Introduction
Description of data
General
Location | Latitude | Longitude | Elevation (m) |
---|---|---|---|
Crown Point, Tobago | 11.1497N | 60.8322W | 12 |
Piarco, Trinidad | 10.5953N | 61.3372W | 15 |
Basic statistics
Year | Number of readings | Max knots | Mean knots | Std. dev. knots | Kurtosis | Skewness |
---|---|---|---|---|---|---|
2000 | 8779 | 21 | 5.454 | 4.841 | − 0.954 | 0.396 |
2001 | 8760 | 20 | 5.654 | 4.874 | − 1.080 | 0.301 |
2002 | 8758 | 21 | 5.634 | 4.721 | − 0.923 | 0.326 |
2003 | 8760 | 21 | 5.356 | 4.653 | − 0.923 | 0.374 |
2004 | 8774 | 20 | 4.483 | 4.467 | − 0.928 | 0.512 |
2005 | 8759 | 26 | 4.226 | 4.600 | − 0.646 | 0.680 |
2006 | 8758 | 22 | 4.842 | 4.834 | − 0.881 | 0.534 |
2007 | 8757 | 20 | 4.794 | 4.867 | − 0.973 | 0.531 |
2008 | 8782 | 23 | 4.478 | 4.882 | − 0.793 | 0.656 |
2009 | 8300 | 94 | 4.974 | 5.128 | 16.473 | 1.486 |
2010 | 8682 | 23 | 5.047 | 5.290 | − 0.891 | 0.591 |
2011 | 8760 | 23 | 5.063 | 5.021 | − 0.749 | 0.555 |
2012 | 8783 | 23 | 5.075 | 5.032 | − 0.839 | 0.547 |
2013 | 8755 | 22 | 5.786 | 5.418 | − 0.878 | 0.482 |
2014 | 8756 | 196 | 5.863 | 5.775 | 132.684 | 4.358 |
2015 | 2160 | 40 | 6.261 | 5.779 | − 0.765 | 0.365 |
Total | 133,083 | |||||
Average | 5.187 | 5.012 | 8.558 | 0.793 |
Year | Number of readings | Max knots | Mean knots | Std. dev. knots | Kurtosis | Skewness |
---|---|---|---|---|---|---|
2000 | 8762 | 30 | 6.744 | 5.189 | − 0.915 | 0.205 |
2001 | 6519 | 264 | 8.393 | 6.732 | 393.540 | 11.340 |
2002 | 8036 | 39 | 7.616 | 5.043 | − 0.728 | 0.122 |
2003 | 8722 | 26 | 8.319 | 4.966 | − 0.848 | − 0.099 |
2004 | 8770 | 45 | 6.949 | 4.685 | − 0.200 | 0.279 |
2005 | 8735 | 214 | 6.906 | 5.296 | 275.285 | 7.409 |
2006 | 8598 | 70 | 7.519 | 4.996 | 1.835 | 0.170 |
2007 | 8752 | 22 | 7.713 | 5.387 | − 1.151 | − 0.111 |
2008 | 7063 | 30 | 7.103 | 5.463 | − 1.089 | 0.089 |
2009 | 3655 | 22 | 6.633 | 4.910 | − 1.126 | 0.061 |
2010 | 8654 | 22 | 6.896 | 5.502 | − 1.231 | 0.090 |
2011 | 8725 | 28 | 6.909 | 5.412 | − 0.973 | 0.158 |
2012 | 8772 | 38 | 6.774 | 5.757 | − 0.855 | 0.318 |
2013 | 8749 | 28 | 7.445 | 5.870 | − 0.996 | 0.201 |
2014 | 8757 | 28 | 7.890 | 5.929 | − 0.990 | 0.163 |
2015 | 2160 | 23 | 6.886 | 5.963 | − 1.104 | 0.279 |
Total | 123,429 | |||||
Average | 7.293 | 5.444 | 41.153 | 1.292 |
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As seen in Table 2, at Piarco, the maximum wind speed recorded is 196 knots at 9:00 a.m. on July 3, 2014. The maximum wind speed on that day otherwise was 16 knots, and the average was 8 knots. A wind speed of 196 knots (363 km/h) is the equivalent of a Category 5 hurricane [25]. 196 knots surpasses the sustained wind speeds of the strongest hurricane on record, Hurricane Patricia in October 2015 [26]. Records from satellite-based models available online [27] confirm that the measurement is erroneous.
