A surface roughness parameterization study near two proposed windfarm locations in Southern Ontario

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by

David J. Laporte B.Sc., Brock University, 2002

A Thesis Submitted in Partial Fulfillment of the Requirements for the Degree of

MASTER OF SCIENCE

in the Department of Geography

c

David J. Laporte, 2010 University of Victoria

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A surface roughness parameterization study near two proposed windfarm locations in Southern Ontario by David J. Laporte B.Sc., Brock University, 2002 Supervisory Committee

Dr. Stanton Tuller, Supervisor (Department of Geography)

Dr. Ian Walker, Departmental Member (Department of Geography)

Dr. Maurice Danard, Outside Member (Department of Computer Sciences)

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Supervisory Committee

Dr. Stanton Tuller, Supervisor (Department of Geography)

Dr. Ian Walker, Departmental Member (Department of Geography)

Dr. Maurice Danard, Outside Member (Department of Computer Sciences)

ABSTRACT

This thesis presents a study on the applicability of common roughness parameter-ization guidelines in determining values of the surface roughness length (z0). These

guidelines are often used for vertical extrapolation of wind speeds in the renewable energy industry.

The specific goal of this thesis is to determine whether these guidelines (most notably the Davenport roughness classification system) can provide a quality esti-mate of the roughness length for wind resource assessment purposes. To test this hypothesis, empirical relationships between calculated values of z0 derived from

loga-rithmic profile fitting and those estimated from subjective terrain analyses guidelines are compared at two prospective wind farm locations in Southern Ontario.

The results suggest that the use of roughness parameterization guidelines for ex-trapolating wind speeds can cause serious underestimation of the local wind resources especially at locations where local topographic challenges exist. Their use in energy assessments should be avoided if possible through on-site measurements of the wind profile.

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List of Tables

Table 2.1 The Revised Davenport roughness classification (Wieringa, 1992) 12 Table 2.2 Classification of terrain roughness (Davenport et al., 2000) . . . 15 Table 3.1 Instrumentation details . . . 32

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List of Figures

Figure 2.1 Typical variation of wind speed with height on a linear and log

scale . . . 5

Figure 2.2 Wind profiles over typical surfaces in idealized logarithmic con-ditions . . . 7

Figure 2.3 Variation of the wind profile below the displacement height . . 8

Figure 2.4 ’ESDU’ roughness classes (Jensen et al., 1984) . . . 13

Figure 2.5 Effect of atmospheric stability on measured wind profiles . . . . 20

Figure 2.6 Multiple internal boundary layers forming downwind of rough-ness changes . . . 25

Figure 3.1 General topography surrounding Sites A and B . . . 30

Figure 4.1 Wind shear profile at Site A, with average values . . . 39

Figure 4.2 Direction-dependent wind speed profiles at Site A . . . 41

Figure 4.3 Direction-dependent wind speed profiles at Site A cont. . . 42

Figure 4.4 Distribution of z0 by time of day at Site A over the entire moni-toring period (white areas represent missing data) . . . 43

Figure 4.5 Distribution of z0 values at Site A throughout the day . . . 43

Figure 4.6 Relationship between wind speeds and z0 at Site A . . . 44

Figure 4.7 Directional distribution of wind at Site A . . . 44

Figure 4.8 Wind shear profile at Site B, with average values . . . 46

Figure 4.9 Direction-dependent wind speed profiles at Site B . . . 47

Figure 4.10Direction-dependent wind speed profiles at Site B cont. . . 48

Figure 4.11Seasonal distribution of z0values at Site B over the entire dataset (white areas represent missing data) . . . 49

Figure 4.12Average distribution of z0 throughout the day at Site B . . . . 50

Figure 4.13Relationship between 50 m wind speeds and z0 at Site B . . . . 51

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Figure 4.15Expected Davenport class (top), and calculated z0 (m) at Site A

(bottom) . . . 54 Figure 4.16Expected Davenport class (top), and calculated z0 (m) at Site B

(bottom) . . . 55 Figure 5.1 Standard binning vs. optimized method . . . 61

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ACKNOWLEDGEMENTS

A great deal of gratitude goes to the staff of the University of Victoria’s Geography Department, particularly to Dr. Stanton Tuller, who provided the guidance and support required to complete this project. Thanks also to Dr. Ian Walker, Dr. Maurice Danard and Dr. Ned Djilali for helpful comments, and to the Positive Power Co-Operative for provision of raw wind data. The author also would like to recognize the financial assistance of the University of Victoria, NSERC and Dr. Jim Salmon of Zephyr North Limited.

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Introduction

1.1 A problem in the wind energy industry

Increasing demand for energy, especially from renewable sources, has led to substan-tial growth in North America’s wind energy industry in the last ten years (Gipe, 2004). This growth was aided by technical advancements in turbine components manufac-turing where, in addition to larger blades, higher towers can be designed from new, lightweight composite materials. As a result of these advancements, turbine nacelles are now mounted on towers up to 120 meters in height, with blade tips of these larger turbines often reaching heights up to 160 meters above ground level at the apex of their rotation.

To accurately determine rates of return on investment when planning a windfarm, wind developers rely on short periods of wind data collected on-site as an indication of the long term wind resource. This monitoring is typically conducted using lower-cost tubular tower designs (reaching 60-80 m agl), and rely on vertical extrapolation techniques to estimate the wind resource at the proposed hub height. The difference between the measured heights and turbine hub height is often in excess of 30 meters. Faced with the difficulty of extrapolating measured wind speeds over greater heights, wind resource consultants rely on equations which govern the vertical distri-bution of wind speed with height (see Chapter 2). One of the parameters in these equations, the aerodynamic roughness length, or z0is dependent on the characteristics

of the surface over which the wind has been flowing.

If z0 is known, it becomes a numeric exercise to extrapolate wind speeds to heights

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be estimated, derived experimentally or calculated using measured data, with each method likely to yield different results (explained further in Chapter 2).

1.2 Implications for the wind energy industry

A failure to parameterize the surface characteristics over which the wind is flowing into an appropriate z0 value has potentially severe implications for a wind development

project, as hub height wind speeds will be either over or under-estimated depending on the degree of error in the parameterization (Kelley et al., 2002). This problem is well-documented within the wind energy industry. Many reviews and studies of the North American and worldwide wind energy industry identify ’improved research and development’ in wind resource assessments as a major priority (Thor and Weis-Taylor, 2002). Particular attention is focused on the problem of assigning roughness lengths (Davenport et al., 2000).

1.3 Objectives of research

This thesis was undertaken to identify problems associated with commonly-used tech-niques for estimating the aerodynamic roughness length, or z0, for vertical

extrapola-tion of wind speeds for wind resource assessment. The main objective is to determine whether these commonly-used techniques (most notably the Davenport roughness classification system) can be used to provide a reliable estimate of the roughness length for wind resource assessment purposes.

