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Based on wind-speed records of Alaska’s 19 first-order weather stations, we analyzed the near-surface wind-speed stilling for January 1, 1984 to December 31, 2016. With exception of Big Delta that indicates an increase of 0.0157 m·s
^{–1}·a
^{–1}, on average, all other first-order weather stations show declining trends in the near-surface wind speeds. In most cases, the average trends are less then –0.0300 m·s
^{–1}·a
^{–1}. The strongest average trend of –0.0500 m·s
^{–1}·a
^{–1} occurred at Homer, followed by –0.0492 m·s
^{–1}·a
^{–1} at Bettles, and –0.0453 m·s
^{–1}·a
^{–1} at Yakutat, while the declining trend at Barrow is marginal. The impact of the near-surface wind-speed stilling on the wind-power potential expressed by the wind-power density was predicted and compared with the wind-power classification of the National Renewable Energy Laboratory and the Alaska Energy Authority. This wind-power potential is, however, of subordinate importance because wind turbines only extract a fraction of the kinetic energy from the wind field characterized by the power efficiency. Since wind turbine technology has notably improved during the past 35 years, we hypothetically used seven currently available wind turbines of different rated power and three different shear exponents to assess the wind-power sustainability under changing wind regimes. The shear exponents 1/10, 1/7, and 1/5 served to examine the range of wind power for various conditions of thermal stratification. Based on our analysis for January 1, 1984 to December 31, 2016, Cold Bay, St. Paul Island, Kotzebue, and Bethel would be very good candidates for wind farms. To quantify the impact of a changing wind regime on wind-power sustainability, we predicted wind power for the periods January 1, 1984 to December 31, 1994 and January 1, 2006 to December 31, 2016 as well. Besides Big Delta that suggests an increase in wind power of up to 12% for 1/7, predicted wind power decreased at all sites with the highest decline at Annette (≈38%), Kodiak (≈30%), King Salmon (≈26%), and Kotzebue (≈24%), where the effect of the shear exponents was marginal. Bethel (up to 20%) and Cold Bay (up to 14%) also show remarkable decreases in predicted wind power.

There is observational evidence of declining trends in the near-surface wind speeds over the last five decades in numerous areas of the world [

McVicar et al. [^{−}^{1}∙a^{−}^{1} for studies with more than 30 sites with observing data for more than 30 years. Assuming, for instance, a linear trend, these declining trends constitute a −0.70 m∙s^{−}^{1} change in v R over 50 years [

Terrestrial stilling is, however, not omnipresent. Some positive trends were reported by McVicar et al. [^{−}^{1}∙a^{−}^{1}. In addition, Hartmann and Wendler [^{−}^{1}∙a^{−}^{1} when comparing period 1951 - 1975 with that of 1977 - 2001 related by these authors to the 1976 Pacific climate shift when the Pacific Decadal Oscillation index changed from the mainly negative values during the first 25-year period to the mainly positive values during the second one. On the contrary, we found a marginal decrease for the period January 1, 1984 to December 31, 2016 denoted as Period I hereafter. Nonetheless, the worldwide evidence for declining near-surface wind speeds and their impact on the sustainability of wind power demands care and attention.

The objective of our paper is two-fold: (a) to provide additional evidence to the process of near-surface wind-speed stilling in Alaska during Period I, and (b) to quantify the impact of a changing wind regime on the wind-power sustainability in the statewide region by considering the change from the period January 1, 1984 to December 31, 1994 denoted as Period II hereafter to the period January 1, 2006 to December 31, 2016 denoted as Period III hereafter. This means that the Period I was divided into three equal periods of 11 years.

To achieve these goals, we consider Alaska’s 19 first-order weather stations as a testbed. First-order stations are defined as those operated by certified observers and are typically operated by the National Weather Service. These sites include a full suite of equipment to measure air pressure and temperature, cloudiness, total precipitation, snowfall, wind speed and wind direction (e.g. [

Declining trends in the near-surface wind speeds notably affect the wind-power potential [

S k i n ¯ = ρ ¯ 2 ( v ^ 2 + v ″ 2 ^ ) v ^ + 1 2 ρ v ″ v ″ 2 ¯ , (1.1)

This equation describes the transfer of mean kinetic energy (MKE) and turbulent kinetic energy (TKE) by the mean wind field and the transfer of TKE by the eddying wind field. Here, ρ and v are the air density and the velocity of the wind field at the same height, respectively. The overbar ( … ¯ ) characterizes the conventional Reynolds mean and a prime ( ' ) the deviation from that. The hat ( … ^ ) denotes the density-weighted average according to Hesselberg [

χ ^ = ρ χ ¯ ρ ¯ , (1.2)

and the double prime ( ' ' ) marks the departure from that. Here, χ is a field quantity like the wind vector, v , and the specific humidity m 1 . It is obvious that ρ ¯ χ ″ ^ = ρ χ ″ ¯ = 0 . Hesselberg’s average can be related to that of Reynolds by [

χ ^ = χ ¯ + ρ ' χ ' ¯ ρ ¯ = χ ¯ { 1 + ρ ' χ ' ¯ ρ ¯ χ ¯ } . (1.3)

Obviously the different means χ ^ and #Math_19#, are nearly equal if | ρ ' χ ' ¯ / { ρ ¯ χ ¯ } | ≪ 1 as used, for instance, in case of the Boussinesq approximation. The Hesselberg average of the wind vector, for instance, is given by v ^ = ρ v ¯ / ρ ¯ . Note that intensive quantities like air pressure, p a , and air density, #Math_23#, are averaged in the sense of Reynolds. Arithmetic rules are given by [

Station and ID Numbers | Location | Latitude | Longitude | Elevation (m) | z_{R} (m) | |
---|---|---|---|---|---|---|

1 | USW00027502 | Barrow WSO | 71.2883˚N | 156.7814˚W | 9.4 | 8 |

2 | USW00026533 | Bettles | 66.9161˚N | 151.5089˚W | 195.7 | 10 |

3 | USW00026411 | Fairbanks INTL | 64.8039˚N | 147.8761˚W | 131.7 | 10 |

4 | USW00026415 | Big Delta FAA/AMOS | 63.9944˚N | 145.7214˚W | 389.2 | 10 |

5 | USW00026510 | McGrath | 62.9575˚N | 155.6103˚W | 101.5 | 10 |

6 | USW00026425 | Gulkana | 62.1592˚N | 145.4589˚W | 476.1 | 10 |

7 | USW00026616 | Kotzebue WSO | 66.8667˚N | 162.6333˚W | 9.1 | 8 |

8 | USW00026617 | Nome WSO | 64.5111˚N | 165.4400˚W | 4 | 8 |

9 | USW00026615 | Bethel | 60.7850˚N | 161.8292˚W | 31.1 | 8 |

10 | USW00026528 | Talkeetna | 62.3200˚N | 150.0950˚W | 106.7 | 8 |

11 | USW00026451 | Anchorage INTL | 61.1689˚N | 150.0278˚W | 36.6 | 8 |

12 | USW00025507 | Homer | 59.6419˚N | 151.4908˚W | 19.5 | 8 |

13 | USW00025503 | King Salmon | 58.6794˚N | 156.6294˚W | 19.2 | 10 |

14 | USW00025339 | Yakutat | 59.5119˚N | 139.6711˚W | 10.1 | 10 |

15 | USW00025309 | Juneau | 58.3567˚N | 134.5639˚W | 4.9 | 10 |

16 | USW00025308 | Annette WSO | 55.0389˚N | 131.5786˚W | 33.2 | 10 |

17 | USW00025713 | St. Paul Island | 57.1553˚N | 170.2222˚W | 10.7 | 10 |

18 | USW00025501 | Kodiak | 57.7511˚N | 152.4856˚W | 24.4 | 10 |

19 | USW00025624 | Cold Bay | 55.2208˚N | 162.7325˚W | 23.8 | 10 |

density-weighted averaging procedure is well appropriate to formulate the balance equation for turbulent systems [

Ignoring in Equation (1.1) the turbulent effects yields

S k i n ¯ = 1 2 ρ ¯ v ^ 2 v ^ . (1.4)

The magnitude of S k i n ¯ is given by

S k i n = | S k i n ¯ | = 1 2 ρ ¯ v ^ 2 | v ^ | = 1 2 ρ ¯ v ^ 3 , (1.5)

where v ^ = | v ^ | . Apparently, the wind-power density is proportional to the cube of wind speed. The rotor of a wind turbine causes a divergence effect expressed by ∇ ⋅ S k i n ¯ ≠ 0 . The wind speed is usually assumed as uniformly distributed over the rotor area of a wind turbine which is a crude assumption. Generally, at a given location, all these quantities vary with time.

As wind turbines only extract a fraction of the kinetic energy from the wind field characterized by the power efficiency (see, e.g., [

C P = P P ∞ , (1.6)

the wind-power potential is of subordinate importance. Here, P is the extracted (or consumed) power, and

P ∞ = 1 2 ρ ¯ A R v ∞ ^ 3 = A R S k i n , ∞ , (1.7)

is the power carried by the flow through the projection of the turbine section region onto the plane perpendicular to it, where v ∞ is the undisturbed wind speed far upstream of the wind turbine, and A R is the rotor area considered as perpendicular to the flow axis.

Therefore, it is indispensable to analyze how wind turbines respond to the declining trends in near-surface wind speeds. Since the wind turbine technology has notably improved during the past 35 years, we followed Mölders et al. [

In Section 2, we describe the data source and the methodology. Here, we also compare the wind-power potential obtained from daily mean averages of wind speed with that based on hourly mean averages of wind speed for the same time interval because the latter is generally larger than the former. This comparison serves for assessing the results of our wind-power predictions for the Periods I, II, and III that are based on daily mean averages of wind speed taken from the Global Historical Climatology Network (GHCN)-Daily [

Wind turbine | Hub height (m) | Swept area (m^{2}) | Cut-in wind speed (m∙s^{−1}) | Rated wind speed (m∙s^{−1}) | Cut-out wind Speed (m∙s^{−1}) | Rated power (kW) | Wind Class |
---|---|---|---|---|---|---|---|

Enercon E-48 | 76 | 1810 | 2-3 | 13.5 | 25 | 800 | IEC IIa |

Suzlon S64 Mark II-1.25 MW | 74.5 | 3217 | 4 | 12.0 | 25 | 1250 | IIa |

General Electric 1.6-82.5 | 80 | 5345 | 3.5 | 11.5 | 25 | 1600 | IEC IIIb |

Senvion MM92 | 78-80 | 6720 | 3 | 12.5 | 24 | 2050 | IEC IIa |

Mitsubishi MWT95/2.4 | 80 | 7088 | 3 | 12.5 | 25 | 2400 | IEC IIa |

Enercon E-82 E4 | 78/84 | 5281 | 2-3 | 16 | 25 | 3000 | IEC IIa |

Siemens SWT-3.6-107 | 80 | 9000 | 3 | 14.0 | 25 | 3600 | IEC Ia |

near-surface wind-speed stilling on the energy conversion at the interface Earth-atmosphere and the wind power is analyzed in Section 3. Note that the decreasing evapotranspiration as reported by McVicar et al. [

To estimate the wind-power potential in Alaska, we considered the daily mean wind data provided by the 19 first-order weather stations in Alaska for Periods I, II, and III. The wind data are taken from the Global Historical Climatology Network (GHCN)-Daily [

Based on these wind data, we assessed these locations for their suitability for wind farms by answering three major questions:

1) Does the location exhibit enough wind speed to generate electrical power in a sufficient manner?

