In Situ

The in situ measurements used in this study come from 70 meteorological sta- tions at coastal sites and from 20 buoys (Fig. 2.1) and are obtained from 2002 to 2012. The data for U.S. sites were obtained from the National Data Buoy Center (http://www.ndbc.noaa.gov/) and depending on the location they were maintained by the Coastal-Marine Automated Network (C-MAN), the National Oceanic and Atmospheric Administration (NOAA) National Ocean Service (NOS), the National Weather Service (NWS), or the Great Lakes Environmen- tal Research Laboratory (GLERL). The data for Canadian sites were obtained from the Ontario Climate Center (http://climate.weather.gc.ca/). All

Figure 2.2: Schematic of the different data sources and the methodology applied to each one to generate wind speed maps and finally an observational wind at- las. For each data stream, the first line describes the number of sites (for coastal stations and buoys) or resolution (for satellites), the second line shows the tem- poral averaging period of the measurements (for coastal stations and buoys) or overpass frequency (for satellites). *For SAR, resolution of the derived wind maps is 500 m while original resolution of Envisat SAR Wide Swath Mode is 150 m. The following lines represent the period of data availability, the data filtering criteria, and the processing steps.

sites are equipped with propeller anemometers. Data are reported every 6 min- utes to 1 hour, with sporadic periods of higher frequency. Because of the high frequency and long record, we assume that diurnal, seasonal, and interannual variability are captured in the mean wind climates derived from these data. The coastal stations have long-term records but represent coastal conditions. The buoys capture offshore conditions but are less numerous and unavailable dur- ing the cold season, when they are removed from the Lakes due to ice formation. Both provide measurements at relatively low heights, with anemometer heights ranging from 6.4 to 46.9 m for the coastal stations and from 3.2 to 5.0 m for the buoys.

Quality Control

Quality control was performed on data from coastal sites and buoys to reduce uncertainties and to prevent seasonal biases from affecting the wind atlas cal- culations. Inaccurate and unrealistic values were identified using the following criteria (Eqs. (2.1a) to (2.1d)) and removed from the time series.

  ~u    < 0.4 m s −1 _(2.1a)   ~u    > 75 m s −1 (2.1b)    ~ui    >   ~ui−1    ∗ 1.5 and    ~ui    >   ~ui+1    ∗ 1.5 if    ~ui    > 15 m s −1 (2.1c) 0◦ > θ > 360◦ (2.1d) The anemometer response can be slow near its cut-in value since it needs to overcome mechanical friction and inertia to start spinning. As a consequence, the observations in the first bin of the observational histogram (0 − 1 ms−1_{) in-}

clude erroneous values as well as wind speeds below 1 ms−1_{. To prevent this}

excessive number of calm recordings from skewing the Weibull distribution fit, Eq. (2.1a) is applied to remove a portion of these erroneous values, while still allowing a sufficient number of low but legitimate wind speed values to remain for the proper fitting of the distribution. Eq. (2.1b) removes possibly erroneous high values [76] that are sometimes present in the original data due to format- ting or recording issues. Instead of defining the maximum allowed variability as a fixed value, Eq. (2.1c) was used to remove any isolated high entries by filter- ing out values that are more than 150% of both the previous and the following entries. This criterion was applied only to very high wind speeds (u > 15 ms−1_at

anemometer height) and filtered out a negligible portion of the data (∼ 0.002%). To avoid seasonal biases, each coastal site was conditioned to keep only sam- pled years of data for which each month had an availability ≥ 70% (e.g. for hourly observations in January the total possible is 24*31 so a minimum of 521 entries was required). Moreover, only sites with at least three years of complete data were kept in the analysis, in order to minimize the impact of interannual variability biases on the wind climate. For the 11-year period considered, the annual mean wind speeds averaged across sites were ∼ 5.0 ms−1_{for buoys and}

∼ 4.8 ms−1 _{for coastal stations, with an interannual variability of ±0.6 ms}−1 _and

±0.5 ms−1respectively. The number of years of data used for each site after qual- ity control varies from 3 to 11 years (Fig. 2.1). Note that Fig. 2.1 does not rep- resent the number of years rejected during quality control, since very few sites were operational during the entire 11-year period. Each year has measurements from at least 3 sites (coastal or buoy) in each lake (Fig. 2.3). The lake with fewest sites is Lake Michigan from 2002 to 2005. In contrast, the most robust represen- tation is for Lake Huron in 2011 and 2012, where 21 sites were available with

2002 2004 2006 2008 2010 2012

Year

Sites per Year and per Lake

Erie Huron Michigan Ontario Superior

Figure 2.3: Number of coastal and buoy sites with complete data records, for each year from 2002 to 2012 for each of the Great Lakes.

complete data.