This research will:

1. Present a detailed review of the history, current trends, and future developments in surface roughness parameterization within the wind energy industry, focusing specifically on two of the most common techniques: vertical extrapolation of measured wind profiles and the Davenport roughness classification system. 2. Summarize the wind and surface roughness characteristics at two meteorological

stations installed for wind resource assessment purposes in southern Ontario. 3. Quantify the difference in surface roughness lengths determined at these two

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4. Discuss the implications that calculations made using these different methods have on the estimated energy content of the wind at an extrapolated height, and suggest measures to reduce uncertainties in the calculation.

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Chapter 2 Literature Review

2.1 Surface layer theory development

The theories used in the vertical extrapolation of wind speeds near the ground are derived from research on the dynamic properties of the lowest layer of the atmosphere, the Atmospheric Boundary Layer (or ABL). This layer of the atmosphere closest to the earth, whose height typically ranges from 200-2000 m above the ground is influenced by contact with the earth’s surface. The lowest 10% of the ABL, called the surface layer is where turbulence and frictional drag from the ground have the most significant effects (Huschke, 1989).

The surface layer of the ABL has been studied extensively due to its accessibility and importance, as all human life resides in this layer. Observed characteristics from these studies were often consistent and were used to form the basis of the similarity theory principles that are used today in defining the behavior of vertical wind profiles within the ABL (Stull, 1988).

Specific scaling relationships (such as the Monin-Obukhov similarity theory) were developed for the surface layer and subsequently proven to be accurate when the winds are not calm, and in heights between 1-200 m above ground (Panofsky et al., 1977). These similarity relationships began to serve as the basis for the scientific study of the most important characteristic of the surface layer for wind energy developers: the logarithmic relationship between wind speed and height above the ground.

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Figure 2.1: Typical variation of wind speed with height on a linear and log scale

2.1.1 The logarithmic wind profile

Empirical studies using Monin-Obukhov similarity relationships revealed that wind speed variation with height in the surface layer of the ABL can often be accurately described by a logarithmic decay curve in neutral atmospheric conditions (Oke, 1987). When wind speeds are plotted against the natural logarithm of height, ln(z), the profile approximates a straight line (Figure 2.1).

This provides the theoretical basis of the logarithmic wind profile, or Prandtl-von Karman equation: uz = u∗ κ ln z z0 (2.1) where uz is the wind speed at height z , u∗ is friction velocity, κ is the von Karman

constant, and z0 is the surface roughness length (variables which are discussed further

in Section 2.2). The plot of the logarithmic wind profile is used to extrapolate wind speed from a measured reference height Href to another, typically higher turbine hub

height (Hnew).

unew = uref

ln(Hnew/z0)

ln(Href/z0)

(2.2) Equation 2.2 is one of the most widely used in the wind energy industry. But to solve this formula, it is necessary to determine z0.

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2.1.2 Surface roughness length

Over most natural terrain, the surface cover is not uniform and changes significantly from location to location. While atmospheric pressure gradient forces are the major control of wind speed and direction in the ABL, winds near the ground are heavily influenced through frictional drag imposed by surface roughness (Oke, 1987). This frictional drag causes turbulence, giving rise to a sharp decrease in wind speed as the underlying surface is approached. The height at which this frictional drag influence is felt is related to the size and distribution of the underlying surface elements.

Theoretically, z0 is defined as the height in meters above the ground at which

the mean wind speed becomes zero when extrapolating the logarithmic wind speed profile downwards through the surface layer (Huschke, 1989). Although technically accurate, this definition is not generally used due to problems with ABL similarity relationships very close to the ground (further examined in Section 2.3.4), as well as problems arising from the use of displacement heights (described in Section 2.1.3).

As z0 is observed to increase with the average height and spacing of individual

elements of the ground cover, such as trees or houses, it is often defined in this fashion (Jackson, 1980). An alternative but related definition suggests that z0 is the size of

turbulent eddies on the ground surface created when winds are disrupted by items on the surface; where larger z0 values indicate larger eddy mixing, and likely larger

surface objects (Panofsky and Dutton, 1984). Other researchers have attempted to give more abstract definitions of z0. Davenport et al. (2000) relate the value of z0

to the effectiveness of a surface area in transforming the energy of the average wind which flows over it into turbulent motion in the boundary layer.

The influence of z0 on the logarithmic wind profile is significant. When z0 is

small, the wind profile increases rapidly with height over a short length, and then is relatively stable above that height. When z0 is large, the profile has a slow and

smooth increase with height (World Meteorological Organization, 1981).

These influences are not immediately felt as an abrupt ’step’ in the wind profile, but rather gradually felt over a given distance or fetch. A number of models were subsequently developed to predict the influence of a change in roughness lengths in the wind profile over fetch distances, which were then incorporated into larger mesoscale wind flow models (Jensen, 1978; Taylor, 1970; Walmsley et al., 1986; Yu et al., 2006).

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Figure 2.3: Variation of the wind profile below the displacement height

2.1.3 Displacement heights

Although in theory the logarithmic shape of the wind profile extends towards the ground until the wind speed reaches zero, it is noted that when large roughness elements uniformly cover greater than 20% of the land surface, the motion of air within these elements becomes sheltered and causes a deviation from the typical logarithmic profile (Davenport et al., 2000). In these cases, the top of these elements tends to act as a proxy surface where the logarithmic profile is valid only above this height. The height of this proxy surface above the ground surface is typically presented in meteorological literature as the displacement height, or(d) (Huschke, 1989).

A displacement height created by fairly uniform roughness elements on the wind profile is illustrated in Figure 2.3. As the average height of the roughness element is approached, wind speeds begin to decrease rapidly with descending height down to and through the average height of the roughness elements.

Displacement heights can be calculated using analytical methods, but are often visually estimated as the height where the mean drag on the surface appears to act (Jackson, 1980). In Figure 2.3, it is straightforward to see that d should be somewhere

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around 7 meters, as the profile curves downwards rapidly below this approximate height.

Extrapolation of the logarithmic wind profile downwards to where the wind speed, u, is zero locates the value of d where d = z − z0 (Riou, 1984). Typically, d is 60-80%

of the height of roughness elements (Huschke, 1989; Panofsky and Dutton, 1984). Mathematically, d can be accounted for in Equation 2.1 to solve for u when a uniform roughness surface exists, such as in a forest with trees of the same height, or a suburban low rise neighborhood:

uz = u∗ κ ln z − d z0 (2.3) Using this equation, wind profile extrapolation can be applied to the air above the uniformly-rough surface. It is only applicable where z ≥ d + z0 (when measurements

are conducted above the displacement height).

It is also possible to calculate the exact location of d from wind and temperature measurements (DeBruin and Moore, 1985; Jackson, 1980; Lo, 1990). However, these studies have not as of yet agreed on an accepted method for use in the wind energy industry.

Other researchers have attempted to calculate d from satellite data (Jasinski et al., 2005; Jasinski and Crago, 1999; Schaudt and Dickinson, 2000), for use in global circulation models with some success. There also exists the possibility of estimating d in forested areas from lidar canopy height research (Frazer et al., 2005). However, none of these advanced techniques are currently in widespread use by the wind energy industry, leading to d being ignored or greatly simplified in most cases.

2.2 History of roughness parameterization

Because a variety of scientific fields are concerned with surface roughness lengths and the calculation of z0, many independent methods of solving for it exist. They

are reviewed in the following sections, building on earlier published summaries by Barthelmie et al. (1993) and Wieringa (1996).