2) Is this electrical power affected by long-term trends in horizontal wind speeds?

3) Are there obstacles such as siting issues present at the location?

The first two questions relate to the basic requirements for establishing a wind farm. The third question assesses the impacts of any kind of energy producing facilities (e.g., power plants fueled with coal, oil, gas, or nuclear elements to hydroelectric dams, tide-power systems, wind farms) on the natural environment. The impact of wind farms on endangered species, avian migrations/habitats, wetlands/protected areas, and subsistence lifestyle must be considered as well. Additionally, for numerous Alaska areas, the ambient temperatures fall below −20˚C in winter which is below the operation range of most wind turbines, except cold climate versions like that of Senvion MM92 which has a lower limit of −30˚C. Frequently icing of rotor blades due to the occurrence of supercooled water in the lower atmospheric boundary layer may affect the outcome of wind power as well. The answers to these questions served as the foundation for evaluating each site in terms of cost-benefits analyses.

First, we analyzed whether the wind speeds observed at a given location during the period under study satisfy the minimum average wind speed requirement. A site must have a minimum annual average wind speed of, at least 4.9 m∙s^{−1} to 5.8 m∙s^{−1} to be considered (American Wind Energy Association, 2009).

The average 〈 v R 〉 for each station was calculated using

〈 v R 〉 = 1 T N ∫ T 0 T N v R ( t ) d t = T d T N ( 1 T d ∫ T 0 T 1 v R , 1 ( t ) d t + 1 T d ∫ T 1 T 2 v R , 2 ( t ) d t + ⋯ + 1 T d ∫ T N − 1 T N v R , N ( t ) d t ) , (2.1)

where t is time, T N = N T d is the period under study, N is the number of days, T d = T i − T i − 1 , i = 1 , 2 , ⋯ , N , is the time period of a day, and v R ( t ) = | v R ( t ) | is the time-dependent horizontal wind speed at anemometer height that usually amounts to z R ≅ 10 m ( ≅ 33 ft ) above the surface. At seven of the 19 first-order stations, wind speed is measured at a height of z R ≅ 8 m ( ≅ 26 ft ) . For all first-order stations, linear trends in daily mean wind speeds are listed in

Equation (2.1) provides the average wind speed for each station. Introducing the daily mean wind speed by

v R , i ¯ = 1 T d ∫ T i − 1 T i v R , i ( t ) d t , (2.2)

where v R , i ( t ) is the wind speed at anemometer height for the time [ T i − 1 , T i ] of the i^{th} day, leads to

〈 v R 〉 = 1 N ∑ i = 1 N v R , i ¯ . (2.3)

As described in the Wind Energy Resource Atlas of the United States, another measure for assessing the wind-power potential at a given location is related to the wind-power class listed in

〈 S k i n , z 〉 = 1 2 T N ∫ 0 T N ρ z ( t ) v z 3 ( t ) d t . (2.4)

Here, ρ z ( t ) is the air density, and v z ( t ) is the wind speed at z. Similar to Equation (2.1), we obtain

〈 S k i n , z 〉 = T d 2 T N ( 1 T d ∫ T 0 T 1 ρ z , 1 ( t ) v z , 1 3 ( t ) d t + 1 T d ∫ T 1 T 2 ρ z , 2 ( t ) v z , 2 3 ( t ) d t + ⋯ + 1 T d ∫ T N − 1 T N ρ z , N ( t ) v z , N 3 ( t ) d t ) (2.5)

where ρ z , i ( t ) and v z , i 3 ( t ) are related to the time of the i^{th} day.

Location | N | 〈 v R 〉 m∙s^{−}^{1} | Δ v R , a m∙s^{−}^{1}∙a^{−}^{1} | Δ v R , P I m∙s^{−}^{1} |
---|---|---|---|---|

Barrow WSO | 12,011 | 5.63 | −0.0001 | −0.03 |

Bettles | 11,629 | 2.43 | −0.0492 | −1.62 |

Fairbanks INTL | 12,019 | 1.97 | −0.0368 | −1.21 |

Big Delta FAA/AMOS | 11,333 | 4.13 | 0.0157 | 0.52 |

McGrath | 12,031 | 2.00 | −0.0405 | −1.33 |

Gulkana | 11,552 | 2.51 | −0.0043 | −0.14 |

Kotzebue WSO | 12,023 | 5.24 | −0.0395 | −1.30 |

Nome WSO | 11,991 | 4.18 | −0.0221 | −0.73 |

Bethel | 12,052 | 5.22 | −0.0269 | −0.89 |

Talkeetna | 11,914 | 2.01 | −0.0389 | −1.28 |

Anchorage INTL | 12,052 | 3.10 | −0.0310 | −1.02 |

Homer | 12,033 | 3.14 | −0.0500 | −1.65 |

King Salmon | 12,054 | 4.33 | −0.0313 | −1.03 |

Yakutat | 12,039 | 2.52 | −0.0453 | −1.50 |

Juneau | 11,556 | 3.33 | −0.0205 | −0.68 |

Annette WSO | 12,047 | 3.56 | −0.0426 | −1.40 |

St. Paul Island | 11,990 | 6.92 | −0.0173 | −0.57 |

Kodiak | 12,049 | 4.84 | −0.0450 | −1.48 |

Cold Bay | 12,051 | 7.19 | −0.0391 | −1.29 |

Introducing the respective daily mean value of this true wind-power density by

S k i n , z , i ¯ = 1 2 T d ∫ T i − 1 T i ρ z , i ( t ) v z , i 3 ( t ) d t (2.6)

provides

〈 s k i n , z 〉 = 1 N ∑ i = 1 N S k i n , z , i ¯ . (2.7)

Unfortunately, the wind speed data taken from the GHCN-Daily do not allow to precisely compute S k i n , z , i ¯ . Even if we consider air density as nearly constant for the i t h day (which leads to the so-called anelastic approximation of the equation of continuity), we have to acknowledge that

( v z , i ¯ ) 3 ≤ v z , i 3 ¯ . (2.8)

This inequality can be verified using Hölder’s inequality for integrals,

| ∫ a b f ( x ) g ( x ) d x | ≤ ( ∫ a b | f ( x ) | p h d x ) 1 p h ( ∫ a b | g ( x ) | q h d x ) 1 q h , (2.9)

where p h ∈ ( 1 , ∞ ) and q h are conjugate exponents obeying

1 p h + 1 q h = 1 , (2.10)

i.e., q h = p h / ( p h − 1 ) . Furthermore, f ( x ) and g ( x ) are real functions ( f , g : [ a , b ] → ℝ ). For the two non-negative measurable functions f ( x ) = v z , i ( x ) and g ( x ) = 1 as well as p h = 3 ⇒ q h = 3 / 2 , and x = t / T d , we obtain

v z , i ¯ = ∫ 0 1 v z , i ( x ) d x ≤ ( ∫ 0 1 v z , i 3 ( x ) d x ) 1 3 = ( v z , i 3 ¯ ) 1 3 (2.11)

and in a further step the Inequality (2.8). Differences

Δ v 3 = v z , i 3 ¯ − ( v z , i ¯ ) 3 v z , i 3 ¯ (2.12)

are illustrated in

on WRF/chem model simulations performed for the area of the Eva Creek wind farm in Interior Alaska. This mean wind speed is representative for heights between 64 and 113 m above ground level [

The daily mean wind speed, v R , i ¯ , is based on observations performed at anemometer height z R . To compute the mean wind speed at higher levels than the anemometer height, z > z R , commonly the power-law profile (e.g., [

v z , i ¯ = v R , i ¯ ( z z R ) p i , (2.13)

is used, where v z , i and v R , i are the wind speeds at the heights z and z R , respectively. Here, the shear exponent ranges from p i = 1 / 7 for near-neutral stability conditions to p i = 1 / 10 for strong lapse rates. Frost [

of Schwartz and Elliot regarding the wind shear characteristics at Central Plains (Texas to North Dakota) tall towers [

Since v R , i ¯ for the i^{th} day is given by

v R , i ¯ = 1 T d ∫ 0 T d v R , i ( t ) d t = Δ T T d ( 1 Δ T ∫ T 0 T 1 v R , i ( t ) d t + 1 Δ T ∫ T 1 T 2 v R , i ( t ) d t + ⋯ + 1 Δ T ∫ T M − 1 T M v R , i ( t ) d t ) (2.14)

where Δ T = T k − T k − 1 , k = 1 , 2 , ⋯ , M , T 0 = 0 , and T d = M Δ T , M is the number of averaging intervals, for instance, of Δ T = 30 min or Δ T = 60 min . The mean wind speed for the k^{th} averaging interval is then given by

v R , i , k ¯ = 1 Δ T ∫ T k − 1 T k v R , i , k ( t ) d t . (2.15)

Thus, we obtain

v R , i ¯ = 1 M ∑ k = 1 M v R , i , k ¯ . (2.16)

In accord with Equation (2.13), the corresponding wind speed at z amounts to

v z , i ¯ = 1 M ∑ k = 1 M v z , i , k ¯ = 1 M ∑ k = 1 M v R , i , k ¯ ( z z R ) p i , k . (2.17)

In case of an exponent p i , k that does not vary with time during the i^{th} day, i.e., p i , k = p i , one obtains Equation (2.13). This equation was used to extrapolate the daily mean wind speeds at z R to both the level of z = 50 m to compute the wind-power density, 〈 S k i n , z 〉 , of the wind field as express by Equation (2.4) and of z = 80 m chosen as the hub height of the wind turbines considered in this study. For each first-order weather station, we considered p = p i = 1 / 10 , p = p i = 1 / 7 , and p = p i = 1 / 5 to cover the range of wind power for various conditions of thermal stratification. Based on these shear exponents, vertical wind profiles were drawn, where p = p i = 1 / 10 causes the weakest and p = p i = 1 / 5 produces the strongest increase of wind speed with height (

〈 v z 〉 = 1 N ∑ i = 1 N v z , i ¯ . (2.18)

at both z = 50 m and z = 80 m .