-
Similarly, a speed of 94 knots was recorded as the maximum wind speed in 2009. This peak wind speed was recorded on June 12 at 11:00 a.m., followed by a measurement of 84 knots at 12:00 p.m.. The average wind speed on that day without these two measurements was 5.9 knots. These two wind speeds are the equivalent of a Category 2 Hurricane according to the Saffir–Simpson scale [25]. However, review of archived daily newspapers, for the next day make no mention of the event [28]. Again, no corroborating records were found to confirm these wind speeds [14] and as such, they were deemed erroneous.
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On February 16, 2015 a wind speed of 40 knots was noted at 9:00 a.m. This would be classified as tropical storm wind speeds according to the Saffir–Simpson scale. Online records corroborate the data for the rest of the day.
-
At Crown Point, Tobago a maximum wind speed of 264 knots is recorded on November 9, 2001 at 11:00 p.m. This wind speed exceeds the world record maximum 3 second surface wind gust of 220 knots. As such, it can safely be concluded that this is an erroneous record. Online records corroborate the data for the rest of the day.
-
Similar methods to those utilised above were used to identify 214 knots recorded on November 20, 2005 at 2:00 p.m., 187 knots on April 20, 2001, 96 knots July 17, 2005, 70 knots at 9:00 p.m. on June 20, 2006, 62 knots on March 20, 2001, 45 knots January 3, 2004 and 39 knots on January 2, 2002 at 11:00 a.m.
Year | Number of readings | Max knots | Mean knots | Std. dev. knots | Kurtosis | Skewness |
---|---|---|---|---|---|---|
2000 | 8779 | 21 | 5.454 | 4.841 | − 0.954 | 0.396 |
2001 | 8760 | 20 | 5.654 | 4.874 | − 1.080 | 0.301 |
2002 | 8758 | 21 | 5.634 | 4.721 | − 0.923 | 0.326 |
2003 | 8760 | 21 | 5.356 | 4.653 | − 0.923 | 0.374 |
2004 | 8774 | 20 | 4.483 | 4.467 | − 0.928 | 0.512 |
2005 | 8759 | 26 | 4.226 | 4.600 | − 0.646 | 0.680 |
2006 | 8758 | 22 | 4.842 | 4.834 | − 0.881 | 0.534 |
2007 | 8757 | 20 | 4.794 | 4.867 | − 0.973 | 0.531 |
2008 | 8782 | 23 | 4.478 | 4.882 | − 0.793 | 0.656 |
2009 | 8298 | 31 | 4.954 | 4.959 | − 1.023 | 0.471 |
2010 | 8682 | 23 | 5.047 | 5.290 | − 0.891 | 0.591 |
2011 | 8760 | 23 | 5.063 | 5.021 | − 0.749 | 0.555 |
2012 | 8783 | 23 | 5.075 | 5.032 | − 0.839 | 0.547 |
2013 | 8755 | 22 | 5.786 | 5.418 | − 0.878 | 0.482 |
2014 | 8755 | 21 | 5.842 | 5.406 | − 1.170 | 0.356 |
2015 | 2159 | 22 | 6.245 | 5.735 | − 1.246 | 0.288 |
Total | 133,079 | |||||
Average | 5.183 | 4.975 | − 0.931 | 0.475 |
Year | Number of readings | Max | Mean | Std. dev. | Kurtosis | Skewness |
---|---|---|---|---|---|---|
2000 | 8762 | 30 | 6.744 | 5.189 | − 0.915 | 0.205 |
2001 | 6516 | 25 | 8.318 | 5.475 | − 0.998 | 0.046 |
2002 | 8035 | 22 | 7.612 | 5.031 | − 0.895 | 0.094 |