2.2.1 Fitting to the wind profile

The definition of z0 is the height above the ground at which the mean wind speed

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can be solved graphically (as the y-axis intercept on a semi-log plot of measurement heights against wind speed), and mathematically (by fitting the log function using a least-squares regression technique) (Robinson, 1962).

Stearns (1970) calculated z0 values for years of wind data by minimizing the sum

of squares error between wind speeds observed at several heights. The height at which the line of best-fit in the wind data intersects with the y (or height) axis corresponded to the surface roughness length. Computerized non-linear regression algorithms such as the Marquardt or the Gauss-Newton method can also be used to solve for z0. These

have the advantage of being less subject to significant errors from errant data (Stull, 1988). However, the accuracy of a sum-of-squares regression fit is greatly improved through prescreening of data according to a quality-of-fit measure. This technique can reduce the uncertainties involved in fitting errant data to the wind profile and has been shown to yield more accurate results (Schaudt, 1998). Compared to other techniques, it is computationally-intensive, but has the advantage of relying solely on data that would be recorded from a typical wind resource measurement campaign. This method is typically used in numerical research studies and wind flow modeling applications. The accuracy of the calculation is heavily dependent on the accuracies in the wind profile measurement. The limitations of this and all other methods are discussed in Section 2.3.

2.2.2 Correlation with average obstacle heights

Microclimatological research suggests that surface roughness is primarily influenced by the average height of individual roughness elements (surface objects) and their density (Sutton, 1953). This led to a number of numerical models relating z0 values

to the height (h) and density (λ) of these elements (Counihan, 1971; Lettau, 1969; Marshall, 1971; Wooding et al., 1973). The most frequently validated of these analyt-ical methods is the one proposed by Lettau (1969), whose field experiments revealed that:

z0 = 0.5¯hS/A (2.4)

where ¯h is the average height of obstacles within the area, S is the total projected frontal area of the obstacles, and A is the surface area of the obstacles. This method works well in areas with relatively large values of S.

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and density of the ground obstacles, to a maximum density coverage of 20% of the surface area. Above 20% density coverage, z0 begins to decrease as the top cover

of the roughness elements becomes a new proxy surface for the wind profile. This problem is addressed by using a displacement height, (d), to simulate the effect of a proxy surface on the wind profile measurements (Panofsky and Dutton, 1984).

Early experimental researchers modified flat surfaces with measurable roughness elements for large-scale roughness change studies. Kutzbach (1961), whose research was used by Lettau (1969) to derive Equation 2.4, placed crates in regularly-spaced grids of different densities over a frozen lake surface. Blackadar et al. (1967) cut large swaths of vegetation near New Jersey swamps. Later studies relied on scaling using standing sticks to simulate shrub vegetation in smaller-scale models (Dong et al., 2001).

With the aid of wind tunnel studies, more detailed models were proposed for industrial areas with measurable distances and building geometries (Bottema, 1996; Petersen, 1997; Tieleman, 2003), and later modified using real world measurements in cities and complex urban areas (Grimmond and Oke, 1999). Correlation attempts associating least squares regression-measured z0 against the geometric qualities of the

existing roughness elements determined that the earlier wind tunnel models could typically only be held to a 30% uncertainty estimate (Fang and Sill, 1992). This type of analysis has recently been referred to as a morphometric approach for z0

determination. Additional types of morphometric approaches are well-documented in Grimmond and Oke (1999).

Due to the complex arrangement of real-world surface elements across the ac-tual terrain, it has been difficult to find all-encompassing relationships between z0

and measurable geometric characteristics of particular surfaces covering a larger ge-ographic area. Although these morphometric approaches are rarely used in wind energy applications, they are commonly-used for z0 determination in urban areas. As

the wind profile near the ground in urban areas is generally not logarithmic, it cannot be modeled using any of the other described techniques (Munn, 1970).

2.2.3 Terrain classification systems

The influence of terrain features on wind profiles within the ABL is widely-researched in various scientific fields. From work in sediment transport, theoretical fluid dy-namics, civil engineering and agricultural meteorology; common ranges, values and

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Table 2.1: The Revised Davenport roughness classification (Wieringa, 1992) Class (m) Landscape Description

1: Sea (0.0002) Open water, tidal flat, snow, with free fetch ≥ 3km. 2: Smooth (0.005) Featureless land with negligible cover, or ice.

3: Open (0.03) Flat terrain with grass or very low vegetation, and widely separated low obstacles, airport runway.

4: Roughly Open (0.10) Cultivated area, low crops, occasional obstacles separated by more than 20 obstacle heights H.

5: Rough (0.25) Open landscape, crops of varying height, scattered shelter belts, etc., separation distance of 15 H.

6: Very Rough (0.5) Heavily used landscape with open spaces = 10 H; bushes, low orchards, young dense forest.

7: Closed (1.0) Full obstacle coverage with open spaces = H, e.g., mature forests, low-rise built-up areas.

8: Chaotic (≥ 2.0) Irregular distribution of very large elements: city centre, big forest with large clearings.

classes for z0 have been established. These generalized approaches have been used

by researchers in these fields since the 1950’s for analytical and descriptive purposes (Sutton, 1953).

One of the most noted of these classifications was created by Davenport (1960) for use by building design engineers calculating wind shear stress. It listed typical values for z0 across a range of broad terrain categories determined from other studies and

engineering experience. This power-law exponent classification system (now known as the Davenport 60’ classification) was redefined in Wieringa (1980) and Wieringa (1992), the latter incorporating two additional classification levels; smooth and sea (Table 2.1).

This early terrain roughness classification was widely used by meteorologists and physicists with interests in the development and science of wind power. In addition to the Davenport system, many other roughness classification lists were published, including ones by Oke (1987) with greater emphasis on urban areas. Although never formally published, the Engineering Sciences Data Unit (ESDU) roughness classes (Figure 2.4) were often cited in wind energy literature (Stull, 1988). For a much more comprehensive list of published surface roughness classes see Wieringa (1992).

As these classification systems began to be widely used in mesoscale modeling applications, their accuracy became the subject of increasing debate (Wieringa, 1986).

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The results of additional research revealed that many historically-popular terrain class reviews (with the exception of the Davenport class) underestimated the actual terrain roughness by a factor of two (Wieringa, 1993). This research led to the Davenport class being the most widely used in North America, although European countries still generally preferred the ESDU estimates.

After the work of Grimmond et al. (1998) on roughness lengths in urban areas, the Oke (1987) list was updated to include results from more detailed observations over urban areas. Improvements to the roughness determination of heavily forested areas was also completed (Bottema et al., 1998; Jasinski and Crago, 1999; Lo, 1990). This cumulative research led to the current version of the Davenport roughness classes in Table 2.2 (Wieringa et al., 2001).

With the exception of very smooth surfaces (’sea’ or ’smooth’ in the Davenport classes), typical roughness assignments are unlikely to be off by more than one class. This implies that z0 is known within a factor of two, corresponding to an exposure

uncertainty of approximately 6% in surface wind speeds (Wieringa, 1986). However, some recent studies have found that in agricultural landscapes, roughness lengths calculated from profile relationships can be over 20 times higher than those commonly reported in the literature (Tsai and Tsuang, 2005).