The respective mean wind-power density 〈 S k i n , z 〉 (see Equation (2.4)) at these heights is illustrated in

surrounding cities and communities, respectively. In most cases, the average trends are less then −0.0300 m∙s^{−}^{1}∙a^{−}^{1}, with exception of Gulkana that only exhibits a value of −0.0043 m∙s^{−}^{1}∙a^{−}^{1} (^{−}^{1}∙a^{−}^{1}, on average, followed by Bettles with −0.0492 m∙s^{−}^{1}∙a^{−}^{1} and Yakutat with −0.0453 m∙s^{−}^{1}∙a^{−}^{1} (

The linear trends shown in

We assess the impact on the sustainability of wind power by quantifying the change in the predicted wind power from Period II (January 1, 1984 to December 31, 1994) to Period III (January 1, 2006 to December 31, 2016).

The reasons for the long-term decrease of the mean horizontal wind speed as

^{1}The inclusion of a vegetation canopy has been discussed, for instance, by Deardorff [

documented by 18 of the 19 first-order weather stations in Alaska are unknown. This long-term decrease, however, may impact not only the generation of electricity using wind power, but also the near-surface air temperature. To address the latter, we considered the energy flux balance at the interface atmosphere assuming bare soil^{1} for simplification. For a given location (characterized, for instance, by the zenith angle, θ , and the azimuthal angle, φ ) it reads (only the components normal to the horizontal surface element play a role)

R S ↓ ( Θ 0 , θ , φ ) ( 1 − α S ( Θ 0 , θ , φ ) ) + ε ( θ , φ ) R L ↓ ( θ , φ ) − ε ( θ , φ ) σ T s 4 ( θ , φ ) − H ( θ , φ ) − E ( θ , φ ) + G ( θ , φ ) = 0 (3.1)

Here, R S ↓ ( Θ 0 , θ , φ ) is the global (direct plus diffusive solar) radiation, Θ 0 = Θ 0 ( θ , φ ) is local zenith angle of the Sun’s center, α S ( Θ 0 , θ , φ ) is the albedo of the short-wave range, R L ↓ ( θ , φ ) is the down-welling long-wave radiation, ε ( θ , φ ) = 1 − α L ( θ , φ ) [

H = − c p , 0 ( ρ ¯ α T ∂ T ^ ∂ z − ρ w ″ Θ ″ ¯ ) (3.2)

and

E = − λ j 1 ^ ( ρ ¯ D m 1 ∂ m 1 ^ ∂ z − ρ w ″ m ″ 1 ¯ ) , (3.3)

where the vertical components of the respective gradients characterize the molecular effects in accord with the laws of Fourier and Fick, respectively, and the covariance terms ρ w ″ Θ ″ ¯ and ρ w ″ m ″ 1 ¯ represent the turbulent effects. Here, α T is the thermal diffusivity, D m 1 is the diffusivity of the water vapor in air, and λ j 1 = h 1 − h j is the specific heat of phase transition, where λ 21 is the specific heat of vaporization, λ 31 is the specific heat of sublimation, respectively. The fluxes of sensible and latent fluxes are usually parameterized by [

H = − ρ ¯ c p , 0 C h ( U R − U s ) ( Θ R ^ − T s ^ ) = c o n s t . (3.4)

and

E = − ρ ¯ λ k 1 ^ C m 1 ( U R − U s ) ( m 1 , R ^ − m 1 , s ^ ) = c o n s t . , (3.5)

where horizontally homogeneous and steady-state conditions are presupposed to fulfill the requirements of the Prandtl layer (also called the atmospheric surface layer, ASL, or the constant-flux layer), the lowest layer of the atmosphere of a thickness of about ten meters. Here, U R = | v R ^ | and U s = | v s ^ | are the mean horizontal wind speeds at z R (subscript R) and at the Earth’s surface (subscript s), where in the case of rigid walls (like layers of soil, snow, and/or ice) the latter is equal to zero, Θ R is the potential temperature at z R , T s is the absolute temperature at the water surface, and m 1 , R and m 1 , s are the corresponding values of the specific humidity. Furthermore, the potential temperature is defined by

Θ = T ( p a 0 p a ) k = T π , (3.6)

where π = ( p a / p a 0 ) k is the Exner-function, p a is the air pressure, and p a 0 is a reference pressure (usually p a 0 = 1000 hPa ). The exponent k is given by

k = R c p ≅ R 0 { 1 + ( R 1 / R 0 − 1 ) m 1 } c p , 0 { 1 + ∑ j = 1 3 ( c p , j c p , 0 − 1 ) m j } . (3.7)

Here, R is the calculated gas constant for moist air, R 0 is the calculated gas constant

for dry air, R 1 is the gas constant for water vapor, c p = ( ∂ h / ∂ T ) p , m j = ∑ j = 0 3 c p , j m j is the specific heat at constant pressure, c p , j = ( ∂ h j / ∂ T ) p , m j is the partial specific

heat at constant pressure, m j = ρ j / ρ is the mass fraction, where ρ j is the partial density for dry air ( j = 0 ), water vapor ( j = 1 ), liquid water ( j = 2 ), and ice ( j = 3 ), respectively. These partial densities obey

∑ j = 0 3 m j = 1 ⇒ m 0 = 1 − ∑ j = 1 3 m j . (3.8)

Furthermore, h is the specific enthalpy, and h j = ( ∂ h / ∂ m j ) T , p is the partial specific enthalpy. Moreover, C h and C m 1 are the local transfer coefficients for sensible heat and water vapor, respectively, given by

#Math_199# (3.9)

and

C m 1 = κ 2 ( κ ( ξ d 2 ) − 1 2 + ln z R z r − Ψ m ( ζ R , ζ r ) ) ( κ B m 1 − 1 + ln z R z r − Ψ m 1 ( ζ R , ζ r ) ) , (3.10)

where Panofsky’s [

Ψ m , h , m 1 ( ζ R , ζ r ) = ∫ z r z R 1 − Φ m , h , m 1 ( z / L ) z d z = ∫ ζ r ζ R 1 − Φ m , h , m 1 ( ζ ) ζ d ζ . (3.11)

Here, κ is the von Kármán constant, ξ d = 2 ( u * / u r ^ ) 2 is the local drag coefficient (e.g., [

Φ m ( ζ ) = z u * κ | ∂ v H ^ ∂ z | ≅ z u * κ ∂ U H ∂ z , (3.12)

Φ h ( ζ ) = z Θ * κ ∂ Θ ^ ∂ z , (3.13)

and

Φ m 1 ( ζ ) = z m 1 * κ ∂ m 1 ^ ∂ z , (3.14)

where ζ = z / L is the Obukhov number, ζ r = z r / L and ζ R = z R / L are the Obukhov numbers for the outer edge of the sublayer, z r , and for the top of the Prandtl layer, z R , and

L = − c p , 0 ρ ¯ u * 3 κ g Θ ^ ( H + 0.61 c p , 0 Θ ^ E λ k 1 ^ ) (3.15)

is the Obukhov stability length. Furthermore, c p , 0 is the specific heat at constant pressure for dry air, U H = | v H ^ | is the mean horizontal wind speed, g is the acceleration of gravity, and Θ ^ is a potential temperature representative for the entire Prandtl layer.

To determine the local drag coefficient and the local similarity function for momentum, the magnitude of the friction stress vector,

| τ | = ρ ¯ C D ( U R − U s ) 2 = c o n s t . (3.16)

with

C D = κ 2 ( κ ( ξ d 2 ) − 1 2 + ln z R z r − Ψ m ( ζ R , ζ r ) ) 2 (3.17)

and in a further step the friction velocity must be computed. Since the thermal stratification of the Prandtl layer varies in the diurnal cycle, the computation of | τ | and u * as well as H and E based on daily mean values of horizontal wind speed, temperature and humidity is, in general, a rather imperfect procedure. Despite the mean wind speed at the surface of rigid walls being zero, calculating of H and E over layers of bare soil, snow, and ice requires, at least, two vertical profile values of mean temperature and mean humidity, for instance, at z R and at the surface. Since these surface values are usually unavailable, soil-vegetation-atmosphere-transfer (SVAT) schemes may be taken into consideration. Mölders et al. [

Assuming that v ^ ( z ) given by Equation (2.13) is equal to

v ^ ( z ) = u * κ ( ln z z 0 − Ψ m ( ζ , ζ 0 ) ) (3.18)

yields [

p = ln { ln ( z z 0 ) − Ψ m ( ζ , ζ 0 ) ln ( z R z 0 ) − Ψ m ( ζ R , ζ 0 ) } 1 ln ( z z R ) . (3.19)

This formula shows that the shear exponent explicitly depends on thermal stratification.

Equations (3.4) and (3.5) suggest that the decrease in the mean horizontal wind speed as demonstrated by the global stilling can reduce the fluxes of sensible and latent heat, and, according to Equation (3.1), can increase the surface temperature. The situation, however, is rather complex because a decrease of evapotranspiration also affects the formation and depletion of clouds and, subsequently, the scattering and absorption of solar radiation and the emission of infrared radiation by hydrometeors. Analyzing such interrelations requires the support by non-hydrostatic models of the meso-scales β / γ [

Usually, MKE can be converted into TKE. In the inertial range, for instance, the TKE is transferred from lower to higher wave numbers until the far-dissipation range is reached, where kinetic energy is converted into heat energy by direct dissipation, J ¯ : ∇ v ^ , and turbulent dissipation, J : ∇ v ″ ¯ , where J is the Stokes stress tensor [

The use of wind farms, however, will contribute to a further decrease of the mean horizontal wind speed [

The axial momentum theory [

C P = 1 2 ( 1 + X ) ( 1 − X 2 ) . (3.20)

Here, X = v w ^ / v ∞ ^ , where v ∞ ^ is the undisturbed wind speed far upstream of the wind turbine, and v w ^ is the undisturbed wind speed far downstream of the wind turbine. This formula serves to derive the Betz-Joukowsky limit [^{−}^{1} to 10 m∙s^{−}^{1} (

The wind power is predicted based on current state-of-the-art wind turbines of different rated powers listed in ^{−}^{3}, air pressure of 1013.25 hPa, and an undisturbed horizontal flow with a turbulence intensity ranging from 0.10 to 0.12.