2003 | 8722 | 26 | 8.319 | 4.966 | − 0.848 | − 0.099 |
2004 | 8769 | 30 | 6.945 | 4.667 | − 0.660 | 0.223 |
2005 | 8733 | 26 | 6.872 | 4.715 | − 0.892 | 0.049 |
2006 | 8597 | 36 | 7.512 | 4.951 | − 0.937 | − 0.055 |
2007 | 8752 | 22 | 7.713 | 5.387 | − 1.151 | − 0.111 |
2008 | 7063 | 30 | 7.103 | 5.463 | − 1.089 | 0.089 |
2009 | 3655 | 22 | 6.633 | 4.910 | − 1.126 | 0.061 |
2010 | 8654 | 22 | 6.896 | 5.502 | − 1.231 | 0.090 |
2011 | 8725 | 28 | 6.909 | 5.412 | − 0.973 | 0.158 |
2012 | 8772 | 38 | 6.774 | 5.757 | − 0.855 | 0.318 |
2013 | 8749 | 28 | 7.445 | 5.870 | − 0.996 | 0.201 |
2014 | 8757 | 28 | 7.890 | 5.929 | − 0.990 | 0.163 |
2015 | 2160 | 23 | 6.886 | 5.963 | − 1.104 | 0.279 |
Total | 123,421 | |||||
Average | 7.286 | 5.324 | − 0.979 | 0.107 |
Methodology
Distribution fitting
Review of probability distribution functions
Birnbaum–Saunders
Exponential
Gamma
Generalized extreme value
Generalized Pareto
Nakagami
Normal
Rayleigh
Weibull
Parameter estimation
Goodness of fit
-
Normalised mean square error (NMSE).
-
Chi-squared statistic.
-
Two sample.
-
Kolmogorov–Smirnov.
-
Coefficient of determination (\(R^2\)).
-
Akaike information criterion (AIC).
-
Bayseian information criterion (BIC).
The normalised mean square error (NMSE)
The Chi-squared statistic
The two-sample Kolmogorov–Smirnov test
Co-efficient of determination, \(R^2\)
Akaike information criterion
Bayesian information criterion
Results and discussion
Rank | NMSE | X2 | KS | \(R^2\) and \(R^2\) Adj | LogL, AIC and BIC |
---|---|---|---|---|---|
1 | Nakagami | Normal | Normal | Nakagami | Birn-Saun |
2 | Weibull | Gen. ext val | Gen. ext val | Gamma | Nakagami |
3 | Gamma | Rayleigh | Rayleigh | Weibull | Gamma |
4 | Exponential | Gen. Pareto | Gen. Pareto | Gen. Pareto | Weibull |
5 | Gen. Pareto | Exponential | Exponential | Exponential | Gen. Pareto |
6 | Rayleigh | Nakagami | Nakagami | Birn-Saun | Exponential |
7 | Normal | Gamma | Weibull | Gen. ext val | Gen. ext val |
8 | Gen. ext val | Weibull | Birn-Saun | Normal | Normal |
9 | Birn-Saun | Birn-Saun | Gamma | Rayleigh | Rayleigh |
Rank | NMSE | X2 | KS | \(R^2\) and \(R^2\) Adj | LogL, AIC and BIC |
---|---|---|---|---|---|
1 | Birn-Saun | Normal | Normal | Birn-Saun | Gen. ext val |
2 | Weibull | Gen. Pareto | Gen. Pareto | Weibull | Birn-Saun |
3 | Gamma | Exponential | Rayleigh | Gamma | Nakagami |
4 | Nakagami | Nakagami | Exponential | Nakagami | Gamma |
5 | Exponential | Gamma | Nakagami | Gen. ext val | Weibull |
6 | Gen. Pareto | Rayleigh | Weibull | Exponential | Exponential |
7 | Rayleigh | Birn-Saun | Gen. ext val | Gen. Pareto | Gen. Pareto |
8 | Gen. ext val | Weibull | Birn-Saun | Normal | Normal |
9 | Normal | Gen. ext val | Gamma | Rayleigh | Rayleigh |