Newer sites-specific roughness classification systems such as the one used by the Ontario Ministry of Natural Resources in their Ontario Wind Resource Atlas are characterized by significantly larger z0 values over forested terrain compared to the

Davenport classes (Ontario Ministry of the Environment, 2007).

2.2.4 Areal averaging of surface roughness

When modeling climatic regimes over large areas, some researchers have resorted to areal averaging of roughness length characteristics. In this, a new effective rough-ness length, z₀ef f, is created based on the averages of the nearby individual surface roughness parameters (Mason, 1988). This technique is widely used in heterogeneous terrain, where roughness lengths vary. z₀ef f is defined as the value of the roughness length which, in homogeneous terrain, gives a value of stress equal to the areally averaged stress occurring in the heterogeneous terrain (Garratt, 1990).

Attempts at calculating roughness lengths over large areas were first done by Fiedler and Panofsky (1972), and later optimized by Walmsley et al. (1986), Taylor (1987), Wieringa (1986) and Mason (1988).

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Table 2.2: Classification of terrain roughness (Davenport et al., 2000) Class (m) Landscape Description

1: Sea (0.0002) Open sea or lake (irrespective of wave size), tidal flat, snow covered flat plain, featureless desert, tarmac and concrete with a free fetch of several kilometers.

2: Smooth (0.005) Featureless land surface without any noticeable obstacles and with negligible vegetation: e.g. beaches, pack ice without large ridges, marsh and snow-covered or fallow open country. 3: Open (0.03) Level country with low vegetation (e.g. grass) and isolated obstacles with separations of at least 50 obstacle heights; e.g. grazing land without windbreaks, heather, moor and tundra, runway area of airports. Ice with ridges across-wind.

4: Roughly Open (0.10) Cultivated or natural areas with low crops or plant covers, or moderately open country with occasional obstacles (e.g. low hedges, isolated low buildings or trees) at relative horizontal distances of at least 20 obstacle heights.

5: Rough (0.25) Cultivated or natural area with high crops or crops of varying height, and scattered obstacles at relative distances of 12 to 15 obstacle heights for porous objects (e.g. shelterbelts) or 8 to 12 obstacle heights for low solid objects (e.g. buildings). Analysis may need d.

6: Very Rough (0.5) Intensively cultivated landscape with many rather large ob-stacle groups (large farms, clumps of forest) separated by open spaces of about 8 obstacle heights. Low densely-planted ma-jor vegetation like bushland, orchards, young forest. Also, area moderately covered by low buildings with interspaces of 3 to 7 building heights and no high trees. Analysis requires d. 7: Skimming (1.0) Landscape regularly covered with similar-size large obstacles, with open spaces of the same order of magnitude as obstacle heights; e.g. mature regular forests, densely built-up area without much building height variation. Analysis requires d. 8: Chaotic ≥ (2.0) City centers with mixture of low-rise and high-rise buildings,

or large forests of irregular height with many clearings. Anal-ysis by windtunnel advised.

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In many land use models, effective roughness lengths over large areas are computed from satellite-derived vegetation indices (Hasager et al., 2003; Jasinski et al., 2005; Jasinski and Crago, 1999). This method is often used in large-scale meteorological models because it maintains data resolution while reducing the required processing time (Garratt, 1977).

Simple areal-averaging for determining z₀ef f is problematic as z0 is interpreted

logarithmically. Therefore, larger values of z0have much more influence on the average

than small values (Mason, 1988; Schmid and Bunzli, 1995).

Walmsley et al. (1986) suggest that the log of the individual roughness components be averaged, while Wieringa (1986) and Mason (1988) argue that the drag coefficients of the components at some height be averaged as an alternative. These methods have been proven effective in many comparative studies (Borak et al., 2005; Bottema et al., 1998; Holtslag, 1984).

2.2.5 Standard deviation measurements

An alternative method introduced by Beljaars (1987) can be used to calculate z0

from the standard deviation of the wind speed, as (σu) is directly proportional to the

degree of surface roughness in neutral atmospheric stability:

σu/u = 1/ln(z/z0) (2.5)

Using this equation, z0can be isolated from a single level of wind data. This technique

is often used with hot-wire quick response anemometers (Liu et al., 2003) or sonic anemometers (Martano, 2000). Since these sensors are not typically used for wind energy resource assessment purposes, it is considered to be outside the scope of this study.

2.2.6 Gustiness measurements

This type of measurement is a variation on the standard deviation technique, incor-porating the ratio of extreme gusts to the average wind speed at a station (Wieringa, 1976, 1993).

This method of deriving z0 has been tested experimentally by Bottema et al.

(1998) and found to give decent agreement with profile-derived measurements. Holt-slag (1984), Ashcroft (1994) and Verkaik (2000) provide examples on using gustiness

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measurements for the estimation of z0 in research meteorology. Its use is limited for

wind resource assessment since it requires a number of recorded variables that are not typically collected, such as component calculations of the wind vector (Barthelmie et al., 1993).

2.2.7 Surface drag coefficient

In addition to the standard deviation and gustiness measurements, some work has been done on using a measurement of the surface drag coefficient for calculating roughness lengths (Mahrt et al., 2001). The drag coefficient is related to surface wind speeds by:

CD(z)= (u∗/uz)2 (2.6)

Combining Equations 2.6 and 2.1 provides:

CD(z) = [κ/ln(z/z0)]2 (2.7)

which can then be used to determine z0 (Wieringa, 1992). However, this method is

limited by its dependency on accurate calculations of u∗.

2.2.8 Power law method

Although not technically a method for determining the surface roughness, it is in-cluded here because it is a widely-used alternative to the use of roughness lengths in the logarithmic wind profile.

Wind profiles are more often described by a power law relationship than a logarith-mic one in the United States, especially in the engineering field. Where logarithlogarith-mic wind profile extrapolation is derived from a theoretical understanding of the way wind flows in the ABL, the power law method is derived empirically from actual wind profile measurements (Gipe, 2004). It is usually given as:

u = u1

z z1

p

(2.8)

where u and u1 are the wind speeds at heights z and z1 respectively, and p is the

power law exponent. This relationship is often referred to as the one-seventh power law, as the most common value of p found in wind energy literature across open

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terrain in neutral stability is 0.14. Algebraically, the exponent p is related to z0 by:

p = 1

ln(z/z0)

(2.9)

Many studies (Farrugia, 2003; Kelley et al., 2002; Sisterton et al., 1983) have determined that wind shear profiles are much greater than 0.14 over most terrain types. Typical values are often in the range of 0.2 to 0.25 in the southwestern United States (Archer and Jacobson, 2003). Sutton (1953) argued that the power-law form of the wind profile is not as accurate as the logarithmic form in neutral stability conditions, especially near the surface. Some studies (Hanafusa et al., 1986; Peterson and Hennessey, 1978; Pneumatikos, 1991) indicate that surface roughness values are not that important when determining the wind profile, and that the power law yields adequate, conservative results.