Wind Climates

To reconcile measurements taken at different heights (anemometer heights for the in situ measurements vary from 3.2 m to 46.9 m) and in different local wind regimes and thus develop an integrated wind resource estimate at a standard height (here of 90 m), the in situ time series of data from each site were used to develop generalizable wind climates (Fig. 2.2) using the Wind Atlas Anal- ysis and Application Program (WAsP) [50]. WAsP is the most widely used model for wind resource assessment. It uses roughness, topography and in- ternal boundary layer models, and the geostrophic drag law to extrapolate the observations from a mast (at anemometer height) to other points in space (often to hub height). The mean wind climates are statistical summaries of wind condi- tions at a given site and are produced as follows: the time series of wind speeds and directions are used to generate 30◦

wind direction sector-specific histograms of the wind speeds (i.e., the observed wind climate in Fig. 2.2) from which the

Weibull scale and shape parameters (A and k, respectively) are derived. Then these wind climates in each sector are generalized by removing the local effects of orography and roughness to obtain a value for the geostrophic wind that is independent of the surface conditions and assumed to be homogeneous within a given area [3]. This value can then be used to obtain the wind climate over an area of approximately a 50 km radius from the station, by reincorporating the orography and roughness characteristics of the target points. In this appli- cation the orography was described using NASA’s Shuttle Radar Topography Mission data at a resolution of 30 arc-seconds (approximately 0.9 km in latitude and 0.6 to 0.7 km in longitude for the Great Lakes geographical location), the over-water roughness length was assumed to be 0.0002 m, and the roughness length over land was assumed to be 0.1 m. Obstacles were not taken into ac- count since the focus of this work is offshore resource assessment. The standard WAsP parameters were used, which include a slightly unstable atmosphere off- shore, with a heat flux of 15 Wm−2_{. Using these assumptions, generalizable wind}

climates (i.e., the statistical wind climate in Fig. 2.2) were derived for heights (z) of 10, 25, 50, 90 and 150 m and roughness lengths (z0) of 0.0002, 0.03, 0.1, and 0.4

m for all buoys and coastal stations following the well established wind atlas methodology [3].

Seasonal Correction

Because the Great Lakes system is a high latitude freshwater system, it is sub- ject to extensive ice cover [77, 64]. This poses a challenge both for prospective wind deployment (though use of ice-cones can greatly reduce foundation load- ing from ice floes [78]) and for accurate quantification of the wind resource, be-

cause during the ice formation months the buoys are removed from the Lakes. During the 11-year period considered, the average length of cold-season data gaps varied from 3.1 to 5.5 months across the buoy locations, with a spatial av- erage of 4.1 months of missing data per cold season per site. Thus a correction was applied to each buoy generalized wind climate to correct for the absence of cold-season data. A reference data set was used in this procedure, namely the National Center for Environmental Prediction (NCEP) North American Re- gional Reanalysis (NARR) [79]. These data are for a nominal height of 10 m, and are available at 3-hourly intervals at a spatial resolution of 32 km. The method applied to correct for the missing buoy observations is based on the measure- correlate-predict method of ratios [80]. For each standard roughness and height, the mean and the mean cubed of the Weibull distribution were calculated ac- cording to Eq. (2.2) [3], where mn _{represents the first moment (i.e., the mean) to}

the nth

power [ms−1_]n

, A the scale parameter [ms−1_{] and k the shape parameter of}

the Weibull distribution, andΓ the gamma function. mn = AnΓ  1+ n k  (2.2) Concurrently, the mean and mean cubed were calculated for the reference time series considering two scenarios: a complete data record that includes the cold season, and a shorter record that includes only the time stamps that coincide with the buoy availability. For those coinciding time stamps, a ratio of the mo- ments was obtained. This ratio and the moments for the complete-record ref- erence series were then used to obtain corrected buoy moments, as given by Eq. (2.3) where the subscript o represents the original buoy series and r the ref- erence series. mn_o,corrected = m n o,short mn_r,shortm n r,complete (2.3)

Once the moments have been corrected, Eq. (2.2) can be used again to recalculate the Weibull parameters A and k, which now describe the corrected generalized wind climate.

Validation of Seasonal Correction

The validity of this seasonal correction was tested on data from the coastal sta- tions, for which complete time series are available. Thus, the method applied in Section 2.2.1 is evaluated here by deriving time series for the coastal stations that mimic the fractured buoy data sets and by comparing them against the complete time series. The all-sector percent errors between the generalizable wind climate derived from the original complete time series and the “corrected” complete se- ries are shown in Fig. 2.4. These errors were calculated for the height of 90 m and four roughness classes for the mean and for wind power density P [Wm−2_],

which is given by Eq. (2.4), where the air density ρ was taken to be 1.225 kgm−3_.

Errors were calculated as (xtrue− xestimate)/xtrue.

