[]; end elseif back==1 weng=M11_10; for i=1:size(RES_V,1) if RES_V(i,1)==17 || RES_V(i,1)==46 dev_V(i,1)=RES_V(i,1); dev_V(i,2)=(-RES_V(i,2)+weng(i,1))/RES_V(i,2)*100; dev_V(i,3)=(-RES_V(i,3)+weng(i,2))/RES_V(i,3)*100; dev_V(i,4)=(-RES_V(i,4)+weng(i,3))/RES_V(i,4)*100; dev_V(i,5)=(-RES_V(i,5)+weng(i,4))/RES_V(i,5)*100; dev_V(i,6)=(-RES_V(i,6)+weng(i,5))/RES_V(i,6)*100; dev_V(i,7)=(-RES_V(i,7)+weng(i,6))/RES_V(i,7)*100; dev_V(i,8)=(-RES_V(i,8)+weng(i,7))/RES_V(i,8)*100; dev_V(i,9)=(-RES_V(i,9)+weng(i,8))/RES_V(i,9)*100; else dev_V(i,1)=RES_V(i,1); dev_V(i,2)=(-RES_V(i,2)+weng(i,1))/RES_V(i,2)*100; dev_V(i,3)=(-RES_V(i,3)+weng(i,2))/RES_V(i,3)*100; dev_V(i,4)=(-RES_V(i,4)+weng(i,3))/RES_V(i,4)*100; dev_V(i,5)=(-RES_V(i,5)+weng(i,4))/RES_V(i,5)*100; dev_V(i,6)=(-RES_V(i,6)+weng(i,5))/RES_V(i,6)*100; dev_V(i,7)=(-RES_V(i,7)+weng(i,6))/RES_V(i,7)*100; dev_V(i,8)=(-RES_V(i,8)+weng(i,7))/RES_V(i,8)*100; dev_V(i,9)=(-RES_V(i,9)+weng(i,8))/RES_V(i,9)*100; dev_V(i,10)=(-RES_V(i,10)+weng(i,9))/RES_V(i,10)*100; dev_V(i,11)=(-RES_V(i,11)+weng(i,10))/RES_V(i,11)*100;

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dev_V(i,12)=0; end end for i=1:size(RES_TI,1) if RES_TI(i,1)==17 || RES_TI(i,1)==46 dev_TI(i,1)=RES_TI(i,1); dev_TI(i,2)=(-RES_TI(i,2)+weng_TI(1,1))/RES_TI(i,2)*100; dev_TI(i,3)=(-RES_TI(i,8)+weng_TI(2,1))/RES_TI(i,8)*100; dev_TI(i,4)=(-RES_TI(i,9)+weng_TI(3,1))/RES_TI(i,9)*100; dev_TI(i,5)=0; else dev_TI(i,1)=RES_TI(i,1); dev_TI(i,2)=(-RES_TI(i,2)+weng_TI(1,1))/RES_TI(i,2)*100; dev_TI(i,3)=(-RES_TI(i,8)+weng_TI(2,1))/RES_TI(i,8)*100; dev_TI(i,4)=(-RES_TI(i,9)+weng_TI(3,1))/RES_TI(i,9)*100; dev_TI(i,5)=(-RES_TI(i,11)+weng_TI(4,1))/RES_TI(i,11)*100; end end end dev_V dev_TI weng_hjp1_res.m M1_24(:,:,1)=[3.16 3.81 4.37 5.07 3.05 3.70 4.26 4.96 2.78 3.44 4.01 4.75 2.08 2.83 3.52 4.55 1.28 2.43 3.52 4.82 3.55 4.14 4.64 5.27 5.64 5.72 5.69 5.71 4.09 4.76 5.30 5.86 4.01 4.62 5.13 5.75 3.79 4.43 4.95 5.61 3.51 4.20 4.75 5.46 ]; M1_24(:,:,2)=[3.73 4.51 5.17 5.99 3.61 4.38 5.04 5.87 3.28 4.06 4.74 5.62 2.45 3.34 4.16 5.37 1.48 2.86 4.15 5.70 4.21 4.90 5.49 6.23 6.70 6.79 6.75 6.77 4.85 5.64 6.28 6.95 4.76 5.48 6.08 6.82 4.50 5.25 5.86 6.64 4.16 4.98 5.63 6.46 ]; M1_24(:,:,3)=[5.48 6.62 7.59 8.80 5.30 6.43 7.40 8.62 4.82 5.97 6.96 8.26 3.62 4.92 6.12 7.89 2.22 4.22 6.11 8.37 6.17 7.19 8.05 9.15 9.80 9.93 9.88 9.92 7.10 8.26 9.20 10.18 6.97 8.03 8.91 9.99