2.2.9 Other techniques

A number of other techniques have been presented for finding z0 in research

through-out the last twenty years. All of these methods have been shown to be successful by their creators, but have not yet received widespread acceptance.

One newer technique that has yet to be systematically scrutinized by testing is the use of sophisticated sensing technologies such as radar or lidar remote sensing equipment (Hasager et al., 2003), laser altimeter data (DeVries et al., 2003), and radar backscatter correlations (Blumberg and Greeley, 1993) to measure detailed surface roughness parameters directly over large areas. These techniques seem to hold some significant promise, but current-generation wind resource modeling software is not designed to handle such detail in z0 distributions.

Experimental techniques have been utilized to determine roughness using the three dimensional component measurements of wind speeds on a sonic anemometer (Sozzi et al., 1998). This technique is limited by the infrequent usage of ultrasonic anemom-etry in current wind resource assessment studies.

Ma and Daggupaty (2000) used a variational method of linear regression to esti-mate z0 based on wind and temperature measurements which reduces the sensitivity

of the analysis to measurement errors compared to those using traditional regression techniques.

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measured by tethered-balloon radiosondes have been completed with some success (Grant, 1991; Hignett and Hopwood, 1994).

There are a wide number of z0 estimating techniques in other academic fields that

involve using specialized equations (in aeolian sediment transport, fluvial dynamics, theoretical fluid dynamics, etc.), that are not discussed because they are not well-suited for meteorological use.

It should also be mentioned that specialized techniques exist for estimating z0

over large bodies of water for offshore wind farms as they experience wave action of varying intensities, although these are not used in North America.

2.3 Problems with established techniques

Despite the variety of methods for estimating z0, an industry standard has yet to be

defined. This is likely caused by problems with each of the above methods. In some instances, specific concerns force the use of different techniques. Regional practices call for specific techniques in other cases. Some of the major problems associated with the above methods for z0 determination are presented below.

2.3.1 Irregular wind profiles

One of the main limitations of wind energy research is that all extrapolation of data generally assumes a neutral, uniform wind profile. In reality, wind shear profiles are dynamic, changing with time and place. They are location-dependent (changing with surface roughness and prevailing wind directions), and also change as a function of the stability of the air within the atmospheric boundary layer (van Lieshout, 2004).

It is easiest to model the variation of u with height in neutral atmospheric condi-tions as natural convection forces on air are greatly reduced (Panofsky and Dutton, 1984). Wind speed profiles in highly stable environments, by contrast, are char-acterized by greater speed with height; while unstable environments have relatively small speed increases with height (Figure 2.5). Plotted on a semi-logarithmic axis, the wind profile in neutral atmospheric stability appears as a straight line, as a downward-curving line in stable atmospheric conditions (where cooling of the surface suppresses vertical mixing), and as an upwards-curving line in unstable atmospheric conditions with thermal mixing of air (Petersen et al., 1997).

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inherent in Monin-Obukhov similarity theory by incorporating stability-correction scaling parameters in profile calculations. However, stability is difficult to determine using standard datasets for wind energy research, requiring air temperature profile measurements from sensors at two different heights (near the bottom and the top of the tower).

Some research has attempted to address this problem through the use of time domain wind profile calculations, adjusted based on probable atmospheric conditions during the time-of day (van Lieshout, 2004).

It is often assumed that when wind speeds are over a certain threshold, the air temperature profile is likely near-neutral. Patil (2006) found that calculated values of z0 in wind speeds under 2 m/s varied by orders of magnitude, but values for wind

speeds over 2 m/s varied only slightly. In practice, the stratification in the atmosphere does not have to be exactly neutral, but the Richardson number should be small (less than 0.01), which is generally satisfied when there are strong winds (Panofsky and Dutton, 1984). Wieringa (1996) found that, at levels above 30 m, the influence of thermal stability on the wind profile becomes important only if the winds are weak.

Although stability corrections are necessary for research-grade wind profile cal-culations (Petersen et al., 1997), they are often overlooked in profile studies in the wind energy industry. Wind energy researchers are mostly concerned with profile relationships in strong winds which would already cause mechanical turbulence. This turbulence effectively renders any stable or unstable conditions neutral, where the logarithmic wind profile applies (Ro and Hunt, 2007).

Other factors can influence the shape of the wind profile. For example, Barthelmie et al. (2007) found that changes in humidity can affect the wind speed profile by up to 5%. Topographic factors can also play a role (discussed below).

2.3.2 Measurement in Rough Terrain

In complex terrain, the effects of hills and valleys act as roughness elements. As wind blows across the topography, pressure differences build between the leeward and windward sides of hills, increasing frictional losses and henceforth the effective surface roughness (Bottema et al., 1998). Problems also exist with the use of friction velocity calculations (see Section 2.3.5) in complex topography, as they will vary heavily according to the slope of the terrain (Park and Park, 2006).

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Kustas and Brutsaert (1986) determined that calculated z0 data from profile

re-lationships in relatively complex terrain (e.g., rolling, 100 m high hills with distances between on the order of 1 km) were in good agreement with standard relationships found in regular, smooth terrain.

2.3.3 Data accuracy requirements

Data must be carefully collected to ensure that it can be properly used for wind profile analysis. One of the main difficulties of meteorological monitoring studies is understanding how far the conclusions reached are affected by the characteristics of the instruments used for monitoring (Sutton, 1953).

Because roughness lengths are usually derived from wind profile data, random errors in the measured profile can have large implications on the estimated z0. A

typical wind resource assessment tower uses 3-4 anemometers at various levels to sample a wind profile. If one of these anemometers is recording data with an error of a few percentage points, it could cause significant error in the wind profile regression fitting. For example, with only two measurement levels a 1% mean wind speed error at one level could result in a 25% error in calculation of z0 (Bottema et al., 1998).

2.3.4 Acceptable height ranges

According to similarity theory, profile relationships within the ABL should be scale-independent. But in reality, the logarithmic profile is not valid above and below certain heights (Panofsky and Dutton, 1984).

During turbulent eddies, air flows perpendicular to the ground surface, creating mixing which disturbs the profile shape near the ground. The height to which these eddies extend and to which the profile is disturbed depends on the roughness of the surface over which the wind is flowing (Beljaars, 1987). Wind will flow in a laminar fashion nearer to the ground over a smooth surface (such as sand or calm water) than it would over a surface covered by high grasses or scattered trees. This dependence is incorporated into the logarithmic wind profile through the influence of z0.

Many researchers have determined that the upper boundary of the surface layer over relatively uniform terrain is between 150-200 m (Bottema et al., 1998; Panofsky and Petersen, 1972). However, recent analyses of meteorological data from two 150 m towers revealed that the theoretical wind profiles based on surface-layer theory

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and Monin-Obukhov scaling are only valid up to heights of 80-100 m (Gryning et al., 2007).

2.3.5 Variables

In addition to wind speeds and heights, a number of additional variables are used in the logarithmic wind profile equations.

von Karman Constant

The von Karman constant is related to the logarithmic wind profile, in that, κ/u∗

is the slope of the linear regression fit of the wind profile (Panofsky and Dutton, 1984). Although κ is defined as a constant in the wind profile equation, there has been much debate over its value. Sutton (1953) showed that the value of κ changes with atmospheric stability. Munn (1970) expanded this, showing that κ is only con-stant when production and dissipation of turbulent kinetic energy are in balance, and recommended incorporating a degree of error in all calculations involving κ.

