Why Do Surf Heights in Hawaii Vary So Greatly From Place to Place and Moment to Moment?

This is an educational outreach product intended for a general audience. Feedback is welcome.
Tagging numbers to surf heights for a given day along a shoreline facing a similar direction is a daunting task because the heights vary so much from place to place and in time. This web page explains why surf heights vary spatially and temporally. Using this information, explicit definitions are given to surf heights as used in forecasts.

Oahu (courtesy of Univ. of Hawaii Coastal Geology Group)

Waves 101 Background Information

One must first understand the basic definitions of wave characteristics and the different words used to describe the life cycle of wind-generated water waves.

Wave height is the vertical distance from trough to crest.
Wave length is the horizontal distance from trough to trough or crest to crest.
Wave period is the time it takes for one full wave length to pass a fixed point.
Seas are waves in the wind generation zone. Seas have a confused nature since they are made of of waves of varying wave periods (lengths).
Swell are waves that have left the generation zone. Waves travel at a speed that increases as the wave period (length) increases. So the longer wave periods race out of the generation area ahead of the shorter periods, a phenomena called dispersion. Swell have a more uniform shape since large areas have similar wave periods (lengths). The wave front, or face of the leading edge of the wave horizontally along the water surface, can stretch horizon to horizon.
- Deep water waves refer to seas or swell in water depths greater than half the wave length.
- Shallow water waves refer to seas or swell in water depths less than half the wave length.
Surf are breaking waves due to interaction with the water basin bottom when the wave height to depth ratio is roughly 0.8; for example, surf of 8 feet breaks in depths of around 10 feet and surf of 40 feet breaks in depths of around 50 feet. The higher the surf, the deeper the water in which it breaks. This assumes a gradual sea floor drop off, as opposed to abrupt depth changes, such as Teahupoo in Tahiti, where the ratio is higher (depth shallower at breaking).

Spatial Variability

Surf heights vary from location to location, especially in Hawaii where coasts face at various orientations, the sea floor shape is complex, and upstream islands cause shadowing, dependent upon incident swell direction and period. Transformation of wave height from deep to shallow water waves, then on to breakers, is caused by various physical phenomena. The most important are:

Friction. Waves feel the bottom due to circular motion of water particles that are set up as waves travel. In shallow water, these orbits drag on the basin bed, which reduces the wave height and speed. The wider the shallow coastal shelf, the more reduction in wave height before a wave reaches the breaking point.
Shoaling is the shallowing of water. Wave speed decreases as the water depth decreases. In turn the wave length compresses for trains of waves as the adjacent waves in the deeper water catch up to slower waves in shallower water. The bunching of waves increases the wave height, reaching the maximum height just before breaking.
Refraction. If the water depth along a given wave front varies, the wave front will bend toward the shallowest areas due to refraction. This occurs as soon as the wave feels the bottom. A difference in water depth along a wave front can occur if
- The direction of travel of the wave front is at an angle to the depth contours.
- The coastal sea bed has ridges and valleys, as typical of most areas in Hawaii. The energy along the wave front converges to the shallowest location, where wave height becomes the highest. Wave height can be greatly magnified at the moment of breaking due to the combined effects of shoaling and refraction . In zones of high refraction, adjacent areas can have little or no breakers.
- Refraction is most notable near the surf zone. However, if the waves feel the bottom further offshore, there can be redirection of swell energy, sending more energy to some surf zones and less to others. This aspect is also an important reason why surf can vary from one surf area to another.

There are other factors that affect surf height such as localized currents and winds, and wave-wave interaction (e.g. backwash, which happens when a wave reflected off the shore heads seaward and meets an incoming breaker, or double-ups, which means crests of two waves of differing wave period or direction arrive simultaneously at the same location). These are not considered in this review.
Scientists have models, such as the Simulating Waves Nearshore (SWAN), that can help visualize the primary physical actions of shoaling and refraction. As the surf grows, the location of the breakers occurs in deeper water, shifting to the outer reefs for the north shore of Oahu. Waimea Bay, which has some of the largest waves closest to shore, is roughly 30% lower than in zones of maximum refraction on outer reefs, such as Outer Log Cabins.
Surf height can also vary along the front of any single wave. In zones of high refraction, the difference between the peak face and wave shoulder is more exaggerated.

