Wave energy charts as voyage planning tools

Pilot charts are key tools for anyone planning an offshore voyage. These charts have been developed through the analysis of weather data gathered over hundreds of years. They graphically present historical climatological data in a sensible and understandable fashion. For each of the world’s ocean basins, a series of 12 monthly charts displays information about winds, currents, wave heights, atmospheric pressure, ice sightings and more. The prudent mariner uses all means to plan a safe voyage and pilot charts provide one of these fundamental means.
    Recent work by a scientist in Canada has produced a thoroughly modern look at one of the most important characteristics of the ocean in a manner analogous to the familiar pilot chart. This work, though motivated by the current interest in renewable energy resources, finds application in voyaging as well. This article describes the new work and attempts to place it in a context useful to voyagers.

Background
Most voyagers are familiar to some extent with numerical wind-wave prediction models. The ubiquitous GRIB files used by many voyagers are selections of data produced by the Global Forecast System (GFS) weather model of the global climate. A model is a computer program which, when initialized with a starting set of observations or measurements, attempts to predict the future. In the case of our GFS example, this includes certain interesting weather features such as wind speed and direction. It makes these predictions at some interval — say for every three hours in the future — and for each of the points in its grid. The interested user requests data for a certain region, and a data file is delivered to the user — by radio, satellite, or Internet — that can then be displayed as scaled wind barbs overlaid on a navigation chart. Thus one set of wind predictions is obtained for a particular segment of a voyage.
    The U.S. National Oceanic and Atmospheric Administration (NOAA) has developed a numerical prediction program for wave climate, the NOAA WAVEWATCH III (NWW3) model. From its origins in 1997, the model is now in its third generation. In addition to prediction runs, NWW3 has also been used to look back in time by using historical data as initial conditions producing outputs called “hindcasts.” These hindcasts have been used to validate and improve the model’s performance through comparison with actual observed data from buoys, land stations, satellites, etc.
    All models are imperfect representations, of course, and NWW3 has its limitations as well. This model works best when the wave energy being considered is unaffected by shallow water; thus NWW3 finds its best utility away from land. Additionally, because of its spatial resolution, it may not be effective at predicting conditions during (spatially) small events such as hurricanes, and again the geographic complexity of coastlines limits its utility there. Also, NWW3 does not currently provide predictions for semi-enclosed areas such as the Mediterranean Sea or the Red Sea — two areas of interest to voyagers.
    That being said however, NWW3 has been shown to be an effective predictor in the world’s oceans from 77° North to 77° South latitude (see http://polar.ncep.noaa.gov/waves/validation.html). It operates on 45,216 points on a 1.25° x 1° (longitude x latitude) grid and produces predictions for significant wave height, peak wave period, primary wave direction, and 10m wind velocities.
    The outputs of the NWW3 model are available on the Internet through NOAA’s Web site (http://polar.ncep.noaa.gov/waves/main_int.html) and through third parties who repackage and distribute the model data (for example, Buoyweather, Weather Underground, etc.).  Anyone with Internet access can freely download NWW3 predictions in graphical, tabular, or text formats.

A global resource

In considering the world’s oceans as sources of renewable energy, Dr. Andrew Cornett of the National Research Council of Canada, recognized the valuable potential in the historical NWW3 data. He gathered 10 years worth of hindcasts, covering the period from February 1997 to January 2006. Each dataset included the NWW3 outputs at three-hour intervals for 10 years. He then used this data to calculate additional information about each grid point: wave energy, wind speed, and wind power density.
    With this wealth of information at hand, Dr. Cornett produced a series of charts that graphically depict statistical global wave energy on a month-by-month basis.
    In addition to the monthly energy charts, he also analyzed the data for variability at the monthly and seasonal level. This information too has been depicted graphically. One further product is a global map of maximum annual significant wave heights.
    These wave power predictions were then compared with actual historical observations at buoys in the western North Atlantic and the eastern North Pacific to validate the work. These comparisons showed good correlation of average annual wave power and its monthly variation.
    The utility of these charts in analyzing potential installations of wave energy projects is enormous. Engineers can compare locations based on total available energy and on the expected month-to-month and season-to-season variability of available energy.