Despite these studies, scientists typically use a constant value for κ of approxi-mately 0.4. Frenzen and Vogel (1995) examined experimental and theoretical results given by others and suggested that κ varies from a maximum of 0.41 in light winds over open water and smooth land surfaces, to a minimum near 0.37 in stronger winds over forests and cities. This range implies that a working value of κ = 0.39 ± 0.01 is to be used for experimental studies. However, its value is still most commonly seen as κ = 0.4 (Stull, 1988).

Friction Velocity

The friction velocity, or u∗ physically represents the shear stress at the ground surface

caused by the wind. It is also sometimes defined as the ratio of the difference between winds measured in a profile (Panofsky and Dutton, 1984). Various definitions in the meteorological literature concerning values of friction velocity have been documented (Weber, 1999). One of the more popular is a simple estimation where u∗ equals 0.14

to 0.15 times the mean wind speed.

The value of friction velocity can be solved from the classic log profile equation:

u∗ =

k(u1− u)

ln(z1/z)

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Displacement Height

Incorrect assumptions in the calculation of d can cause systematic errors in z0

(Bot-tema et al., 1998). Mihailovic (1999) presented experimental evidence that there is a significant departure of the wind profile above a vegetative surface from that predicted by the logarithmic relationship, when values of the displacement height are improperly used. This effect can be easily seen on a plotted profile using an estimated value for d; if the estimation is high, the profile will curve downward beginning near the ideal value of d. When it is low, the plotted profile will curve upwards (Stull, 1988).

2.3.6 Upstream roughness effects

Early research determined that roughness changes cause modified flow downwind of a change in roughness (Jackson, 1976). Multiple valid profile relationships were calculated upstream of urban areas by Karlsson (1986). He found that both the power law and logarithmic wind profile calculations provide a good estimate of the profile description, but separate calculations need to be made as multiple internal boundary layers (or IBL’s) can form downwind of major roughness changes.

This can be seen graphically in Figure 2.6. For wind blowing from the left, three internal boundary layers develop as winds flow over the urban built area (First IBL), the forested area (Second IBL), and the flat area (Third IBL). The profile is then divided into three sections downwind at the wind turbine (pictured), with the furthest roughness length mainly determining the wind profile shape for the first IBL, while the middle and closest roughness types are the dominant determinates of the wind profile shape across the second and third IBL.

In order to take into account land surfaces which have varying and non-uniform distribution of objects, the distribution of these elements upwind at a site must be analyzed for some downstream, or fetch, distance. The extent of this fetch distance depends on the wind speeds and atmospheric stability during the measurement regime (Rohatgi and Nelson, 1994). This was investigated in detail by Sempreviva et al. (1990, 1988), who determined the heights and downwind distances at which roughness change effects were to be applied. These guidelines are now used in some wind resource modeling programs, but are not universally accepted. Generally, a fetch-height ratio of 100:1 to 200:1 is used (Mason, 1988). Thus, a measurement at 50 m above ground level would require a fetch distance of between 5 and 10 km to

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account for upstream surface effects. Others quote that fetch distances of over 20 km can influence effective roughness lengths (Sempreviva et al., 1990). Wieringa (1993) suggests that the fetch distance will be greater for a rough/smooth surface than it would be for a smooth/rough surface transition.

It is also common to find a corresponding change in ground surface temperatures at roughness boundaries due to the different characteristics of the respective surfaces. In some cases, this may cause rapid changes in heat flux, imposing a strong modifying influence on wind profiles near the ground which can be observed for some distance downwind (World Meteorological Organization, 1981).

The IBL layers shown in Figure 2.6 are presented as sharp boundaries only in theory. In practice, a transition layer will exist along each boundary where the wind and other atmospheric properties tend to be affected by the two surfaces.

2.3.7 Modification of the surface roughness length

In a study on wind speed trends on the west coast of Canada, Tuller (2004) noted that the significant increase in the average measured wind speed at one site in particular was not reflected at other stations over the same time period and suggested changes in surface roughness at the site over time as a potential cause. Long-term changes in surface roughness lengths over time on wind speeds was given as a likely cause of the reduction in wind speeds over the past 30 years as a result of a re-greening project in the Northern Ontario city of Sudbury (Tanentzap et al., 2007). In these cases, the surrounding terrain roughness can change with the construction of suburbs, clear cutting or planting of trees, etc. This is only rarely accounted for in wind resource studies, as records do not often indicate the changes in the surrounding landscape over time.

Although z0 is usually considered to be independent of u, in some cases it decreases

with increasing wind speeds due to the effects of strong winds smoothing rough ob-stacles (Sutton, 1953). A classic example is a strong wind blowing down long grasses. Another problem of the same nature is found in wind profiles over water surfaces. In this case, the roughness of the waves is a function of the strength of the wind, as greater winds produce more turbulent wave action (Chamberlain, 1983).

There are also significant changes in the roughness values of surfaces between summer and winter due to the seasonal changes in sparse deciduous vegetation, crops, or to terrain smoothing by snow cover (Wieringa, 1986).

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Jacobs and Van Boxel (1988) found significant differences in both z0 and d in maize

crops during measurements made at different times during the growing season. In studies over grassy surfaces, Grimenes and Thue-Hansen (2004) found that roughness lengths change according to small differences in the terrain, becoming much larger during ’transition’ seasons when large masses of snow and patchy grass clumps existed. Patil (2006) has documented three distinct seasonal variations in z0 over terrain in

India corresponding to times of summer, monsoon, and winter conditions.

2.4 Comparison of calculation methods

A number of different methods are used in the wind energy industry to determine z0, the choice of which can have a significant effect on the results (Barthelmie et al.,

1993). Weidinger et al. (2000) noted that among the surface parameters used in wind profile calculations, the largest error is caused by the uncertainty in estimating roughness lengths.

Because various methods exist for calculating z0, researchers have attempted to

use experimental data to compare the results of different analysis techniques. Pneu-matikos (1991) compared experimental calculations of wind profiles from lower mon-itoring levels extrapolated upwards via three methods; a power law relationship and a fit to the logarithmic wind profile formula with and without incorporated stability effects. It was determined that log wind profiles incorporating stability effects were best at estimating wind speed distributions with height.

Barthelmie et al. (1993) compared five different techniques, also finding that stability-corrected wind profile regression fitting gave the optimum results and sug-gested that this method be used if available. Bottema et al. (1998) evaluated the variations of z0 as calculated by the gustiness method of Wieringa against the profile

method and found them to be in moderate agreement with each other. MacKinnon et al. (2004) found that areal-averaged model results gave similar estimates of z0 to

aerodynamically-determined values.

Overall, most of these studies agreed that, while all of the methods give adequate results using a quality dataset, incorporation of stability effects on profile-based cal-culation of the wind resource is a widely-used and accurate method.

