Squares Forming In The Ocean

[Haziel Barbour]

Beforewe get into the physics of cross seas, let's review how ocean waves form. As the National Oceanic and Atmospheric Administration notes, "Waves are created by energy passing through water, causing it to move in a circular motion. However, water does not actually travel in waves."

The wind is mostly responsible for the creation of ocean waves, which shouldn't be confused with waves created by earthquakes, hurricanes, landslides and volcanic eruptions. As the wind blows, it transfers energy to the surface of the water creating a constant disturbance that results in a wave crest.

Cross seas generally occur along coastal areas, and they are rare. Yet, there is one place along the west coast of France where cross seas occur with astonishing regularity. The geology of the Isle of Rh makes it perfectly situated for their formation.

The site is a tourist attraction that brings thousands to the island's lighthouse each year to view the phenomenon at a safe distance. It's a bit odd to think that waves intersecting at different angles would draw so many people, but really, when was the last time you saw nature create squares in water?

With a squared sea, the water can be difficult to navigate for boaters, as well as swimmers. Part of what makes square waves dangerous is that they generate powerful rip currents, and powerful waves, which can reach nearly 10 feet (3 meters) high, more than enough to swamp a large boat. A study found that "a large percentage of ship accidents occurred in crossing sea states."

You can usually spot two opposing swells in shallow waters, such as those off the Isle of Rh, and off Tel Aviv, Israel. Scientists say cross seas are an example of the Kadomstev-Petviashvili equation at work. The formula describes nonlinear wave motion and is often used to explain how different weather systems interact with one another.

In short, if you see a square wave, you want to get out of the water immediately as they pose real danger. However, it might not be so easy to see the pattern the two swells make when you're swimming, so your best bet is not too go too far out.

The spatial distribution of weights allocated to the data casts used in the calculation of the mean salinity at the 20-m level for the indicated grid point (water depth 45 m). The weights for individual casts are represented by the size of the circles

(a) Rms residuals between the CARS climatology and the temperature data in regions enclosing the EAC and the central Tasman Sea (the two regions are shown in Fig. 12). Further curves show the residual for independent XBT data in each region. (b) As for (a) but for data in a Leeuwin Current region and the WMO square 3110. (c) Mean difference between observed T and S and CARS temporal climatology (full line), for the indicated regions. (d) As for (c) using salinity data. (e) As for (b) but using salinity data.

Rms residuals (normalized by a priori noise estimates) between CARS and temperature data for the Tasman/Coral Sea region at (a) surface and (b) 300-m level. These residuals derive from locally weighted versions of the rms residual and the a priori noise [Eq. (6)]

A new four-dimensional ocean interpolation system based on locally weighted least squares fitting is presented. A loess filter is used to interpolate irregularly spaced data onto a uniform grid. This involves projecting the data onto quadratic functions of latitude and longitude while simultaneously fitting annual and semiannual harmonics by weighted least squares. The smoothness scale of the mapping method adapts to match the data density, thus producing gridded estimates with maximum resolution. The filter has a vertical dimension, such that the data on adjacent levels are included in the computation. This greatly reduces the effects of discontinuities in data distributions between adjacent levels, since the estimates at each level are no longer independent. The loess scheme has been further modified so that the weighting of data points is adjusted to allow for the influence of both bathymetry and land barriers. This allows the bathymetry to influence the mapped fields in a natural way, reduces leakage of structure between deep and shallow regions and produces far more realistic coastal gradients. The flexibility of the loess approach has allowed further adjustments to compensate for irregularities in spatial and temporal sampling. The mapping is shown to be statistically consistent with an objective measure of the a priori noise of the dataset. Departures of the mapped fields from independent surface temperature climatologies and mean vertical sections derived from withheld expendable bathythermograph (XBT) data are within error limits.

The calculation of mean fields from large sets of historical data is a major task in oceanographic data analysis. The resulting regularly gridded maps are a valuable reference tool for characterizing ocean regions, providing a background field for climate studies, and for validating model results. A clear example of this is given by the widespread adoption of the World Ocean Atlas (Levitus 1982) as a standard reference. However, the irregular sampling density and accuracy of ocean observations, and lack of statistical stationarity, generally makes the production of maps a difficult exercise. Furthermore, where coastal geometry and bathymetry are complex, many of the commonly used interpolation methods are not capable of obtaining realistic gridded fields (Brasseur et al. 1996; Dunn and Ridgway 2001, hereafter DR).

Many existing ocean climatologies are designed for resolving basinwide scales and hence are highly smoothed (Levitus 1982). Consequently, they are not capable of resolving boundary currents, frontal systems, eddy fields, and other permanent features with small spatial scales. New high-resolution observations from satellite platforms and output from general circulation models demonstrate that the spatial structure of the mean flow is influential down to the mesoscale thus, existing climatologies are clearly inadequate (Walker and Wilkin 1998; Roemmich and Sutton 1998; Webb 2000).

We demonstrate the components of the system within a case study covering the seas around the Australian continent. These waters contain many dynamically interesting and often unique features. In the Tasman Sea off eastern Australia, the East Australian Current (EAC) is a major western boundary current, with highly energetic mesoscale eddies associated with its poleward flow (Nilsson and Cresswell 1981; Mulhearn 1987). The Indonesian islands to the north act as a permeable barrier to flow from the Pacific to the Indian Oceans, thus playing a central role in the redistribution of mass and heat in the global system (Godfrey and Golding 1981). Furthermore, the very existence of the unique dynamics of the Leeuwin Current flowing poleward along the western Australian coast has only relatively recently been recognized (Cresswell and Golding 1980).

We describe procedures to assemble a complete in situ dataset for the region and the techniques that have been applied for estimating a gridded climatology. This climatology is entitled CSIRO (Commonwealth Scientific and Industrial Research Organisation) Atlas of Regional Seas (CARS). In section 2 we present the data used in the analysis, and detail the associated quality control methods. The loess methodology is described in section 3, including the topographic adjustments, and in section 4 we specify how the system is applied to the dataset. A description of sampling problems encountered and how they have been addressed is found in section 5. Finally the results are given in section 6. These include an analysis of the residuals, validation against independent data and an example of the mean fields.

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