Based on discrete power-curve data, we determined the empirical fitting parameters A, K, Q, B, S, and u of the general logistic function

P ( v ) = A + K − A ( 1 + Q exp { − B ( v − S ) } ) 1 u , (4.1)

where P ( v ) represents the power generated by the respective wind turbine at the wind speed v at hub height. The parameters obtained are listed in

X = v w ^ / v ∞ ^ | C p | v ∞ , R ^ ( m ⋅ s − 1 ) | Δ v R = v ∞ , R ^ − v w , R ^ ( m ⋅ s − 1 ) | ||||
---|---|---|---|---|---|---|---|

p = 1 / 10 | p = 1 / 7 | p = 1 / 5 | p = 1 / 10 | p = 1 / 7 | p = 1 / 5 | ||

0.333 | 0.593 | 6.1 | 5.6 | 4.9 | 4.1 | 3.7 | 3.3 |

0.618 | 0.500 | 2.3 | 2.1 | 1.9 | |||

0.682 | 0.450 | 1.9 | 1.8 | 1.6 | |||

0.733 | 0.400 | 1.6 | 1.5 | 1.3 | |||

0.778 | 0.350 | 1.3 | 1.2 | 1.1 | |||

0.818 | 0.300 | 1.1 | 1.0 | 0.9 |

Wind turbine | A | K | Q | B | S | u |
---|---|---|---|---|---|---|

Enercon E-48 | −24.9 | 811.2 | 0.54 | 1.0 | 10.9 | 2.3 |

Suzlon S64 Mark II -1.25 MW | −56.5 | 1250.6 | 3.88 | 2.0 | 9.6 | 4.5 |

General Electric 1.6-82.5 | −315.7 | 1601.3 | 1.66 | 2.0 | 9.8 | 7.2 |

Senvion MM92 | −267.6 | 2050.4 | 19.5 | 1.9 | 8.5 | 6.2 |

Mitsubishi MWT95/2.4 | −270.4 | 2403.3 | 12.2 | 1.5 | 8.8 | 4.9 |

Enercon E-82 E4 | −113.8 | 3038.8 | 1.49 | 0.6 | 10.6 | 1.7 |

Siemens SWT-3.6-107 | −414.3 | 3599.6 | 40.0 | 1.4 | 9.0 | 5.4 |

For each period, we calculated the average power output by

〈 P W T 〉 = ∫ v c i v c o f ( v ) P ( v ) d v . (4.2)

Here, v c i is the cut-in wind speed, v c o is the cut-out wind speed, and f ( v ) is the probability density function of a given horizontal wind speed at hub height, v, occurring during a period. It is expressed by the Weibull two-parameter distribution [

f ( v ) d v = k W c W ( v c W ) k W − 1 exp ( − ( v c W ) k W ) d v , (4.3)

where k W and c W represent the shape and scale parameters, respectively (e.g., [

F ( v ) = 1 − exp ( − ( v c W ) k W ) , (4.4)

where F ( v ) → 1 for v → ∞ . The shape and scale parameters are determined for each of Alaska’s 19 first-order weather stations for Period I by fitting the histograms of the normalized cumulative frequency of the predicted wind speeds at the hub height z = 80 m using the three different shear exponents, p = 1 / 10 , p = 1 / 7 and p = 1 / 5 . For Barrow, Big Delta, Kotzebue, Nome, Bethel, King Salmon, Juneau, Annette, St. Paul Island, Kodiak, and Cold Bay, k W and c W were also determined for Periods II and III.

shows both the fitted normalized cumulative frequency for Period I and the corresponding Weibull distribution at hub height obtained for Cold Bay using p = 1 / 7 . The results are listed in

The probability that the daily mean wind speed does not meet the cut-in speed requirements of the different wind turbines considered in this study is given by

P 1 = P [ 0 , v c i ) = F ( v c i ) . (4.5)

Furthermore, the probability that the daily mean wind speed is in the range between v c i and the wind speed of the rated power, v p r , is given by

P 2 = P [ v c i , v p r ) = F ( v p r ) − F ( v c i ) . (4.6)

The probability that the daily mean wind speed exceeds v p r results in

P 3 = P [ v p r , v max ) = F ( v max ) − F ( v p r ) , (4.7)

where F ( v max ) ≅ 1 for the maximum value v max of the daily mean wind speed. For the purpose of simplification, a common cut-in wind speed of v c i = 3.0 m ⋅ s − 1 and a common wind speed of the rated power of v p r = 13.0 m ⋅ s − 1 are assumed. Both wind speeds are averages derived from the wind turbine specifications (

The ratio of the average power output, 〈 P W T 〉 provided by a wind turbine to its rated power, P R , is the capacity factor

C F = 〈 P W T 〉 P R . (4.8)

The capacity factor may empirically be related to the ratio R P = P 3 / ( P 2 + P 3 ) .

Because of Inequality (2.8), we must expect that hourly mean wind speeds provide higher wind-power outputs than daily mean wind speeds. To estimate possible deviations, we used (a) the hourly mean wind speeds and (b) daily mean wind speeds both related to the wind speed measurements at anemometer height z R = 8 m ( 26 ft ) at Bethel performed from January 1, 1979 to December 31, 1983. Results obtained at z = 80 m are illustrated in

Location | Period | Shape parameter k W | Scale parameter c W (m∙s^{−}^{1}) | ||||
---|---|---|---|---|---|---|---|

Shear exponent p | |||||||

1/10 | 1/7 | 1/5 | 1/10 | 1/7 | 1/5 | ||

Barrow WSO | I | 2.451 | 2.458 | 2.460 | 7.568 | 8.362 | 9.554 |

II | 2.683 | 2.708 | 2.703 | 7.517 | 8.326 | 9.505 | |

III | 2.267 | 2.269 | 2.272 | 7.444 | 8.237 | 9.409 | |

Bettles | I | 2.289 | 2.306 | 2.270 | 3.373 | 3.686 | 4.151 |

Fairbanks INTL | I | 1.707 | 1.715 | 1.698 | 2.803 | 3.062 | 3.442 |

Big Delta FAA/AMOS | I | 1.274 | 1.280 | 1.212 | 5.178 | 5.657 | 6.154 |

II | 1.141 | 1.140 | 1.154 | 4.892 | 5.206 | 6.026 | |

III | 1.349 | 1.338 | 1.346 | 5.229 | 5.830 | 6.450 | |

McGrath | I | 1.702 | 1.711 | 1.694 | 2.902 | 3.170 | 3.566 |

Gulkana | I | 1.190 | 1.188 | 1.185 | 3.385 | 3.681 | 4.149 |

Kotzebue WSO | I | 1.868 | 1.889 | 1.889 | 6.994 | 7.763 | 8.865 |

II | 2.094 | 2.102 | 2.100 | 7.591 | 8.400 | 9.594 | |

III | 1.688 | 1.692 | 1.693 | 6.397 | 7.083 | 8.091 | |

Nome WSO | I | 1.873 | 1.880 | 1.879 | 5.753 | 6.374 | 7.279 |

II | 2.132 | 2.063 | 2.076 | 5.938 | 6.504 | 7.438 | |

III | 1.693 | 1.700 | 1.701 | 5.393 | 5.972 | 6.825 | |

Bethel | I | 2.443 | 2.452 | 2.449 | 6.990 | 7.736 | 8.835 |

II | 2.714 | 2.718 | 2.561 | 7.520 | 8.312 | 9.371 | |

III | 2.290 | 2.276 | 2.294 | 6.719 | 7.423 | 8.495 | |

Talkeetna | I | 1.710 | 1.716 | 1.722 | 2.757 | 3.062 | 3.502 |

Anchorage INTL | I | 2.295 | 2.306 | 2.315 | 4.146 | 4.596 | 5.253 |

Homer | I | 2.247 | 2.248 | 2.257 | 4.213 | 4.669 | 5.334 |

King Salmon | I | 2.271 | 2.276 | 2.277 | 5.685 | 6.223 | 7.016 |

II | 2.675 | 2.805 | 2.686 | 6.276 | 6.968 | 7.741 | |

III | 2.031 | 2.065 | 2.041 | 5.369 | 5.903 | 6.637 | |

Yakutat | I | 1.733 | 1.741 | 1.725 | 3.394 | 3.706 | 4.176 |

Juneau | I | 1.556 | 1.554 | 1.552 | 4.458 | 4.862 | 5.491 |

II | 1.700 | 1.693 | 1.721 | 4.760 | 5.195 | 5.887 | |

III | 1.424 | 1.424 | 1.421 | 4.097 | 4.465 | 5.049 | |

Annette WSO | I | 1.797 | 1.783 | 1.795 | 4.657 | 5.069 | 5.743 |

II | 2.052 | 2.050 | 2.114 | 5.183 | 5.663 | 6.468 | |

III | 1.624 | 1.624 | 1.618 | 4.056 | 4.421 | 4.995 |

St. Paul Island | I | 2.449 | 2.450 | 2.462 | 9.235 | 10.103 | 11.396 |
---|---|---|---|---|---|---|---|

II | 2.610 | 2.593 | 2.610 | 9.400 | 10.273 | 11.587 | |

III | 2.278 | 2.278 | 2.287 | 8.989 | 9.839 | 11.093 | |

Kodiak | I | 2.055 | 2.113 | 2.058 | 6.306 | 6.959 | 7.777 |

II | 2.386 | 2.378 | 2.392 | 7.003 | 7.656 | 8.635 | |

III | 1.898 | 1.900 | 1.906 | 5.764 | 6.304 | 7.177 | |

Cold Bay | I | 2.507 | 2.510 | 2.508 | 9.725 | 10.641 | 11.989 |

II | 2.705 | 2.710 | 2.706 | 10.118 | 11.069 | 12.470 | |

III | 2.358 | 2.360 | 2.362 | 9.289 | 10.165 | 11.455 |

capacity factor, C F , h . As expected, we obtained for p = 1 / 5 (stable stratification) always the highest values of 〈 P W T , h 〉 and C F , h for each wind turbine, followed by those for p = 1 / 7 (neutral stratification) and p = 1 / 10 (unstable stratification). The General Electric 1.6 - 82.5 and Senvion MM92 have the highest and second highest capacity factor, respectively. This result agrees with that of Mölders et al. [

Δ P W T , h = 〈 P W T , h 〉 − 〈 P W T , d 〉 〈 P W T , h 〉 . (5.1)

For p = 1 / 10 this relative difference is always positive, i.e., the predicted wind power based on hourly mean wind speeds always exceeds that calculated with daily mean wind speeds. For the shear exponents p = 1 / 7 and p = 1 / 5 ,

however, positive as well as negative values of Δ P W T occur. Negative values can be attributed to the fitted curves of the normalized frequencies in case of the daily mean wind speeds. In contrast to the case of the hourly mean wind speeds, these fitted curves slightly overestimated the normalized frequencies in the range from 9 m∙s^{−}^{1} to 15 m∙s^{−}^{1}. Thus, we must expect that for the same period, hourly mean wind speeds provide slightly higher average wind-power outputs, 〈 P W T , h 〉 , than daily mean wind speeds, 〈 P W T , d 〉 .