The following chapter will outline a study to calculate profile-based z0 at two

potential wind development sites influenced by relatively complex surface roughness lengths. It will show that the potential errors produced by visual estimation of z0

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from terrain roughness classes can lead to a 20% average error in the estimated wind resource as compared to profile-based calculations. When other factors become involved, such as complex topography, this error can easily be on the order of 50-100%.

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Chapter 3 Data and Methods

3.1 Introduction

Two study sites in Ontario were chosen for the analysis. Both of these sites (hereafter referred to as Sites A and B) are meteorological tower installations specifically de-signed for wind energy resource assessment purposes. The installation of these towers was done in general accordance with wind industry guidelines (AWS Scientific, 1997). Both towers are owned by a single non-profit cooperative based in Southern Ontario. Because active development is underway at these sites as of 2009, some specific siting details are not provided. As this work is concerned only with profile measurements, specific wind speed data are not discussed as per the request of the data owners.

3.2 The study area

Most wind farm sites in Canada are located on agricultural land. It is usually quite flat, with less obstacles around to modify the wind flow. Farmers receive more income from a large wind turbine on their property than they could with any sort of crop occupying the same area. Farmlands are also located near existing hydro transmission corridors, roads and large cities, facilitating the access to and demand for power. Because farmland is favorable for wind development, two locations on agricultural land were chosen. These locations were selected largely due to the availability of data. Specific details of both sites and additional information about the region of interest are given below.

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Figure 3.1: General topography surrounding Sites A and B

3.2.1 Physiography of the study area

A general topographic overview of the site locations is shown in Figure 3.1. Site A

Site A was installed in early 2003 on the top of a small hill. The monitoring mast is a 50 m tubular steel tower, with cup anemometers at 30, 40, and 50 m above the ground and wind vanes at 30 and 50 m. The surrounding land use is primarily rural and agricultural, broken by scattered woodlots. There is a large urban center to the southeast of the site approximately 10 km away. The topography surrounding Site A is surrounded by small drumlins. The monitoring tower is placed at the crest of a drumlin with the lee side facing west.

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Site B

Site B was installed in 2005 and is located in an agricultural field near the north shore of Lake Erie. Instrumentation is the same configuration as site A; a tubular steel tower with cup anemometers at 30, 40, and 50 m and vanes at 30 and 50 m.

This is a coastal site, with a large open fetch of water approximately 500 meters south of the site. The rest of the landscape surrounding the station is heavily agricul-tural, with scattered agricultural communities. Wooded shelterbelts follow lot lines running parallel to the shoreline.

Topographically, this site is very flat for many kilometers, with elevations gradu-ally rising further from the large water body to the south. The only exceptions are small depressions created by a river bank approximately 2 kilometers north of the site and a steep bluff along the shoreline of Lake Erie. The bluff varies in height from 5 to 10 m near the site, and lies approximately 500 m south of the site at its closest.

3.2.2 Climate of the study area

This area of southwestern Ontario has a moderate humid continental climate accord-ing to the K¨oppen classification system. Synoptic conditions in this region usually emanate from the southern United States or western Canada, but are often signifi-cantly altered as they cross the large water bodies in the Great Lakes region. Annual temperature ranges are narrow due to the moderating effect of the nearby water bod-ies. On average, the coldest temperatures in the region occur in January and the warmest in July (Atmospheric Environment Service, 1984). Due to the mildness of the climate in this region, most of its precipitation falls as rain. Snowfall levels are light to moderate.

Similar to other areas in North America, the seasonal climate of southern Ontario is dominated by high pressure systems and lower wind speeds in the summer, with the reverse occurring during the winter. The prevailing wind direction is southwest due to the heavy influence of the westerly winds, the major wind belt of the middle latitudes between 35 to 60 degrees north and south (Scott, 1996). Average 10 m wind speeds in this area are estimated at approximately 2.5 and 3.7 m/s at Sites A and B, respectively (Ontario Ministry of the Environment, 2007).

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3.2.3 Equipment and measurements

This section summarizes the monitoring equipment and configurations used at both sites. Range and accuracies of the instruments are provided in Table 3.1, and the instrumentation is briefly discussed.

Monitoring mast

Both sites used a 50 m high tubular steel tower that is 152 mm in diameter, guyed out at six heights in four directions. This is a standard tower used in the wind energy industry.

Sensor booms

All sensors were mounted on 1.15 m long booms extending out from the tower at the same orientation. Because the sensor boom mounting procedures were exactly the same for every level, profile relationships should not be affected by the placement of the booms.

Wind speed

Wind speeds at all levels were measured using NRG Maximum #40 3-cup anemome-ters, the most widely used anemometer for wind resource monitoring in North Amer-ica. All measurements were sampled at a 3-second rate and averaged over 10 minute intervals.

Wind direction

Wind directions were measured using NRG #200P wind vanes. Measurements were sampled at a 3-second rate and averaged over 10 minute intervals. Average directions were determined using a unit-vector calculation done by the datalogger.

Table 3.1: Instrumentation details

Variable Instrument Range Units Accuracy Interval Wind Speed NRG Max #40 Cup 1 to 96 m/s m/s +/- 0.1 m/s 3 sec Wind Direction NRG #200P Vane 360 deg deg +/- 3 deg 3 sec

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Air temperature

Air temperature was measured on-site using an NRG #110S temperature sensor, mounted inside a Gill 6-plate radiation shield at 2 m above ground level. One minute sampling was done, with ten-minute averages being recorded by the datalogger. Data collection and storage

All data were logged and processed by an NRG Systems Symphonie datalogger, which is designed specifically for wind energy applications. Scaling factors and multipliers were used to convert raw voltage measurements into wind speed and direction. Data were averaged in the datalogger by arithmetic means for wind speed and air temper-ature, and via a unit-vector calculation for wind direction. All data were collected remotely using cellular transmission to an e-mail account in a proprietary format, and subsequently converted into comma-delimited text files for processing.

3.3 Requirements for analysis

Data quality is of the utmost importance when processing multiple levels of anemom-etry data to determine z0. A high degree of confidence in the supplied profile data

must be ensured prior to processing and interpretation of results. This confidence can be achieved by adhering to simple guidelines while processing data and by using data which meet stringent selection criteria. Failure to follow these criteria can easily result in corrupted research results. In his review of roughness calculation studies, Wieringa (1992) had to reject the results of more than half of the published studies, as they did not meet specific selection criteria and could cause erroneous comparisons. Karlsson (1986) rejected over 1/3 of the data collected from over 400 hours of profile data to assure a high data quality in his wind profile dataset.

3.3.1 Sufficient monitoring period length

Wind speed and direction vary over time. Consequently, wind profiles and z0 values

also will vary across timescales. In North America, for example, winds are lighter in summer and fall, and increase throughout winter and into spring. Wind speeds tend to vary on a diurnal scale; peaking in the late afternoon when the air is most

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unstable. This is typical in the summertime but less noticeable in winter, when convective heating forces are not as strong.

A year of data is generally regarded as a minimum for an accurate wind energy feasibility study (Corotis et al., 1977). However, others recommend at least two years of continuous monitoring for an accurate indication of the wind potential at most sites (Salmon and Walmsley, 1999). A monitoring period of at least a full continuous year is necessary because wind patterns and, correspondingly, surface roughnesses can change in each of the four Canadian seasons. Both sites A and B had over a full year of quality wind data.