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6.59 7.69 8.59 9.73 6.10 7.30 8.25 9.47 ]; M1_24(:,:,4)=[5.60 6.77 7.76 9.00 5.42 6.57 7.56 8.81 4.91 6.08 7.10 8.43 3.63 4.97 6.21 8.05 2.09 4.22 6.19 8.55 6.33 7.37 8.25 9.37 10.12 10.24 10.17 10.18 7.30 8.49 9.46 10.46 7.17 8.25 9.15 10.26 6.77 7.90 8.82 9.99 6.26 7.48 8.46 9.71 ]; M1_24(:,:,5)=[2.32 2.91 3.40 4.01 2.25 2.82 3.31 3.93 2.02 2.60 3.10 3.76 1.44 2.09 2.70 3.59 0.54 1.68 2.67 3.81 2.73 3.21 3.64 4.20 4.56 4.57 4.54 4.57 3.11 3.71 4.20 4.70 3.09 3.62 4.06 4.61 2.90 3.46 3.91 4.49 2.65 3.26 3.75 4.37 ]; M1_24(:,:,6)=[2.49 3.01 3.45 4.00 2.41 2.92 3.36 3.91 2.19 2.71 3.16 3.75 1.64 2.23 2.78 3.58 1.00 1.91 2.77 3.80 2.80 3.26 3.66 4.15 4.46 4.52 4.49 4.51 3.23 3.75 4.18 4.63 3.17 3.65 4.05 4.54 2.99 3.50 3.91 4.42 2.77 3.31 3.75 4.30 ]; M1_24(:,:,7)=[2.97 3.59 4.12 4.77 2.88 3.49 4.01 4.67 2.61 3.24 3.78 4.48 1.96 2.67 3.32 4.28 1.20 2.29 3.31 4.54 3.35 3.90 4.37 4.96 5.32 5.39 5.37 5.38 3.85 4.48 4.99 5.53 3.78 4.36 4.83 5.42 3.58 4.18 4.66 5.28 3.31 3.96 4.48 5.14 ]; M1_24(:,:,8)=[2.86 3.45 3.96 4.59 2.76 3.35 3.86 4.49 2.50 3.10 3.62 4.30 1.85 2.53 3.17 4.10 1.07 2.15 3.16 4.36 3.23 3.76 4.21 4.78

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5.16 5.22 5.19 5.19 3.72 4.33 4.82 5.33 3.65 4.21 4.66 5.23 3.45 4.03 4.50 5.09 3.19 3.81 4.31 4.95 ]; M2_10(:,:,1)=[1.69 2.04 2.34 2.71 1.64 1.98 2.28 2.66 1.49 1.84 2.15 2.55 1.13 1.53 1.89 2.44 0.71 1.32 1.89 2.58 1.90 2.21 2.48 2.82 3.01 3.05 3.04 3.05 2.18 2.54 2.83 3.13 2.14 2.47 2.74 3.07 2.03 2.37 2.64 3.00 1.88 2.25 2.54 2.92]; M2_10(:,:,2)=[2.18 2.63 3.02 3.50 2.11 2.55 2.94 3.43 1.91 2.37 2.76 3.28 1.42 1.94 2.42 3.13 0.82 1.65 2.41 3.32 2.46 2.86 3.21 3.64 3.93 3.98 3.95 3.96 2.84 3.30 3.67 4.06 2.78 3.20 3.55 3.98 2.63 3.07 3.43 3.88 2.43 2.91 3.29 3.77 ]; M2_10(:,:,3)=[3.51 4.24 4.86 5.63 3.39 4.11 4.74 5.52 3.08 3.81 4.45 5.28 2.29 3.13 3.90 5.05 1.36 2.67 3.89 5.35 3.96 4.61 5.16 5.86 6.31 6.39 6.35 6.36 4.56 5.30 5.91 6.53 4.47 5.15 5.72 6.41 4.23 4.94 5.51 6.24 3.91 4.68 5.29 6.07 ]; M2_10(:,:,4)=[3.76 4.54 5.20 6.03 3.63 4.40 5.07 5.91 3.29 4.08 4.76 5.65 2.44 3.34 4.17 5.40 1.43 2.84 4.16 5.73 4.24 4.93 5.53 6.28 6.77 6.85 6.81 6.82 4.89 5.69 6.33 7.00 4.80 5.52 6.13 6.87 4.53 5.29 5.91 6.69 4.19 5.01 5.67 6.51 ]; M2_10(:,:,5)=[2.31 2.89 3.38 3.99 2.24 2.81 3.30 3.91 2.01 2.58 3.09 3.74 1.43 2.08 2.68 3.57