Our predicted wind power obtained for Barrow, Big Delta, Kotzebue, Nome, Bethel, King Salmon, Juneau, St. Paul Island, Kodiak, and Cold Bay for Periods I, II, and III using p = 1 / 10 , p = 1 / 7 and p = 1 / 5 , is listed in

Weather station | p | Period | Wind turbine | ||||||
---|---|---|---|---|---|---|---|---|---|

E-48 (kW) | S64 Mk II-1.25 MW (kW) | GE 1.6-82.5 (kW) | MM92 (kW) | MWT95/2.4 (kW) | E-82E4 (kW) | SWT-3.6-107 (kW) | |||

Barrow WSO | 1/10 | I | 230 | 360 | 584 | 731 | 766 | 672 | 977 |

II | 222 | 346 | 574 | 717 | 745 | 643 | 940 | ||

III | 225 | 352 | 566 | 710 | 746 | 662 | 958 | ||

1/7 | I | 287 | 456 | 707 | 887 | 943 | 848 | 1221 | |

II | 282 | 450 | 708 | 887 | 937 | 826 | 1199 | ||

III | 279 | 443 | 683 | 858 | 915 | 833 | 1192 | ||

1/5 | I | 367 | 589 | 869 | 1094 | 1188 | 1117 | 1575 | |

II | 368 | 592 | 881 | 1108 | 1197 | 1104 | 1573 | ||

III | 355 | 567 | 836 | 1054 | 1145 | 1087 | 1525 | ||

Big Delta FAA/AMOS | 1/10 | I | 138 | 211 | 333 | 421 | 448 | 422 | 592 |

II | 135 | 207 | 321 | 406 | 436 | 418 | 581 | ||

III | 135 | 205 | 328 | 414 | 438 | 409 | 577 | ||

1/7 | I | 162 | 250 | 387 | 488 | 524 | 500 | 697 | |

II | 151 | 232 | 355 | 448 | 484 | 468 | 648 | ||

III | 167 | 258 | 400 | 505 | 541 | 514 | 718 | ||

1/5 | I | 191 | 296 | 445 | 560 | 610 | 597 | 821 | |

II | 187 | 291 | 435 | 548 | 598 | 590 | 808 | ||

III | 199 | 309 | 468 | 590 | 639 | 616 | 855 | ||

Kotzebue WSO | 1/10 | I | 207 | 322 | 510 | 642 | 680 | 619 | 885 |

II | 239 | 375 | 589 | 740 | 785 | 711 | 1019 | ||

III | 178 | 275 | 439 | 553 | 585 | 535 | 763 | ||

1/7 | I | 254 | 400 | 612 | 771 | 827 | 770 | 1089 | |

II | 291 | 461 | 700 | 881 | 947 | 880 | 1247 | ||

III | 219 | 341 | 528 | 665 | 711 | 664 | 938 | ||

1/5 | I | 318 | 504 | 744 | 938 | 1022 | 986 | 1371 | |

II | 363 | 577 | 842 | 1062 | 1161 | 1125 | 1562 | ||

III | 276 | 434 | 647 | 816 | 886 | 854 | 1186 | ||

Nome WSO | 1/10 | I | 130 | 194 | 335 | 422 | 435 | 385 | 557 |

II | 130 | 192 | 340 | 428 | 437 | 382 | 555 | ||

III | 119 | 178 | 304 | 383 | 396 | 355 | 510 | ||

1/7 | I | 168 | 257 | 423 | 532 | 556 | 497 | 716 | |

II | 168 | 257 | 430 | 540 | 561 | 495 | 717 | ||

III | 152 | 232 | 381 | 480 | 503 | 455 | 651 | ||

1/5 | I | 224 | 351 | 549 | 690 | 734 | 674 | 960 |

II | 229 | 359 | 568 | 713 | 755 | 681 | 978 | ||
---|---|---|---|---|---|---|---|---|---|

III | 203 | 316 | 495 | 623 | 663 | 614 | 870 | ||

Bethel | 1/10 | I | 189 | 290 | 490 | 613 | 634 | 550 | 803 |

II | 221 | 345 | 574 | 717 | 744 | 642 | 939 | ||

III | 175 | 266 | 452 | 567 | 585 | 510 | 743 | ||

1/7 | I | 242 | 380 | 611 | 765 | 804 | 709 | 1028 | |

II | 281 | 448 | 706 | 884 | 933 | 823 | 1194 | ||

III | 223 | 349 | 563 | 706 | 741 | 657 | 950 | ||

1/5 | I | 320 | 510 | 774 | 973 | 1044 | 956 | 1365 | |

II | 357 | 573 | 853 | 1074 | 1160 | 1075 | 1527 | ||

III | 296 | 471 | 720 | 905 | 969 | 888 | 1267 | ||

King Salmon | 1/10 | I | 110 | 157 | 293 | 368 | 372 | 325 | 472 |

II | 134 | 195 | 363 | 454 | 458 | 395 | 576 | ||

III | 101 | 144 | 266 | 336 | 340 | 300 | 434 | ||

1/7 | I | 142 | 212 | 375 | 470 | 480 | 418 | 608 | |

II | 179 | 271 | 476 | 594 | 607 | 519 | 761 | ||

III | 131 | 193 | 340 | 428 | 438 | 384 | 558 | ||

1/5 | I | 195 | 301 | 500 | 626 | 652 | 572 | 830 | |

II | 238 | 374 | 612 | 765 | 798 | 693 | 1012 | ||

III | 178 | 273 | 451 | 567 | 591 | 524 | 758 | ||

Juneau | 1/10 | I | 79 | 112 | 202 | 256 | 261 | 235 | 337 |

II | 85 | 121 | 220 | 279 | 284 | 254 | 364 | ||

III | 71 | 101 | 179 | 228 | 233 | 212 | 302 | ||

1/7 | I | 100 | 146 | 252 | 319 | 329 | 297 | 425 | |

II | 109 | 160 | 277 | 350 | 360 | 322 | 463 | ||

III | 89 | 130 | 223 | 283 | 292 | 265 | 379 | ||

1/5 | I | 134 | 203 | 333 | 421 | 441 | 401 | 573 | |

II | 146 | 222 | 368 | 463 | 484 | 435 | 625 | ||

III | 119 | 179 | 295 | 373 | 391 | 359 | 510 | ||

Annette WSO | 1/10 | I | 75 | 104 | 195 | 248 | 251 | 224 | 322 |

II | 91 | 126 | 239 | 302 | 304 | 269 | 388 | ||

III | 57 | 76 | 146 | 187 | 187 | 171 | 243 | ||

1/7 | I | 97 | 139 | 250 | 316 | 322 | 287 | 413 | |

II | 117 | 171 | 306 | 386 | 393 | 345 | 500 | ||

III | 73 | 102 | 188 | 239 | 242 | 218 | 312 | ||

1/5 | I | 134 | 201 | 341 | 429 | 445 | 396 | 571 | |

II | 164 | 249 | 422 | 530 | 548 | 482 | 699 |

III | 102 | 150 | 261 | 329 | 339 | 304 | 437 | ||
---|---|---|---|---|---|---|---|---|---|

St. Paul Island | 1/10 | I | 347 | 555 | 828 | 1042 | 1125 | 1046 | 1483 |

II | 360 | 577 | 861 | 1083 | 1169 | 1081 | 1537 | ||

III | 329 | 524 | 785 | 988 | 1067 | 996 | 1409 | ||

1/7 | I | 401 | 643 | 933 | 1176 | 1287 | 1236 | 1725 | |

II | 416 | 668 | 966 | 1219 | 1334 | 1277 | 1786 | ||

III | 381 | 609 | 886 | 1118 | 1222 | 1176 | 1639 | ||

1/5 | I | 472 | 755 | 1062 | 1342 | 1491 | 1495 | 2041 | |

II | 489 | 783 | 1098 | 1389 | 1544 | 1548 | 2115 | ||

III | 448 | 715 | 1011 | 1276 | 1417 | 1420 | 1938 | ||

Kodiak | 1/10 | I | 156 | 236 | 401 | 504 | 521 | 459 | 665 |

II | 191 | 294 | 494 | 619 | 641 | 558 | 813 | ||

III | 130 | 193 | 334 | 421 | 433 | 383 | 554 | ||

1/7 | I | 196 | 304 | 496 | 623 | 652 | 579 | 837 | |

II | 237 | 373 | 598 | 750 | 788 | 697 | 1010 | ||

III | 163 | 248 | 411 | 517 | 539 | 481 | 693 | ||

1/5 | I | 252 | 396 | 615 | 774 | 824 | 754 | 1076 | |

II | 306 | 487 | 744 | 934 | 1000 | 914 | 1306 | ||

III | 217 | 339 | 534 | 672 | 713 | 650 | 928 | ||

Cold Bay | 1/10 | I | 379 | 608 | 894 | 1126 | 1224 | 1154 | 1626 |

II | 409 | 659 | 959 | 1209 | 1318 | 1246 | 1754 | ||

III | 349 | 558 | 828 | 1043 | 1129 | 1060 | 1496 | ||

1/7 | I | 434 | 697 | 997 | 1258 | 1385 | 1351 | 1872 | |

II | 466 | 749 | 1063 | 1343 | 1483 | 1453 | 2010 | ||

III | 402 | 644 | 930 | 1174 | 1287 | 1246 | 1731 | ||

1/5 | I | 502 | 802 | 1116 | 1411 | 1577 | 1608 | 2176 | |

II | 535 | 855 | 1181 | 1494 | 1675 | 1721 | 2321 | ||

III | 469 | 749 | 1052 | 1329 | 1480 | 1494 | 2031 |

hub height for each of these weather stations non-linearly depends on the shear exponent of the power law (see Equation (2.13)). For p = 1 / 10 , each wind turbine provides the lowest wind-power output. Whereas the opposite is true in case of p = 1 / 5 . Consequently, the capacity factor for each wind turbine is the lowest for p = 1 / 10 and the highest for p = 1 / 5 (see

Based on the capacity factors for Period I, Cold Bay, St. Paul Island, Barrow, Bethel, and Kotzebue would be very good candidates for wind farms, as already found by Cooney and Kramm [

Weather station | p | Period | Wind turbine | |||||||
---|---|---|---|---|---|---|---|---|---|---|

E-48 (%) | S64 Mk II-1.25 MW (%) | GE 1.6-82.5 (%) | MM92 (%) | MWT95/2.4 (%) | E-82E4 (%) | SWT-3.6-107 (%) | ||||

Barrow WSO | 1/10 | I | 28.4 | 28.8 | 36.5 | 35.7 | 31.9 | 22.3 | 27.1 | |

II | 27.4 | 27.6 | 35.9 | 35.0 | 31.0 | 21.3 | 26.1 | |||

III | 27.8 | 28.1 | 35.4 | 34.6 | 31.1 | 21.9 | 26.6 | |||

1/7 | I | 35.4 | 36.4 | 44.2 | 43.3 | 39.3 | 28.1 | 33.9 | ||

II | 34.9 | 36.0 | 44.3 | 43.3 | 39.0 | 27.4 | 33.3 | |||

III | 34.5 | 35.4 | 42.7 | 41.9 | 38.1 | 27.6 | 33.1 | |||

1/5 | I | 45.4 | 47.1 | 54.3 | 53.4 | 49.5 | 37.0 | 43.8 | ||

II | 45.4 | 47.4 | 55.1 | 54.1 | 49.9 | 36.6 | 43.7 | |||

III | 43.8 | 45.4 | 52.3 | 51.4 | 47.7 | 36.0 | 42.4 | |||

Big Delta FAA/AMOS | 1/10 | I | 17.0 | 16.9 | 20.8 | 20.5 | 18.7 | 14.0 | 16.5 | |