P= 1 2ρA 3_{Γ 1+} 3 k ! (2.4) The approach is generally robust. For the first moment (i.e., the mean), all errors were within 10%. When averaged across roughness classes, the mean error was -0.8 %, the median -1.3%, and the standard deviation 4.1%. For the power den- sity, the cube relation of the scale factor (A3 _{in Eq. (2.4)) amplifies uncertainties}

and the errors are higher. They were within 25%, with a roughness-averaged mean of -1.8%, a median of -3.3%, and a standard deviation of -10.6%. As in- dicated, the mean error is generally negative which indicates that the moment- ratio correction method slightly under-corrects for the sampling bias introduced by the removal of buoys due to the presence of ice on the Lakes.

0.0002

0.03

0.1

0.4

Roughness Length (m)

30

20

10

0

10

20

30

Percent Error (%)

AΓ(1 +1/k)

0.5ρA

_{Γ(1 +3/k)}

Figure 2.4: Percent errors for the first moment of the Weibull distribution and for power density at 90 m when using NARR as a reference series and the method of ratios to correct for the seasonal bias artificially introduced in the data from coastal stations. The box plots are spatial averages across the coastal stations. For each coastal station, the number of years of data considered differs and is given in Fig. 2.1.

Seasonal Correction Results

The differences between the predicted wind resource at 90 m before and after the buoy correction are shown in Table 2.1 for wind speed u and wind power density P as given by Eq. (2.4). They were highest for Lake Superior, where the predicted P was ∼ 34% higher after the correction for missing data due to ice cover, and lowest for Lake Erie, where it was ∼ 14% higher. The predicted resource at 90 m offshore was also calculated using the artificially incomplete May-Oct coastal time series and their complete Jan-Dec counterparts, for the 70 coastal stations. The results are shown in bold in Table 2.1. Consistent with prior modeling analysis that has indicated higher wind speeds during the cold season and the importance of ice cover to determining wind regimes over lakes [69],

application of the correction increases the wind resource and exhibits variation across the Lakes. In terms of power density, the highest difference for the coastal stations is seen for Lake Erie (∆P ∼ 57%) and the lowest for Lake Superior (∆P ∼ 28%).

Table 2.1: Difference (xa f ter − xbe f ore) in wind resource at 90 m as predicted by

WAsP (wind speed u and power density P) before and after the seasonal cor- rection was applied to data from the buoys and to the artificially incomplete coastal sites (boldface), calculated at each site and spatially averaged over each Lake (number of sites per Lake is given).

∆u [ms−1_{] ∆u [%] ∆P [Wm}−2_{] ∆P [%] Number of}

Sites Superior 0.8, 0.6 11.8, 10.2 125, 74 33.8, 28.1 4, 14 Michigan 0.7, 0.7 10.2, 12.2 116, 105 26.1, 37.9 2, 19 Huron 0.4, 0.5 6.5, 9.5 58, 66 15.3, 31.2 6, 18 Erie 0.3, 0.9 5.3, 15.7 44, 126 13.8, 57.0 4, 12 Ontario 0.7, 0.8 11.2, 13.5 90, 107 27.4, 49.6 4, 7

Predicted Wind Speeds

Once the correction was applied, the generalized wind climates for each buoy and coastal station were used in WAsP to produce 90 wind resource maps cen- tered at each of the 90 sites. For the coastal stations, the resource maps extended over a radius of 25 km. Because the buoys are offshore where winds are likely to be more homogeneous, resource maps for the buoys extended out to 50 km from the center. The resource maps were discretized with 1 km resolution. The 90 individual maps were then merged using bilinear interpolation as the resam- pling method, considering a weighted average of the four closest pixel centers. Once combined, the map was gridded using a kriging method [81] to gener- ate a homogenized wind resource at 90 m (Fig. 2.5). The spatial heterogeneity of the resource map (localized maxima and minima) are the result of the data

sparseness and the interpolation, and re-emphasizes the value of integration of over-lake remote sensing data. Since each site produced an individual resource map (25 km x 25 km for coastal stations and 50 km x 50 km for buoys), the proximity of sites seen at some locations led to the overlapping of individual resource maps. Upon interpolation and gridding, the overlapping areas intro- duce some uncertainty in the wind resource at the buoy locations, as is seen by the mean bias values in Fig. 2.5 for Lake Ontario and Lake Saint Clair. Hereafter, “bias" refers to a measure of the uncertainty in the method determined by the difference in an observed and interpolated value. The bias is given by Eq. (2.5), where u90M is the mean wind speed at 90 m as predicted by the method being

presented, and u90W is the mean wind speed at 90 m as predicted by WAsP from

ice season-corrected buoy data. Root-mean-square errors (RMSE) are calculated according to Eq. (2.6) where Nbuoysis the number of buoy sites being used in the

error calculation. bias= u90M − u90W (2.5) RMS E = v u u t P buoys u90M − u90W
2 Nbuoys (2.6) The bias values ranged from -0.4 to 0.8 ms−1 _{(Fig. 2.5), with a mean bias of ∼}

0.0 ms−1_{when averaged over all buoy locations, and a RMSE of ∼ 0.2 ms}−1_.