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0.53 1.67 2.66 3.79 2.72 3.19 3.62 4.17 4.53 4.54 4.52 4.55 3.09 3.69 4.18 4.68 3.07 3.60 4.04 4.59 2.89 3.44 3.89 4.47 2.64 3.25 3.73 4.34 ]; M2_10(:,:,6)=[2.10 2.54 2.92 3.38 2.04 2.47 2.84 3.31 1.84 2.28 2.67 3.17 1.37 1.87 2.33 3.02 0.79 1.59 2.33 3.21 2.37 2.77 3.10 3.52 3.80 3.84 3.82 3.82 2.74 3.19 3.55 3.93 2.69 3.10 3.43 3.85 2.54 2.96 3.31 3.75 2.35 2.81 3.18 3.65 ]; M2_10(:,:,7)=[2.76 3.33 3.82 4.43 2.67 3.24 3.72 4.34 2.42 3.00 3.50 4.15 1.80 2.46 3.07 3.97 1.07 2.10 3.06 4.21 3.11 3.62 4.06 4.61 4.96 5.02 4.99 5.00 3.58 4.17 4.64 5.14 3.52 4.05 4.50 5.04 3.33 3.88 4.34 4.91 3.08 3.68 4.16 4.78 ]; M2_10(:,:,8)=[2.87 3.46 3.97 4.60 2.77 3.36 3.87 4.51 2.51 3.11 3.63 4.31 1.87 2.55 3.18 4.12 1.09 2.17 3.17 4.37 3.23 3.77 4.22 4.79 5.16 5.23 5.20 5.20 3.73 4.34 4.83 5.34 3.66 4.21 4.67 5.24 3.46 4.04 4.51 5.10 3.20 3.82 4.32 4.96 ]; weng_TI=[1.78 1.51 1.02 1.18 1.23 1.14 1.48 1.27]*1e-1;%[10m 24m] weng_hjp3_res.m M11_10(1,:)=[4.59 4.47 4.20 3.68 3.68 4.89

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6.02 5.59 5.41 5.21 5.00 ]; M11_10(2,:)=[6.85 6.68 6.27 5.49 5.49 7.31 8.99 8.35 8.07 7.78 7.47 ]; M11_10(3,:)=[6.89 6.72 6.29 5.47 5.43 7.41 9.21 8.51 8.23 7.93 7.60 ]; M11_10(4,:)=[5.55 5.41 5.08 4.44 4.44 5.92 7.29 6.77 6.54 6.31 6.05 ]; M11_10(5,:)=[6.45 6.29 5.91 5.19 5.19 6.87 8.43 7.84 7.58 7.31 7.02 ]; M11_10(6,:)=[4.89 4.76 4.47

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3.92 3.92 5.21 6.41 5.95 5.75 5.55 5.32 ]; M11_10(7,:)=[5.26 5.12 4.81 4.21 4.21 5.60 6.89 6.40 6.19 5.97 5.73 ]; weng_TI=[1.85 1.22 1.39 1.54]*1e-1;

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