II | 16.7 | 16.6 | 20.1 | 19.8 | 18.2 | 13.8 | 16.1 | |||

III | 16.6 | 16.4 | 20.5 | 20.2 | 18.3 | 13.5 | 16.0 | |||

1/7 | I | 20.0 | 20.0 | 24.2 | 23.8 | 21.8 | 16.6 | 19.4 | ||

II | 18.6 | 18.5 | 22.2 | 21.9 | 20.1 | 15.5 | 18.0 | |||

III | 20.6 | 20.6 | 25.0 | 24.6 | 22.5 | 17.0 | 20.0 | |||

1/5 | I | 23.5 | 23.7 | 27.8 | 27.3 | 25.4 | 19.8 | 22.8 | ||

II | 23.1 | 23.3 | 27.2 | 26.7 | 24.9 | 19.5 | 22.5 | |||

III | 24.5 | 24.7 | 29.3 | 28.8 | 26.6 | 20.4 | 23.7 | |||

Kotzebue WSO | 1/10 | I | 25.5 | 25.7 | 31.9 | 31.3 | 28.3 | 20.5 | 24.6 | |

II | 29.5 | 30.0 | 36.8 | 36.1 | 32.7 | 23.5 | 28.3 | |||

III | 22.0 | 22.0 | 27.5 | 27.0 | 24.4 | 17.7 | 21.2 | |||

1/7 | I | 31.4 | 32.0 | 38.3 | 37.6 | 34.4 | 25.5 | 30.2 | ||

II | 35.9 | 36.9 | 43.7 | 43.0 | 39.5 | 29.2 | 34.6 | |||

III | 27.0 | 27.3 | 33.0 | 32.4 | 29.6 | 22.0 | 26.0 | |||

1/5 | I | 39.3 | 40.3 | 46.5 | 45.8 | 42.6 | 32.7 | 38.1 | ||

II | 44.8 | 46.2 | 52.6 | 51.8 | 48.4 | 37.3 | 43.4 | |||

III | 34.0 | 34.7 | 40.5 | 39.8 | 36.9 | 28.3 | 33.0 | |||

Nome WSO | 1/10 | I | 16.1 | 15.5 | 20.9 | 20.6 | 18.1 | 12.8 | 15.5 | |

II | 16.1 | 15.3 | 21.3 | 20.9 | 18.2 | 12.7 | 15.4 | |||

III | 14.7 | 14.2 | 19.0 | 18.7 | 16.5 | 11.7 | 14.2 | |||

1/7 | I | 20.7 | 20.5 | 26.4 | 25.9 | 23.2 | 16.5 | 19.9 | ||

II | 20.8 | 20.5 | 26.9 | 26.4 | 23.4 | 16.4 | 19.9 | |||

III | 18.8 | 18.6 | 23.8 | 23.4 | 21.0 | 15.1 | 18.1 | |||

1/5 | I | 27.7 | 28.0 | 34.3 | 33.7 | 30.6 | 22.3 | 26.7 |

II | 28.3 | 28.7 | 35.5 | 34.8 | 31.4 | 22.6 | 27.2 | ||||
---|---|---|---|---|---|---|---|---|---|---|---|

III | 25.1 | 25.3 | 30.9 | 30.4 | 27.6 | 20.3 | 24.2 | ||||

Bethel | 1/10 | I | 23.3 | 23.2 | 30.6 | 29.9 | 26.4 | 18.2 | 22.3 | ||

II | 27.3 | 27.6 | 35.9 | 35.0 | 31.0 | 21.3 | 26.1 | ||||

III | 21.5 | 21.3 | 28.3 | 27.6 | 24.4 | 16.9 | 20.6 | ||||

1/7 | I | 29.9 | 30.4 | 38.2 | 37.3 | 33.5 | 23.5 | 28.6 | |||

II | 34.7 | 35.8 | 44.1 | 43.1 | 38.9 | 27.2 | 33.2 | ||||

III | 27.6 | 27.9 | 35.2 | 34.4 | 30.9 | 21.7 | 26.4 | ||||

1/5 | I | 39.5 | 40.8 | 48.4 | 47.5 | 43.5 | 31.6 | 37.9 | |||

II | 44.1 | 45.8 | 53.3 | 52.4 | 48.3 | 35.6 | 42.4 | ||||

III | 36.6 | 37.7 | 45.0 | 44.1 | 40.4 | 29.4 | 35.2 | ||||

King Salmon | 1/10 | I | 13.6 | 12.5 | 18.3 | 18.0 | 15.5 | 10.8 | 13.1 | ||

II | 16.6 | 15.6 | 22.7 | 22.1 | 19.1 | 13.1 | 16.0 | ||||

III | 12.5 | 11.5 | 16.6 | 16.4 | 14.2 | 9.9 | 12.0 | ||||

1/7 | I | 17.6 | 16.9 | 23.4 | 22.9 | 20.0 | 13.8 | 16.9 | |||

II | 22.1 | 21.7 | 29.8 | 29.0 | 25.3 | 17.2 | 21.1 | ||||

III | 16.1 | 15.5 | 21.3 | 20.9 | 18.3 | 12.7 | 15.5 | ||||

1/5 | I | 24.1 | 24.1 | 31.2 | 30.5 | 27.2 | 18.9 | 23.1 | |||

II | 29.4 | 30.0 | 38.2 | 37.3 | 33.3 | 23.0 | 28.1 | ||||

III | 21.9 | 21.8 | 28.2 | 27.7 | 24.6 | 17.4 | 21.0 | ||||

Juneau | 1/10 | I | 9.7 | 9.0 | 12.6 | 12.5 | 10.9 | 7.8 | 9.4 | ||

II | 10.5 | 9.7 | 13.7 | 13.6 | 11.8 | 8.4 | 10.1 | ||||

III | 8.7 | 8.1 | 11.2 | 11.1 | 9.7 | 7.0 | 8.4 | ||||

1/7 | I | 12.3 | 11.7 | 15.8 | 15.6 | 13.7 | 9.8 | 11.8 | |||

II | 13.4 | 12.8 | 17.3 | 17.1 | 15.0 | 10.7 | 12.9 | ||||

III | 10.9 | 10.4 | 13.9 | 13.8 | 12.2 | 8.8 | 10.5 | ||||

1/5 | I | 16.5 | 16.2 | 20.8 | 20.5 | 18.4 | 13.3 | 15.9 | |||

II | 18.1 | 17.7 | 23.0 | 22.6 | 20.2 | 14.4 | 17.4 | ||||

III | 14.7 | 14.4 | 18.4 | 18.2 | 16.3 | 11.9 | 14.2 | ||||

Annette WSO | 1/10 | I | 9.3 | 8.3 | 12.2 | 12.1 | 10.4 | 7.4 | 8.9 | ||

II | 11.2 | 10.1 | 14.9 | 14.7 | 12.7 | 8.9 | 10.8 | ||||

III | 7.0 | 6.1 | 9.1 | 9.1 | 7.8 | 5.6 | 6.7 | ||||

1/7 | I | 11.9 | 11.1 | 15.6 | 15.4 | 13.4 | 9.5 | 11.5 | |||

II | 14.4 | 13.6 | 19.1 | 18.8 | 16.4 | 11.4 | 13.9 | ||||

III | 9.0 | 8.2 | 11.7 | 11.6 | 10.1 | 7.2 | 8.7 | ||||

1/5 | I | 16.5 | 16.0 | 21.3 | 20.9 | 18.5 | 13.1 | 15.9 | |||

II | 20.3 | 19.9 | 26.4 | 25.8 | 22.8 | 16.0 | 19.4 | ||||

III | 12.6 | 12.0 | 16.3 | 16.1 | 14.1 | 10.1 | 12.1 | ||
---|---|---|---|---|---|---|---|---|---|

St. Paul Island | 1/10 | I | 42.8 | 44.4 | 51.7 | 50.8 | 46.9 | 34.6 | 41.2 |

II | 44.4 | 46.2 | 53.8 | 52.8 | 48.7 | 35.8 | 42.7 | ||

III | 40.6 | 42.0 | 49.0 | 48.2 | 44.4 | 33.0 | 39.1 | ||

1/7 | I | 49.5 | 51.4 | 58.3 | 57.4 | 53.6 | 40.9 | 47.9 | |

II | 51.3 | 53.4 | 60.4 | 59.5 | 55.6 | 42.3 | 49.6 | ||

III | 47.0 | 48.7 | 55.4 | 54.5 | 50.9 | 39.0 | 45.5 | ||

1/5 | I | 58.2 | 60.4 | 66.4 | 65.5 | 62.1 | 49.5 | 56.7 | |

II | 60.3 | 62.7 | 68.7 | 67.7 | 64.3 | 51.3 | 58.7 | ||

III | 55.3 | 57.2 | 63.2 | 62.3 | 59.0 | 47.0 | 53.8 | ||

Kodiak | 1/10 | I | 19.3 | 18.9 | 25.1 | 24.6 | 21.7 | 15.2 | 18.5 |

II | 23.6 | 23.5 | 30.9 | 30.2 | 26.7 | 18.5 | 22.6 | ||

III | 16.0 | 15.5 | 20.9 | 20.5 | 18.1 | 12.7 | 15.4 | ||

1/7 | I | 24.2 | 24.3 | 31.0 | 30.4 | 27.2 | 19.2 | 23.2 | |

II | 29.3 | 29.8 | 37.4 | 36.6 | 32.8 | 23.1 | 28.1 | ||

III | 20.1 | 19.8 | 25.7 | 25.2 | 22.5 | 15.9 | 19.3 | ||

1/5 | I | 31.1 | 31.7 | 38.5 | 37.7 | 34.3 | 25.0 | 29.9 | |

II | 37.8 | 39.0 | 46.5 | 45.6 | 41.7 | 30.2 | 36.3 | ||

III | 26.8 | 27.1 | 33.4 | 32.8 | 29.7 | 21.5 | 25.8 | ||

Cold Bay | 1/10 | I | 46.8 | 48.7 | 55.9 | 54.9 | 51.0 | 38.2 | 45.2 |

II | 50.5 | 52.7 | 59.9 | 59.0 | 54.9 | 41.2 | 48.7 | ||

III | 43.1 | 44.6 | 51.8 | 50.9 | 47.1 | 35.1 | 41.5 | ||

1/7 | I | 53.6 | 55.7 | 62.3 | 61.4 | 57.7 | 44.7 | 52.0 | |

II | 57.5 | 60.0 | 66.4 | 65.5 | 61.8 | 48.1 | 55.8 | ||

III | 49.6 | 51.5 | 58.1 | 57.3 | 53.6 | 41.2 | 48.1 | ||

1/5 | I | 61.9 | 64.2 | 69.8 | 68.8 | 65.7 | 53.2 | 60.4 | |

II | 66.0 | 68.4 | 73.8 | 72.9 | 69.8 | 57.0 | 64.5 | ||

III | 57.9 | 59.9 | 65.8 | 64.8 | 61.7 | 49.5 | 56.4 |

Rural Alaska, fossil fuel is particularly expensive; wind power may contribute to holding costs affordable. The generation of wind power at Barrow would strongly be limited by the operating temperature range unless cold climate versions of wind turbines like Senvion’s MM92 CCV with limits of −30˚C and lower would be deployed. At Annette and Juneau wind power is generally ineffective.

