Mean values over 2º×2º squares

It has been demonstrated by numerous authors that satellite altimeter data can be used to obtain accurate estimates of monthly and annual mean Hs in offshore locations,

averaged over squares of 2º latitude by 2º longitude (e.g. Carter et al, 1991; Young, 1994; Woolf et al, 2003). Cotton and Carter (1994) show that the monthly mean Hs

calculated from 5 or more altimeter transects of a 2º×2º square surrounding a buoy compares well to the continuous measurements made by the buoy, with an RMS error of around 0.2 m. From 1992 onwards there have been at least 2 altimeters flying at all times. This means that using the combined data from TOPEX, Poseidon, Jason, ERS-2, ENVISAT and GFO, there are a minimum of 7 transects per month through each 2º×2º square surrounding the NDBC buoys. The mean number of transects per month is 21, with only 1.5% of squares having less than 10 passes per month. However, the sampling rate of a given geographical area depends on the latitude, on the number of satellites operating at that time and on the relative phasing of the various satellite orbits (Queffeulou and Croizé-Fillon, 2007).

In this section the use of altimeter data as a large-scale tool for identifying areas of interest for wave energy development is investigated. The monthly mean Pelamis power calculated from buoy data is compared to the monthly mean from the altimeter

measurements in the surrounding 2º×2º square. Only the deep water buoys have been considered in this comparison, since the assumption of stationarity on this scale is not valid in shallow water. Again, the median value of the altimeter transect through the square has been used to reduce sampling variability. Since the data from the tandem missions are so close in time, these effectively represent duplicate measurements.

Therefore the average of the data from the tandem missions has been used so as not to bias the estimate of monthly mean. In the case of the TOPEX phase B orbit, some additional information is gained where the phase B ground track falls within the square and the phase A track does not. For our analysis we have discarded months where the buoy is recording for less than 90% of the time.

Figure 4.7 shows scatter plots of altimeter monthly and annual mean Pelamis power against the values from the NDBC buoys. There is evidence that the variance of the error in monthly mean power increases with the mean power, however this is not observed so strongly for the annual mean power. The error in monthly mean is a function of the error in individual measurements, the number of measurements and the autocorrelation structure of the monthly time series. Typically, as the monthly mean power increases, the monthly variability also increases, meaning that more samples are

Challenor and Carter (1994) for stationary distributions sampled at regular intervals.

Their analytic method is not appropriate here, since time series of wave parameters are non-stationary due to seasonal variation. Also, using altimeter data from multiple missions produces irregular sampling intervals. It is still useful to examine the effect of sampling rate empirically: Figure 4.8 shows the correlation of the altimeter monthly mean with the buoy monthly mean against number of altimeter transects. There is a slight increase in correlation from 20 < n ≤ 30 to n > 30 transects, but it is not significant at the 95% level. It can be inferred that, due to the autocorrelation in the data, sampling at a greater rate than once daily brings only marginal improvement.

Figure 4.7. Scatter plots of altimeter against buoy monthly and annual mean Pelamis power.

Figure 4.8. Correlation of altimeter monthly mean Pelamis power with buoy monthly mean Pelamis power against number of transects, with 95% confidence limits.

The reason that the error in annual mean is not as strongly dependent on the annual mean value as was observed for the monthly means is probably a result of the seasonal

variability. In our dataset, there is large seasonal variability at the higher power locations. Over the entire dataset the altimeter monthly mean was found to have a bias of 8.2 ±1.5 kW and RMSE of 32.6 ±1.4 kW. The annual mean was found to have a bias of 7.1 ±2.8 kW and RMSE of 12.9 ±1.6 kW. Since using altimeter data in 2º×2º squares is only indicative of the resource in that area, there is little use in being more precise about the uncertainty in relation to sampling and variability of the resource.

There is not enough buoy data to test the accuracy of the long term, multi-year averages in 2º×2º squares. However, the errors in annual mean are approximately normally distributed so if it assumed that the error each year is independent of the previous year, then the standard deviation in error will decrease as 1/√n, where n is the number of years the data is averaged over. Figure 4.9 shows a global map of the annual mean Pelamis power in 2º×2º squares for the period 1996-2005. Since this average is taken over ten years, the standard deviation of the error is 12.9/√10 = 4.1 kW. As discussed above, this value is only indicative and dependent on the level of variability in the resource.

From Figure 4.9 it is immediately obvious that the most energetic areas are in the Southern Ocean, followed by the North Atlantic, North Pacific and Southern Indian Ocean. Figure 4.10 shows a global map of the mean Pelamis power over the periods December-February and June-August, between 1996 and 2005. It is clear that the North Atlantic and North Pacific show a much stronger seasonal variability than the Southern Ocean. Also the effect of the summer monsoon winds in the Arabian Sea is clearly visible.

These maps differ from other satellite climatologies in that they show the mean power produced by a WEC rather than the mean Hs. WEC power depends on both Hs and Te

and will reach a maximum (the rated power of the device) at some value. This means that maps of mean values of Hs do not translate directly to maps of mean WEC power.

The maps produced in this section make it is possible to directly compare estimates of energy yield from wave farms situated in different areas.

Figure 4.9. Annual mean Pelamis power in 2°×2° squares for the period 1996-2005 from the combined altimeter dataset.

Figure 4.10. Mean Pelamis power in 2°×2° squares over December-February (top) and June-August (bottom) for the period 1996-2005 from the combined altimeter dataset.