A big winter storm is brewing in the North Atlantic. Meteorologists on TV exclaim that there is a developing storm system just south of Iceland, and that the current position of the polar front will most likely steer the low called “Gertrud” towards northern Norway. While a TV correspondent in Reykjavik reports of the most recent storm damage, people in coastal communities of Norway and Scotland are getting alarmed: If the storm moves to northern Norway, the entire coast will be affected along its way before Gertrud hits land. While mountain people tie down everything that’s loose, harbor towns are not only concerned about the wind – it is the rising water level and large ocean waves that’s causing them headaches. Fishermen started to secure their boats and managers on offshore rigs consider to evacuate their platforms. Now everyone wants to know more detail: how much water is going to pile up, and how big is the largest wave going to be?
The path of low pressure Gertrud is predicted by computer simulations that forecast the state of the atmosphere – we get a prediction of how much wind to expect and where it is going to rain, based on physical laws describing atmospheric flow. But this atmosphere model isn’t telling us what the ocean is doing, even though storm surges and waves are ultimately caused by wind blowing over the ocean’s surface. In addition to the weather prediction model, an ocean model is used to forecast ocean currents and sea level, in the same way as the atmosphere model forecasts wind and air pressure – just with water instead of air. Both models are connected: The atmosphere model tells the ocean model how the wind is blowing. If wind is blowing towards land for a long time, water will pile up at the coast and and coastal communities know whether it will be necessary to secure dikes with sandbags or not.
For everyone offshore, a prediction of wave height is crucial for safety. Wave information are also for needed search and rescue drift forecasts (Study on waves and forecasts). Wave forecasts (yr.no, click on location on map) are different from atmosphere or ocean forecasts. Although they are located just in between, they aren’t included in either atmosphere or ocean models because waves are much smaller than features like low pressure systems or oceanic current whirls. More than that: waves are much too small and too many to forecast every single one of them – and luckily we don’t really care how high the exact wave is that strikes land tomorrow at 18:42. Rather, we need to know some statistical properties of all waves: How high are the biggest ones, how often do they strike and how steep are they? That is, we need a statistical wave model. Other than atmosphere and ocean models, which forecasts the 3-dimensional flow of air or water, statistical wave models predict the growth and decay of wave energy.
Every wave contains energy. And while its wavelength or height can change while a wave is moving over shallow ground, its energy is conserved. We also know from physics how wave energy grows if the wind pushes a wave forward, and how energy disappears into friction if a wave breaks. This enables us to formulate a wave prediction model based on wave energy. Now we rarely see only one kind of wave when we’re out on sea. The ocean surface consists of a mix of waves: Long waves, short waves, northerly and north-westerly waves. And an bunch in between. Wind feeds energy to the small waves, blowing against the small ripples and pushing them forward. Some of these ripples will interact and form larger ripples, and even larger ones after many of such encounters. After an hour or two, we’re not talking ripples any more but meter-high waves called wind sea, still with ripples on top that continue to feed the larger waves.
When making a wave forecast with a statistical wave model, we formulate the growth and decay of wave components in terms of an energy spectrum: each wave component with a certain wave length and direction has energy that evolves with time. In terms of the wave spectrum, energy from the wind enters the spectrum at short wavelengths. Non-linear interactions between wave components then transfer energy to longer wavelengths, meaning that swell is created. Breaking waves release energy from the wave spectrum, creating ocean turbulence and plunging surf break on beaches.
Surface gravity waves are dispersive, meaning that the longer waves actually move faster than the short ones. They even move away from the storm that has caused them, escaping it and hit the land before the storm does. These waves, often more than 50 meter long, are now called swell. Swell can travel thousands of kilometers across oceans, and break on a beach where people were never concerned about the storm that caused these waves.
Three days after Gertrud has passed Iceland, the low pressure strikes land 400 km further south than predicted by the atmosphere model. However, wave heights in the North Sea and on the shore-break at Stavanger were well predicted. Waves are so predictable because they travel for several days before reaching the shore: Tomorrows wave height depends on yesterdays wind. And even if the exact course of a low pressure center is difficult to predict, wind speed and direction in an area away from the low pressure are still quite right. Consider this example: On a Sunday, a professional wave surfer might just buy her plane ticket to some beach on the other side of the globe for Tuesday because some really good swell is predicted for that exact beach on Friday. She knows her swell is well predictable, the wave energy released in the surf break was creating days before and far away.