The typical distribution of the capacity factor is illustrated in

Δ P W T , I I = 〈 P W T , I I 〉 − 〈 P W T , I I I 〉 〈 P W T , I I 〉 , (5.2)

at each of the weather stations, where 〈 P W T , I I 〉 is the average wind power predicted for Period II and 〈 P W T , I I I 〉 is that predicted for Period III. Besides Big Delta that suggests a relative increase in wind power of up to 12% for p = 1 / 7 , we found notable relative decreases in the predicted wind power of about 38% for Annette, followed by Kodiak (≈30%), King Salmon (≈26%), and Kotzebue (≈24%), where the effect of the shear exponents was marginal in these instances. Bethel with about 17% for p = 1 / 5 and about 20% for p = 1 / 10 and p = 1 / 7 , Juneau with about 18% hardly affected by the shear exponents, and Cold Bay with about 14% for p = 1 / 10 to 10% for p = 1 / 5 also show remarkable relative decreases in predicted wind power. In case of Nome, the relative decrease in the predicted wind power is less than 12%. However, the results notably depend on both the chosen wind turbine and the shear exponent. St. Paul Island exhibits a small relative decrease of about 8% hardly affected by the shear exponents. Barrow shows a relative increase mainly for p = 1 / 7 and p = 1 / 5 , but this increase is less than 5%.

In case of Annette, predicted wind power dramatically decreased due to the near-surface wind-speed stilling from Period II to Period III, but with respect to Period I, wind-power generation at Annette is generally ineffective. The same is true for Juneau despite the relative decrease in the predicted wind power is twice as small as compared with Annette. At Cold Bay, Bethel and Kotzebue, which were very good candidates for wind farms based on Period I, the near-surface wind-speed stilling notably shrinks wind-power generation. The same is true in the case of Kodiak and King Salmon.

For the purpose of simplification, the probabilities P 1 , P 2 , and P 3 given by Equations (4.5) to (4.7) were computed for Periods I, II, and III using a common cut-in wind speed of v c i = 3.0 m ⋅ s − 1 and a common wind speed of the rated power of v p r = 13.0 m ⋅ s − 1 . The results are listed in

Based on wind-speed record of its 19 first-order weather stations, we analyze the near-surface wind-speed stilling in the State of Alaska, USA during the period reaching from January 1, 1984 to December 31, 2016 denoted as Period I. With exception of Big Delta that indicates an increase of 0.0157 m∙s^{−}^{1}∙a^{−}^{1}, on average, all other first-order weather stations indicate declining trends in the near-surface wind speeds. In most cases, the average trends are less than −0.0300 m∙s^{−}^{1}∙a^{−}^{1}, with exception of Gulkana that only exhibits a value of −0.0043 m∙s^{−}^{1}∙a^{−}^{1}. The strongest trend was found at Homer with −0.0500 m∙s^{−}^{1}∙a^{−}^{1}, on average, followed by Bettles with −0.0492 m∙s^{−}^{1}∙a^{−}^{1} and Yakutat with −0.0453 m∙s^{−}^{1}∙a^{−}^{1}. At Barrow, however, the declining trend is marginal.

With respect to the National Renewable Energy Laboratory and the Alaska Energy Authority, the mean wind speed and the mean wind-power density computed for the Period I served to determine the wind-power class for each first-order weather station. This study finds Bettles, Fairbanks, McGrath, Gulkana, Talkeetna, Anchorage, Homer, and Yakutat are related to wind-power class 1, termed as “poor”. These stations are impractical options for wind farms because they are unable to meet the basic criteria. The wind speeds at these locations would not be high enough to sufficiently supply power to the surrounding cities and communities, respectively. Also, they would experience a lot of days without receiving any power because the wind speed was not high enough to overcome the turbines cut-in wind speed. Thus, even though they indicate remarkable declining trends in the near-surface wind speeds, these first-order weather stations were not further considered in our prediction of wind power.

This wind-power potential, however, is of subordinate importance because wind turbines only extract a fraction of the kinetic energy from the wind field as characterized by the power efficiency. Since the wind turbine technology has notably improved during the past 35 years, we hypothetically used seven currently available wind turbines of different rated power (Enercon E-48, Suzlon

Weather station | p | Period | P 1 | P 2 | P 3 |
---|---|---|---|---|---|

Barrow WSO | 1/10 | I | 0.098 | 0.879 | 0.023 |

II | 0.082 | 0.906 | 0.013 | ||

III | 0.120 | 0.851 | 0.029 | ||

1/7 | I | 0.077 | 0.871 | 0.052 | |

II | 0.061 | 0.904 | 0.035 | ||

III | 0.096 | 0.844 | 0.060 | ||

1/5 | I | 0.056 | 0.825 | 0.118 | |

II | 0.043 | 0.860 | 0.097 | ||

III | 0.072 | 0.804 | 0.124 | ||

Big Delta FAA/AMOS | 1/10 | I | 0.393 | 0.568 | 0.040 |

II | 0.436 | 0.517 | 0.047 | ||

III | 0.377 | 0.590 | 0.033 | ||

1/7 | I | 0.358 | 0.587 | 0.055 | |

II | 0.413 | 0.528 | 0.059 | ||

III | 0.337 | 0.609 | 0.054 | ||

1/5 | I | 0.342 | 0.574 | 0.084 | |

II | 0.361 | 0.551 | 0.088 | ||

III | 0.300 | 0.623 | 0.077 | ||

Kotzebue WSO | 1/10 | I | 0.186 | 0.773 | 0.041 |

II | 0.133 | 0.821 | 0.046 | ||

III | 0.243 | 0.720 | 0.037 | ||

1/7 | I | 0.153 | 0.776 | 0.071 | |

II | 0.108 | 0.810 | 0.082 | ||

III | 0.208 | 0.730 | 0.061 | ||

1/5 | I | 0.121 | 0.751 | 0.127 | |

II | 0.083 | 0.766 | 0.151 | ||

III | 0.170 | 0.723 | 0.107 | ||

Nome WSO | 1/10 | I | 0.256 | 0.734 | 0.010 |

II | 0.208 | 0.787 | 0.005 | ||

III | 0.310 | 0.679 | 0.012 | ||

1/7 | I | 0.215 | 0.763 | 0.022 | |

II | 0.183 | 0.801 | 0.015 | ||

III | 0.267 | 0.710 | 0.023 | ||

1/5 | I | 0.172 | 0.777 | 0.051 |

II | 0.141 | 0.818 | 0.041 | ||
---|---|---|---|---|---|

III | 0.219 | 0.731 | 0.050 | ||

Bethel | 1/10 | I | 0.119 | 0.871 | 0.011 |

II | 0.079 | 0.909 | 0.012 | ||

III | 0.146 | 0.843 | 0.011 | ||

1/7 | I | 0.093 | 0.878 | 0.028 | |

II | 0.061 | 0.905 | 0.034 | ||

III | 0.119 | 0.853 | 0.028 | ||

1/5 | I | 0.069 | 0.855 | 0.076 | |

II | 0.053 | 0.848 | 0.099 | ||

III | 0.088 | 0.842 | 0.070 | ||

King Salmon | 1/10 | I | 0.209 | 0.790 | 0.001 |

II | 0.130 | 0.869 | 0.001 | ||

III | 0.264 | 0.733 | 0.002 | ||

1/7 | I | 0.173 | 0.822 | 0.005 | |

II | 0.090 | 0.907 | 0.003 | ||

III | 0.219 | 0.775 | 0.006 | ||

1/5 | I | 0.135 | 0.848 | 0.017 | |

II | 0.075 | 0.907 | 0.018 | ||

III | 0.180 | 0.801 | 0.019 | ||

Juneau | 1/10 | I | 0.417 | 0.578 | 0.005 |

II | 0.366 | 0.630 | 0.004 | ||

III | 0.474 | 0.521 | 0.006 | ||

1/7 | I | 0.376 | 0.614 | 0.010 | |

II | 0.326 | 0.665 | 0.009 | ||

III | 0.433 | 0.557 | 0.010 | ||

1/5 | I | 0.324 | 0.654 | 0.022 | |

II | 0.269 | 0.711 | 0.020 | ||

III | 0.380 | 0.599 | 0.022 | ||

Annette WSO | 1/10 | I | 0.365 | 0.633 | 0.002 |

II | 0.278 | 0.721 | 0.001 | ||

III | 0.458 | 0.540 | 0.001 | ||

1/7 | I | 0.325 | 0.671 | 0.005 | |

II | 0.238 | 0.758 | 0.004 | ||

III | 0.413 | 0.584 | 0.003 | ||

1/5 | I | 0.268 | 0.719 | 0.013 | |

II | 0.179 | 0.809 | 0.013 |

III | 0.355 | 0.636 | 0.009 | ||
---|---|---|---|---|---|

St. Paul Island | 1/10 | I | 0.062 | 0.839 | 0.099 |

II | 0.049 | 0.853 | 0.097 | ||

III | 0.079 | 0.823 | 0.098 | ||

1/7 | I | 0.050 | 0.794 | 0.157 | |

II | 0.040 | 0.801 | 0.159 | ||

III | 0.065 | 0.784 | 0.152 | ||

1/5 | I | 0.037 | 0.712 | 0.251 | |

II | 0.029 | 0.712 | 0.259 | ||

III | 0.049 | 0.713 | 0.238 | ||

Kodiak | 1/10 | I | 0.195 | 0.793 | 0.012 |

II | 0.124 | 0.864 | 0.013 | ||

III | 0.251 | 0.739 | 0.009 | ||

1/7 | I | 0.155 | 0.821 | 0.024 | |

II | 0.102 | 0.868 | 0.030 | ||

III | 0.216 | 0.764 | 0.019 | ||

1/5 | I | 0.131 | 0.812 | 0.056 | |

II | 0.077 | 0.853 | 0.070 | ||

III | 0.173 | 0.782 | 0.045 | ||

Cold Bay | 1/10 | I | 0.051 | 0.823 | 0.126 |

II | 0.037 | 0.824 | 0.140 | ||

III | 0.067 | 0.823 | 0.110 | ||

1/7 | I | 0.041 | 0.768 | 0.191 | |

II | 0.029 | 0.758 | 0.213 | ||

III | 0.055 | 0.778 | 0.167 | ||

1/5 | I | 0.030 | 0.676 | 0.294 | |

II | 0.021 | 0.652 | 0.327 | ||

III | 0.041 | 0.699 | 0.260 |

S64 Mark II-1.25 MW, General Electric 1.6 - 82.5, Senvion MM92, Mitsubishi MWT95/2.4, Enercon E-82 E4, and Siemens SWT-3.6-107) and three different shear exponents to assess the wind-power sustainability under changing wind regimes. These machines were chosen because of an increase in rated power by an increment of about 400 kW. The three shear exponents p = 1 / 10 , p = 1 / 7 , and p = 1 / 5 were considered to cover the range of wind power for various conditions of thermal stratification.