Rank | NMSE | X2 | KS | \(R^2\) and \(R^2\)2 Adj | LogL, AIC and BIC |
---|---|---|---|---|---|
1 | Gen. Pareto | Normal | Normal | Gen. Pareto | Birn-Saun |
2 | Exponential | Gen. ext val | Gen. ext val | Exponential | Nakagami |
3 | Gen. ext val | Rayleigh | Rayleigh | Gen. ext val | Gamma |
4 | Normal | Gen. Pareto | Gen. Pareto | Nakagami | Weibull |
5 | Nakagami | Exponential | Exponential | Normal | Gen. Pareto |
6 | Rayleigh | Nakagami | Nakagami | Gamma | Exponential |
7 | Gamma | Gamma | Birn-Saun | Weibull | Gen. ext val |
8 | Weibull | Weibull | Weibull | Rayleigh | Normal |
9 | Birn-Saun | Birn-Saun | Gamma | Birn-Saun | Rayleigh |
Rank | NMSE | X2 | KS | \(R^2\) and \(R^2\) Adj | LogL, AIC and BIC |
---|---|---|---|---|---|
1 | Exponential | Normal | Rayleigh | Exponential | Gen. ext val |
2 | Gen. Pareto | Gen. Pareto | Normal | Gen. Pareto | Birn-Saun |
3 | Weibull | Exponential | Gen. Pareto | Nakagami | Nakagami |
4 | Gamma | Nakagami | Weibull | Gamma | Gamma |
5 | Nakagami | Gamma | Gen. ext val | Weibull | Weibull |
6 | Birn-Saun | Rayleigh | Exponential | Birn-Saun | Exponential |
7 | Rayleigh | Birn-Saun | Nakagami | Normal | Gen. Pareto |
8 | Normal | Weibull | Birn-Saun | Rayleigh | Normal |
9 | Gen. ext val | Gen. ext val | Gamma | Gen. ext val | Rayleigh |
Application-specific information criterion
Distribution | Expected energy/MWh | %Difference from actual |
---|---|---|
Actual | 155,270 | 0 |
Generalized extreme value | 163,810 | 5.50 |
Generalized Pareto | 142,140 | − 8.46 |
Normal | 139,560 | − 10.12 |
Nakagami | 139,560 | − 14.59 |
Rayleigh | 179,520 | 15.62 |
Gamma | 81,110 | − 47.76 |
Weibull | 72,843 | − 53.09 |
Birnbaum–Saunders | 295,810 | 90.51 |
Exponential | 4.0429E−08 | − 100 |
Distribution | Expected energy/MWh | %Difference from actual |
---|---|---|
Actual | 111,560 | 0 |
Normal | 113,930 | 2.12 |
Nakagami | 121,920 | 9.28 |
Rayleigh | 123,060 | 10.30 |
Generalized Pareto | 97,240 | − 12.84 |
Gamma | 77,874 | − 30.20 |
Generalized extreme Value | 71,804 | − 35.64 |
Weibull | 71,187 | − 36.19 |
Exponential | 0.00012435 | − 100.00 |
Birnbaum–Saunders | 403,780 | 261.94 |
Location | |||
---|---|---|---|
Distribution | Parameter | Crown Point | Piarco |
Birnbaum–Saunders | beta | 0.1009 | 1.0274 |
gamma | 9.636 | 2.6596 | |
Exponential | lambda | 7.3244 | 5.1314 |
Gamma |
k
| 0.3606 | 0.4944 |
theta | 20.314 | 10.4568 | |
Generalized extreme value | xi | − 0.15 | 4.2971 |
sigma | 4.9517 | 0.437 | |
mu | 5.0824 | 0.1016 | |
Generalized Pareto | xi | − 0.2299 | − 0.2013 |
Sigma | 8.7412 | 6.2781 | |
Theta | 0.0001 | 0.0001 | |
Nakagami | Mu | 0.1807 | 0.2244 |
omega | 82.1115 | 51.0448 | |
Normal | sigma | 7.3244 | 4.971 |
mu | 5.3352 | 5.1314 | |
Rayleigh | sigma | 6.4075 | 5.052 |
Weibull | lamda | 5.3442 | 3.9135 |
k
| 0.4825 | 0.6195 |