3.3.2 Absence of local topography

The presence of local topography can influence the wind profile, making isolating the effects of surface roughness on the wind profile more difficult. Thermal turbulence exacerbated by complex topography can break down of the typical logarithmic wind profile as heavy mixing of air occurs. Only recently have researchers been able to start even basic modeling of these types of terrain using Computational Fluid Dynamics (CFD) techniques (Landberg et al., 2003). As both of the stations were located in relatively smooth terrain, topographic influences were ignored in the data processing.

3.3.3 Data completeness

It is very important to have a complete data set representing not only a minimum record length of an entire year, but also a relatively complete set of observations. A dataset missing three weeks of records from the summer would likely have an overestimated average wind speed than would a complete dataset, as summer wind speeds tend to be relatively low.

As no energy analyses were being done on the dataset, less emphasis was placed on ensuring its completeness. The only requirement was that the profile data be complete across all three height levels. If one of the levels was missing data from a time period, all records from that time period were removed from the analysis.

3.3.4 Data accuracy

Calculation of z0 from vertical wind profiles is highly susceptible to small errors

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factory-calibrated within ±3 degrees of accuracy in wind direction and 0.1 m/s in wind speed.

3.3.5 Neutral atmospheric stability

In conditions of neutral stability where mechanical turbulence is the dominant mix-ing force, a logarithmic wind speed profile extendmix-ing over the entire surface layer is formed. z0 is easily determined in these conditions by extrapolating the logarithmic

wind profile downwards to a wind speed of zero. In a mixture of different atmospheric stability conditions z0 becomes more difficult to quantify.

As atmospheric stability could not be directly determined on-site using available data, a filtering technique was used. Processing of 10 minute averages was only done where the 50 m average wind speed was at or above 6 m/s. These periods of high wind speed coincide with periods of approximately neutral atmospheric stability (Barthelmie et al., 1993; Wieringa, 1976). This approach is useful for wind resource assessment studies in the absence of direct stability calculation, since at wind speeds under 6 m/s at 50 meters, most large turbines would generate little usable power.

3.4 Data analysis

This section will cover the methods used to process direction-dependent roughness classes from Sites A and B.

3.4.1 Binning of data

Terrain characteristics surrounding wind monitoring stations in Canadian landscapes are rarely homogeneous. With the exception of the prairie provinces (which can be surrounded for kilometers by flat or gently undulating agricultural fields), most sites are typically near distinct changes in surface roughness. Many promising locations for wind development are located nearby large water bodies, large cities or forested areas. If a meteorological monitoring site is located near the shoreline of a water body, winds coming from over water would likely have lower roughness values than would winds coming over land surfaces. To account for this, roughness lengths are often calculated in directionally-dependent sectors or ’bins’.

Present approaches to determining the size of these bins vary. A generally-accepted method is to assign approximate roughness values in direction dependent

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sectors, usually as twelve or sixteen compass point bins of 30 or 22.5 degrees, respec-tively. In more homogeneous terrain, eight compass points can be used (using 45 degree bins). For the purposes of this study, bins were separated into twelve compass points of 30 degrees centered on cardinal points.

3.4.2 Using the Davenport roughness classes

Roughness lengths in each of the bins were estimated using visual matching tech-niques. The general appearance of the land was visually analyzed with the aid of National Topographic System maps and recent airphotos in Google Earth, and as-signed a roughness length according to the Davenport class categories (from Table 2.2) they most closely represented.

3.4.3 Processing of profile data

Raw wind data from the stations were first converted from a proprietary database format to comma-delimited ASCII text. Data were transferred ’as-is’, with no scale or offsets applied. The comma-delimited dataset was processed using a custom-designed Visual Basic program written by the author. This computer program sequentially scans ten-minute records (located on one row in the comma-delimited dataset), ap-pending each measurable parameter of interest (wind speed and direction) into a temporary location. Wind speed profiles are then binned into one of the 12 direc-tion sectors. As each 10-minute average is binned, a linear least-squares regression fitting is done on data within each bin that meets all the requirements for analysis listed in Section 3.3. This determines the shape of the wind profile in each direction bin. Assuming the profile data generally follows a log-linear trend, a linear least-squares regression line can be fitted to each direction-dependent dataset revealing the roughness length as the point where the equation-derived wind profile line crosses the y-axis. The regression algorithm (in pseudocode) is written as:

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Note that this is provided for reference purposes to openly document the least-squares regression fitting, slope and y-intercept calculations. For the functional pro-gram written in Visual Basic, please contact the author.

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Chapter 4 Results

4.1 Analytical results

The analysis results for sites A and B are presented in the following subsections. These statistics were generated prior to filtering of wind speeds below 6 m/s as they are used to validate the selection of suitable datasets for profile calculations. Both measured wind shear profiles follow generally logarithmic trends, and as such were deemed suitable for roughness comparison calculations.

4.1.1 Site A

A total of 106,056 complete records were processed from the 26 month dataset. Ap-proximately 50,000 of these records were deemed unsuitable based on the data pro-cessing criteria. Almost all of the rejected data occurred due to wind speeds below the 6 m/s threshold. A small percentage of data were also rejected for missing values in the profile calculations.

Wind shear profile

The measured average wind speeds at all three levels (shown in Figure 4.1 as black diamond points) exhibit a good fit to a typical logarithmic wind profile (in red). Wind shear profiles by direction

Although the directionally-dependent profiles exhibit a strong logarithmic relation-ship when combined, it is worth noting that profiles do vary significantly across 30

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A surface roughness parameterization study near two proposed windfarm locations in Southern Ontario

Contents

List of Tables

List of Figures

Introduction

1.1

A problem in the wind energy industry

1.2

Implications for the wind energy industry

1.3

Objectives of research

Chapter 2

Literature Review

2.1

Surface layer theory development

2.1.1

The logarithmic wind profile

2.1.2

Surface roughness length

2.1.3

Displacement heights

2.2

History of roughness parameterization

2.2.1

Fitting to the wind profile

2.2.2

Correlation with average obstacle heights

2.2.3

Terrain classification systems

2.2.4

Areal averaging of surface roughness

2.2.5

Standard deviation measurements

2.2.6

Gustiness measurements

2.2.7

Surface drag coefficient

2.2.8

Power law method

2.2.9

Other techniques

2.3

Problems with established techniques

2.3.1

Irregular wind profiles

2.3.2

Measurement in Rough Terrain

2.3.3

Data accuracy requirements

2.3.4

Acceptable height ranges

2.3.5

Variables

2.3.6

Upstream roughness effects

2.3.7

Modification of the surface roughness length

2.4

Comparison of calculation methods

Chapter 3

Data and Methods

3.1

Introduction

3.2

The study area

3.2.1

Physiography of the study area

3.2.2

Climate of the study area

3.2.3

Equipment and measurements

3.3

Requirements for analysis

3.3.1

Sufficient monitoring period length

3.3.2

Absence of local topography

3.3.3

Data completeness

3.3.4