Based on the capacity factors for Period I, Cold Bay, St. Paul Island, Barrow, Kotzebue, and Bethel would be very good candidates for wind farms. Kodiak, Nome, King Salmon, and Big Delta may be considered for specific reasons like the reduction of fossil fuel consumption which always plays a notable role in Rural Alaska. However, wind-power generation at Cold Bay, Bethel and Kotzebue is notably affected by this near-surface wind-speed stilling. The same is true in case of Kodiak and King Salmon, where the impact of this wind-speed stilling currently prevents sustainability of wind power at these two communities. As mentioned before, wind-power generation at Annette and Juneau is generally ineffective.

Cold Bay located in the Aleutians East Borough is an ideal site for a wind farm. It has a very high wind-power potential expressed by the wind-power class of 6, termed as “outstanding”. As illustrated in ^{−}^{1} for p = 1 / 10 to 9.67 m∙s^{−}^{1} for p = 1 / 5 . They broadly coincide with the maxima of the power efficiencies of machines like General Electric 1.6 - 82.5, Senvion MM92, and Mitsubishi MWT95/2.4. For all three periods, the probability P 1 is very low, but the P 3 is very high (see

According to the Alaska Energy Data Gateway (https://akenergygateway.alaska.edu/community-data-summary/1418448/), between 2008 and 2013, the average power consumption (residential, commercial, and other) was about 2509 MWh. This means that one of the smaller wind turbines considered here would already be able to supply the community’s power demand for much of the year without much support by Diesel generators. (Nevertheless, a spinning reserve is intended to protect the system against unforeseen events such as generation outages, sudden load changes or a combination of both.) The near-surface air temperature ranges from −25.0˚C observed on January 30, 2000 to 25.0˚C observed on July 13, 1960 [

There is, however, a significant drawback. The Alaska-breeding population of Steller’s Eider currently listed as threatened under the Endangered Species Act (ESA) and a State of Alaska species of special concern, regularly occurs on Izembek National Wildlife Refuge, near Cold Bay [

With respect to all three periods, the differences in wind-power generation between St. Paul Island located in the Bering Sea and Cold Bay are of secondary importance. St. Paul Island has a wind-power class of 6 as well. The probability

density functions determined for all three shear exponents and all three periods slightly differ from those of Cold Bay. Compared with those of Cold Bay, the modes are slightly shifted to lower wind speeds leading to a slightly higher probability P 1 and a slightly lower probability P 3 . Thus, the capacity factors determined for St. Paul Island are somewhat lower than the corresponding ones of Cold Bay. As illustrated in

Based on the Alaska Energy Data Gateway, the average power consumption (residential, commercial and others) from 2009 to 2013 was about 3945 MWh mainly generated by using oil. The smaller wind turbines considered in this study would be able to supply the community’s power demand for much of the year without much support by Diesel generators. The near-surface air temperature ranges from −28.3˚C observed on March 14, 1971 to 18.9˚C observed on August 25, 1987 [

St. Paul Island has a wind power history. As stated on its website (http://www.tdxpower.com/projects-commercial), the Tanadgusix Corporation (TDX) contracted with Northern Power designed and installed a wind/diesel system on St. Paul Island. The site is an airport and industrial complex with airline offices, equipment repair, and storage facilities. After completion, TDX Power began operating the first Native owned and operated independent, hybrid wind/diesel power plant in Alaska. Formally commissioned in 1999, this project capitalized on the emerging hybrid technology as a way to combat escalating fossil fuel prices. The major generation for the hybrid system is provided by a 225-kW Vestas V27 wind turbine. The system supplies electricity and space heat to an 88,000 SF industrial/airport facility and has reduced fuel consumption at the complex by 45%. Future plans involve expanding the wind power capacity and heating infrastructure. A total of 3 Vestas V27 wind turbines are currently installed, and a project is underway to connect the microgrid to the St. Paul municipal utility grid.

In its Systems Performance Analyses of Alaska Wind-Diesel Projects of 2009 (DOE/GO-102009-2712), the US Department of Energy (DOE) pointed out that in 2004 the wind turbine had a non-scheduled availability of 100% and a capacity factor of more than 40% and that the operating wind turbine has experienced a capacity factor of almost 32%. Using the power curve of the Vestas V27 machine taken from Mölders et al. [^{−}^{1} for p = 1 / 10 to 7.33 m∙s^{−}^{1} for p = 1 / 5 . The capacity factor ranges from C F , d = 31.7 % at R P = 0.032 for p = 1 / 10 to and C F , d = 40.7 % at R P = 0.077 for p = 1 / 5 .

Again, there is a significant drawback. St. Paul Island is home to millions of seabirds nesting in colonies along its steep shores. Rare birds are found here each year during spring migration. Also, St. Paul Island is considered a top North American bird watching destination [

Barrow located on the Chukchi Sea coast is the northernmost city of the United States. It has a remarkable wind-power potential expressed by the wind-power class of, at least, 3, termed as “fair”. The probability density functions for all three shear exponents determined for all periods notably differ from those of Cold Bay. There is a shift in the modes by 2 m∙s^{−}^{1} or so to lower mean wind speeds. This leads to a remarkably higher probability P 1 and a notably lower probability P 3 . Thus, the capacity factors determined for Barrow are notably lower than the corresponding ones of Cold Bay and St. Paul Island. As shown in

Based on the Alaska Energy Data Gateway, the average power consumption (residential and commercial) between 2008 and 2013 was about 48,909 MWh. The electricity was mainly produced using natural gas from nearby gas, only a very small amount was generated using oil. A power consumption of about 50 GWh would require numerous medium-scale wind turbines.

The generation of wind power at Barrow is strongly limited by the operating temperature range. The near-surface air temperature ranges from −48.9˚C observed on February 3, 1924 to 26.1˚C observed on July 13, 1993 [

Kotzebue located at the north-western corner of the Baldwin Peninsula in the Kotzebue Sound, has a notable wind-power potential expressed by the wind-power class of 4, termed as “good”. The wind-power density and average wind speed at hub height are relatively high signifying that it could generate a lot of power. The probability density functions determined for all three shear exponents and all three periods, however, notably differ from those of Cold Bay. There is a notable shift in the modes to lower mean wind speeds ranging from 2 m∙s^{−}^{1} to 4 m∙s^{−}^{1} or so. Thus, P 1 is notably higher and P 3 is notably lower, and, hence, the capacity factors determined for Kotzebue are notably lower than the corresponding ones of Cold Bay and St. Paul Island. As illustrated in

According to the Alaska Energy Data Gateway, the average power consumption (residential, commercial, and other) between 2009 and 2013 was about 20510 MWh. An average amount of 1955 MWh is related to wind power which corresponds to 9.5% (but 15.8% in 2013) of the net generation of electricity.

According to DOE’s Systems Performance Analyses of Alaska Wind-Diesel Projects of 2009 (DOE/GO-102009-2711) the wind farm consists of fifteen 50-kW AOC 15/50 and Entegrity Wind Systems EW50; one 100-kW Northern Power Systems Northwind 100/19 A, and one remanufactured Vestas V17, i.e., the total rated power is 0.925 MW. However, a power consumption of about 20 GWh would require some medium-scale wind turbines.

The near-surface air temperature ranges from −50.0˚C observed on March 16, 1930 to 29.4˚C observed on June 22, 1991 [

About 90 miles east of Kotzebue lies the Selawik National Wildlife Refuge. During the short Arctic summers, large numbers of white-fronted geese and tundra swans arrive along with sandhill cranes and a horde of other shorebirds.

Lastly, Bethel is the largest community on the Kuskokwim River, approximately 80 km upstream from where the river flows into Kuskokwim Bay. Bethel has a remarkable wind-power potential expressed by the wind-power class of, at least, 3 termed as “fair”. The probability density functions for all three shear exponents determined for all periods notably differ from those of Cold Bay. There is a shift in the modes by more than 2 m∙s^{−}^{1} to lower mean wind speeds. Thus, P 1 is remarkably higher and P 3 is notably lower, and, hence, the capacity factors determined for Bethel are notably lower than the corresponding ones of Cold Bay and St. Paul Island. The average capacity factor ranges for Period I from 24.9% at R P = 0 .012 for p = 1 / 10 to 41.3% at R P = 0 .082 for p = 1 / 5 , for Period II from 29.2% at R P = 0 .013 for p = 1 / 10 to 46.0% at R P = 0 .105 for p = 1 / 5 , and for Period III from 23.0% at R P = 0 .013 for p = 1 / 10 to 38.3% at R P = 0 .077 for p = 1 / 5 (see

According to the Alaska Energy Data Gateway, the average power consumption (residential, commercial, and other) between 2008 and 2013 was about 39749 MWh. A power consumption of about 40 GWh would require numerous medium-scale wind turbines.

The near-surface air temperature ranges from −44.4˚C observed on January 28, 1989 to 30.6˚C observed on August 9, 2003 [

A potential problem with Bethel is that it is surrounded by the Yukon Delta National Wildlife Refuge which supports one of the largest aggregations of water birds in the world. Thus, wind turbines could strongly impact the wildlife in that area by killing countless birds.

Based on our study, one may conclude that wind-stilling affects wind-power generation in Alaska to a notable degree. Thus, prior to installing new wind farms, assessments of suitability for power generation should look at the entire record of available data to identify trends in P 1 , P 2 , and P 3 . Obviously, the distribution of these probabilities affects productivity. These aspects may also optimize the choice of turbine and sustainability of wind power. Also, like in the permitting process of power plants and other industrial complexes, a full environmental impact assessment must be performed to protect the subsistence lifestyle in the immediate area of the potential farm, wildlife, eco-systems and local climate. While the assessment of the impacts on endangered species, migrating birds and birds that are part of a subsistence lifestyle is straight forward, assessment of the impacts on local climate requires numerical modeling techniques. The mixing of air due to the rotor blades and the consequent more frequent neutral conditions alter the cloud and precipitation formation in the near-field. Such changes in the water cycle are known to affect ecosystems again with potential impacts on birds, fish and game and hence a subsistence lifestyle.

We would like to express our thanks to Prof. Dr. Gerd Wendler, Geophysical Institute of the University of Alaska Fairbanks, and Brian Hartmann for helpful comments and fruitful discussion.

The authors declare no conflicts of interest regarding the publication of this paper.

Kramm, G., Mölders, N., Cooney, J. and Dlugi, R. (2019) Near-Surface Wind-Speed Stilling in Alaska during 1984-2016 and Its Impact on the Sustainability of Wind Power. Journal of Power and Energy Engineering, 7, 71-124. https://doi.org/10.4236/jpee.2019.77006