Table 5.3 CP occurrence frequencies and their associated wave event statistics. The wave height threshold θ used to define the wave events wasθ = 3.5 m for this data.
CP CP03 CP07 CP08 CP09
Occurrence frequency (p(CP)) %
Summer 6.54 6.49 5.85 4.15
Autumn 5.41 5.55 4.83 5.27
Winter 6.07 4.66 4.30 5.31
Spring 5.53 5.70 5.58 4.74
All Seasons 5.89 5.60 5.13 5.13 Contribution to extreme events (p(CP | θ)) %
Summer 0.00 26.6 0.00 0.00
Autumn 7.89 10.5 0.66 10.5
Winter 9.52 11.1 4.76 17.5
Spring 5.26 44.7 0.00 7.89
All Seasons 7.38 16.2 1.48 11.1
have traveled from the greatest distances. However, there are occasions when dω/dt for wave events with long wave periods are similar to those with small wave periods.
Such events may therefore be grouped unrealistically close to one another, perhaps due to neglecting dissipation effects. Incorrect spatial and temporal placement can create errors when linking CPs with the swell origins. Therefore outlier values need to be removed from the spatial and/or wave characteristic groupings prior to analysis of their associated CPs. Here we eliminated frequency values that were more than one standard deviation from the mean.
Fig. 5.6 shows all the unique swell events for the Durban data and illustrates some of the above-mentioned issues with the procedure. The swell origins are the small dots and they are coloured according to the magnitude of their wave periods. The swell origins largely behave as expected with the shorter period waves forming closer to shore than the longer period waves. However there are examples when this is not the case due to the reasons noted above. Some events are also estimated to have formed over Madagascar which is obviously not possible.
The linking of CPs to wave origins based on the spatial grouping method (Fig. 5.7) showed high variability that suggests erroneous coupling of storm origins with CP anomalies. However the method of grouping based on wave characteristics (Fig. 5.8) performed much better in this regard. Pringle et al. (2014) noted that it is possible for a specific storm to belong to a number of classes during its development because the set of classes represent different atmospheric states with no attached temporal information. The relative orientation of high and low pressure anomalies is also not directly incorporated into the CP classification procedure. This may be important for discriminating between waves from different directions because the locations of high and low pressures influences the direction of the surface wind field that drives wave formation. In general the strongest winds occur in the zone between high and low pressures where the pressure gradient is high. However the results in Fig. 5.9 indicate that the CP classification algorithm can successfully discriminate between wave spectra of varying strength and direction. Therefore we propose that the CPs are a physically meaningful way to describe complex wave climates.
Although the algorithm has limitations it can have significant benefits in some applications. The linking of spectral wave energy to CPs is valuable in spectral wave models. As shown in § 5.3 different circulation patterns produce different spectral shapes. It would therefore be erroneous to assume the same spectral shape for all wave conditions or to use the default spectral characteristics provided by some spectral wave
models (e.g. SWAN). The link between the spectral data and the CPs can be used to fit a parametric model to the spectral data to study the impacts of specific CPs on the coastline. For example the specific spectral shape for swell produced by tropical cyclones can be used to model their potential impacts. This may also be useful for the study of climate change phenomena where one could study the changes in forcing mechanisms as opposed to directly investigating the wave data.
Another important application of the algorithm may be found in the statistical analysis of extreme wave events and wave climate modelling. Firstly it provides a physically meaningful way to identify independent events. Furthermore it provides a method to differentiate and model wave directional spectra in complex wave climates.
The classical method of defining independent events uses wave height thresholding and cannot reliably define statistically independent events. The proposed algorithm avoids the mixing of statistically independent events by linking them to specific meteorologi- cal systems in terms of their CPs. An example is shown in Fig 5.10 of a recorded wave event on the east coast of South Africa with two different causal weather systems.
These two events may have been grouped as one using the two week time threshold proposed by Corbella & Stretch (2012d). Li et al. (2014) used the classical method of defining storm independence when they proposed a method of modelling multi- variate storm parameters. In their method they identified that their model failed to capture the physical limits of the storm driving forces. Camus et al. (2011) utilised classification algorithms to group wave events with similar characteristics within a complex wave climate for modelling purposes. The more recent work by Camus et al. (2014); Espejo et al. (2014) also developed the links between atmospheric CPs and the aforementioned wave climate. However these links were found after CP classifica- tion, whereas in the method presented here the derivation of the CP classes is based a priori on their link to the wave climate. This distinction and its benefits are further discussed by Bárdossy et al. (2015). The results shown in § 5.3.2, 5.3.3 and Figs 5.7, 5.8 indicate that grouping events with similar characteristics on the assumption that they are driven by similar CPs is valid at our case study site. Exploiting these links can significantly improve statistical models.
4.5 3.0 1.5 0.0 1.5 3.0 4.5
0° 10°E 20°E 30°E 40°E 50°E 50°S
40°S 30°S 20°S 10°S
0° 10°E 20°E 30°E 40°E 50°E 50°S
40°S 30°S 20°S 10°S
(a) (b)
2001/4/4 2001/4/5 2001/4/6 2001/4/7 2001/4/8 2001/4/9 2001/4/10 Date
0 1 2 3 4 5 6
Hs (m)
(c)
Fig. 5.10 An example of storm wave events in 2001 with two different driving weather systems: (a) a mid-lattitude cyclone occurring on 2001/04/03, and (b) a tropical cyclone occurring on 2001/04/08. Both events may have been grouped as one storm by traditional threshold based methods. A threshold of 3.5m is shown by the dashed line in (c)