DEFENSORES DEL PUEBLO EN EL ECUADOR.

The approach described in the previous section was used to generate monthly mean wind speed predictions at each station included in the BADC-7 class. In the following pages the results from Lerwick station are presented though the rest figures and tables can be found in Appendix (G).

When the data at Lerwick station was fitted to the proposed model it was found that different order of SARIMAX produced the minimum FPE than the models presented when the wind speed was averaged over the UK. There were two reasons for this result. Firstly, the targeted time series were different on each occasion; in the first case, data from ERA-40 were averaged over

the whole UK whereas in the second case the data was retrieved from a distinct geographical location within the UK. Secondly, the local anomalies at each site were more easily revealed than when the wind speed was averaged over a whole region. This averaging procedure suppressed any effects from local anomalies, and hence it was reasonable to expect differences between the two models.

Cases Order FPE V

Wind speed (3, 1, 1, 1)(0, 1, 1)12 1.207 1.13

SST (4, 1, 1, 1)(0, 1, 1)12 1.195 1.114

MSL (0, 1, 1, 1)(0, 1, 1)12 1.23 1.168

SST gradient (8, 1, 1, 1)(0, 1, 1)12 1.171 1.074

Table 5.10: Identifying the order of the best SARIMAX on the training dataset for each model at

Lerwick

Similarly to before, the orders of the models were determined by assessing the MSE in each case. The most promising remarks were drawn when the model developed was compared with the models presented by Kritharas et al. [100]. As Table (5.11) demonstrates the proposed model increased the efficacy in the predictions by 10.04%, 12.8% and 14.6%. In the case of the whole UK (Table 5.9), MSL was the best predictor at all stations. However, in the case of each station SST gradient exhibited the lowest errors. The exception was Aberporth achieving the lowest errors when using the SST. That station is located in Wales and therefore it is assumed that these differences may be attributed to each station’s microclimate and local anomalies, though this requires further investigation. It is noted that this research is confined to the development of a statistical model without intending to investigate the underlying processes of atmospheric physics. Although the two disciplines (i.e. wind energy and meteorology) are often intertwined, because of the nature of wind and its relationship with atmospheric phenomena, it is beyond the scope and potential of this work to explore this area. However, it would be prudent for follow-up research to focus on this direction incorporating both fields.

Table (5.11) shows the statistical errors achieved by the models when they were introduced in the testing dataset. The best model was proved to be the one that used wind speed as the exogenous input.

The results for the rest of the BADC-7 stations are shown in Appendix (G). Figures (5.15) - (5.16) illustrate the performance of the proposed model. The ACF and PACF plots testify that the data fitted well to the model and there was no remaining autocorrelation in the data.

Cases Order MSE MEms−1 Wind speed (3, 1, 1, 1)(0, 1, 1)12 1.120 0.014 SST (4, 1, 1, 1)(0, 1, 1)12 1.20 −0.044 MSL (0, 1, 1, 1)(0, 1, 1)12 1.155 0.005 SST gradient (8, 1, 1, 1)(0, 1, 1)12 1.248 0.056 (atm. pres.) (6, 1, 1, 1)(0, 1, 1)12 1.245 −0.003 (rh) (7, 1, 1, 1)(0, 1, 1)12 1.284 −0.011 (atm temp.) (7, 1, 1, 1)(0, 1, 1)12 1.311 0.072

Table 5.11: Order of the best SARIMAX at Lerwick and corresponding statistical errors

Assessing the ME was a way to identify if the forecasts were biased. ME, or else, the forecast bias is determined by checking if the residuals show a trend which may reveal consistent differences between actual values and previously generated forecasts. Similar to all the other statistical errors, ME is expressed in ms−1when looking at forecasting errors in wind speed and in kW when looking at the prediction errors in wind power.

As Table (5.11) indicates, the ME is very close to zero which means that the forecasts generated by the models were not biased. In addition to Table (5.11), Figure (5.17) serves as a direct visual comparison of the models used in this study since it shows the Absolute Error (AE) for the validation dataset. Figure (5.17) confirms that the minimum errors occurred when the SARIMAX model used wind speed as an exogenous input.

1997 1998 1999 2000 2001 2002 3 4 5 6 7 8 9 10 11 12 1997 1998 1999 2000 2001 2002 4 5 6 7 8 9 10 11 12 1997 1998 1999 2000 2001 2002 4 5 6 7 8 9 10 11 12 13 1997 1998 1999 2000 2001 2002 3 4 5 6 7 8 9 10 11 12 W i n d s p e e d ( m s - 1 ) Time (months) Wind speed Wind speed W i n d s p e e d ( m s - 1 ) Time (months) Wind speed SST W i n d s p e e d ( m s - 1 ) Time (months) Wind speed MSL W i n d s p e e d ( m s - 1 ) Time (months) Wind speed SST gradient

Figure 5.15: Predictions of SARIMAX models at Lerwick

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 A C F Lags 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 P A C F Lags

1998 1999 2000 2001 2002 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 A b s ol u t e E r r or ( m s - 1 ) Time (months)

SARIMAX Wind speed

1998 1999 2000 2001 2002 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 A b s ol u t e E r r or ( m s - 1 ) Time (months) SARIMAX (msl Ref. [100]) 1998 1999 2000 2001 2002 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 A b s ol u t e E r r or ( m s - 1 ) Time (months)

SARIMAX (temp Ref. [100])

1998 1999 2000 2001 2002 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 A b s ol u t e E r r or ( m s - 1 ) Time (months) SARIMAX (rh Ref. [100])