Application to voyaging
In a manner perfectly analogous to the application of pilot charts, voyagers can consult these wave energy prediction charts in planning offshore voyages. Using the appropriate monthly chart and tracing the intended route on the chart, one is graphically presented with the climatologically expected wave conditions. Obviously, the higher the wave energy, the more dynamic the sea state. Voyagers can tweak times and routes for more favorable conditions, if desired.
    Wave energy is a single number that represents a complex natural condition. From the voyager’s point of view, there are two important concepts to keep in mind. First, wave energy in deep water varies proportionally with the period of the wave; the longer the period, the greater the energy. Second — and more significant to sailors — the wave energy varies proportionally with the square of the wave height. In other words, all else being equal, a 4-foot wave carries four times the energy of a 2-foot wave.
    Another use of the charts is in considering seasonal variability. For example, a glance at the Seasonal Variation Index for the Atlantic shows much higher variability in the North Atlantic than in the South Atlantic. This suggests that while there may be a preferred season or month for doing a North Atlantic crossing, by contrast a South Atlantic crossing is likely to encounter similar conditions regardless of season.
    Finally, considering the Maximum Significant Wave Height chart, one is again reassured that the tropical crossing is a ‘milk run’ compared to the higher latitudes.
    The skeptic may comment that this has already been covered in the pilot charts, and perhaps that’s true. However the data is presented in a novel and easily grasped fashion — including seasonal variability and maximum wave heights; they are convenient for voyage planning and validated against actual long-term observations. Most voyagers agree that when it comes to route planning and weather information, more is better.

Model convergence
As voyagers become more familiar with numerical prediction models, the concept of ‘convergence’ is encountered. Generally speaking, convergence occurs when multiple, independent models show agreement in their predictions. This agreement serves to reinforce the probability that the predictions will be accurate.
    One key aspect of convergence is that the models must be independent. It does little good to run a model twice and say, “Hey! The outputs agree!” This isn’t convergence. This is redundancy.
    Each run of the NWW3 model is initialized with the outputs of the GFS weather prediction model; the same GFS model that is also the source of the GRIB file data that voyagers typically download. Since the NWW3 outputs depend on the GFS inputs, they generally “agree” on their predictions of wind speed and direction.
    This is a clear case of redundancy — seeing the same data twice — and not convergence. Don’t be fooled by this apparent agreement.

Wave height
Anyone who has spent time at sea — or at the beach — knows that no two waves are alike. They have different heights, arrive with different intervals between adjacent waves, and seem to come from different directions. Real waves are very complex.
    To be truly useful, the complex output of a dynamic wave model like NWW3 has to be boiled down to useable numbers that people can relate to. The most important number from a voyager’s point of view is the significant wave height.
    The significant wave height is defined as the average height of the largest one-third of the waves. Its basis comes from the experience of trained observers: we tend to see the larger waves and not the smaller ones, and we mentally average them over time. So when a forecast derived from NWW3 is presented, the predicted heights are the significant wave heights.
    It is very important to remember that the waves are being treated statistically as a Rayleigh distribution (see http://en.wikipedia.org/wiki/Rayleigh_distribution for details) and that in fact, one out of 10 waves will be higher than the stated prediction. One out of 100 will be larger than 1.5 times the prediction, and one out of 1,000 will be larger than 1.8 times the predicted height. Individual waves may be up to twice the significant wave height.
    To consider a real world example, suppose you wanted to sail from the Virgin Islands to Grenada, a close reach in most cases. It’s winter and the wind has been blowing a steady 20 knots for a couple days. The forecast is MOTS.
    First, at 20 knots a fully developed sea occurs in about 45 hours. Since it’s been blowing and will keep blowing, you can expect a significant wave height of 8 feet and an average period of about six seconds. With a period of six seconds, that’s 10 waves per minute, 100 waves every 10 minutes, and 1,000 waves every one hour and forty minutes. Every 10 minutes you can expect a 12-foot wave and once every couple hours you’ll see a 16 footer. I’d hang in the Virgins a little longer.

Acknowledgements
Special thanks to Dr. Andrew Cornett at the Canadian Hydraulics Centre of the National Research Council of Canada for permission to abstract from his work and for the monthly wave energy charts produced specifically for this article. Dr. Cornett’s work was previously published in The Proceedings of the 18th (2008) International Offshore and Polar Engineering Conference. The paper may be downloaded from http://www.isope.org.

By Ocean Navigator