Temporal Variability

At a fixed surf zone location, wave heights vary with time. For an individual wave, the height is greatest at the moment of maximum cresting just before the top portion of the wave falls forward, excluding wave heights associated with backwash or double-ups. Over a period of time, the heights of waves follow a Rayleigh distribution. Thus the most numerous wave heights are less than the average wave height. In oceanography, statistics are used to define frequency-of-occurrence parameters related to waves:

Significant Wave Height, or H1/3 is the average of the highest one-third of all wave heights over a period of time. This is the parameter most often used to describe deep water seas or swell. It has been shown that an experienced observer on a ship watching the seas will estimate the heights close to the H1/3. Waves typically arrive in groups of similar size with a rough estimate of three waves per group. Groups of waves with H1/3 heights arrive on average every 3 +/- 2 minutes.
H1/10 is the average of the highest one-tenth of waves. Groups of waves with H1/10 heights arrival on average every 9 +/- 6 minutes.
H1/100 is the average of the one percent highest waves. Groups of such waves arrive roughly at 75 +/- 30 minute intervals, and are referred to by surfers as sneaker or clean-up sets. Since larger waves break in deeper water, and the water basin depth increases with distance from shore, H1/100 waves break further out, most often catching the surfers on the shoreward side of the falling crest; hence the name clean-up set. Though infrequent, H1/100 waves are common enough to deserve attention.

Waimea Bay (photo: Kimbal Milikan, Dept. of

Oceanography, University of Hawaii)
Given any single one of these parameters, one can calculate the others since they differ by a multiplicative constant as defined by the Rayleigh Distribution.
An application of the Rayleigh Distribution can be seen in the way visual surf observations are made. Reports emphasize the smaller percent of larger waves and are given in a range which estimates the heights of commonly arriving sets with the arrival frequency decreasing as the value within the range increases. Nominally, these observations represent the H1/3 to H1/10, occasionally H1/100 heights.
The amount of wave energy arriving along a shore also has longer scale variations on the order of 30 minutes to a few hours. These groups of groups are referred to as wave envelopes. The number of waves per set and the spacing between wave envelopes is related to the width and proximity of the wave generating zone, with wider and closer sources making more frequent arrivals.

NOAA NWS/NESDIS Collaborative Surf Forecast Table

The Honolulu Forecast Office of the NOAA National Weather Service (NWS), in collaboration with the NOAA National Environmental Satellite and Information Service (NESDIS) Hawaii/Pacific Islands Liaison Office produces a 5-day nearshore swell, surf, and wind forecast table and discussion.

Background

Extensive research was undertaken to seek the most accurate surf forecasts, based on historical north shore Oahu visual surf observations and buoy data. The daily surf reports are made by experienced observers of the H1/3 to H1/10 breakers during the most active period of the daylight hours in the zones of highest refraction, such as Sunset Beach. For days when outer reefs have the zones of highest refraction, Waimea Bay is used as the observing location since breakers are closer to shore and surfers serve as height benchmarks. The H1/10 records were assembled by Mr. Larry Goddard (1968-1987) and Mr. Patrick Caldwell (1987-present). Since historic reports have been made in the colloquial Hawaii scale, the first task was to learn if these observations were valid. The study showed the observations were consistent in time. The next tasks were to translate the observations from Hawaii scale to trough-to-crest heights (peak face) and to develop an empirical formula that estimates surf heights based on deep water swell. It was designed by fitting north shore Oahu H1/10 visually observed surf heights to the H1/3 and dominant wave period as measured by a buoy 3 miles offshore of Waimea Bay. In Hawaii, all coastal regions have relatively narrow shelves, steep sea bed slopes, and zones of high refraction; thus, the empirical scheme is applicable to other coasts. Additional research has been completed to understand north shore Oahu wave-induced coastal flooding potential based on historic records of coinciding high surf and tides.

Collaborative Table Surf Height Definition

Surf height refers to peak face. The output of the empirical formula was designed to match the observing scheme, so visual reports can be used as validation.

Temporally, the collaborative table gives expected surf heights for daylight hours during the active spells of highest waves (wave envelopes) as a range defined as H1/3 to H1/10. The H1/100 can be calculated as 1.32 times H1/10. Because of the course resolution in observing waves, the empirical output is rounded up to the nearest even integer, erring high for safety.
Spatially, the forecast heights refer to surf in the zones of high refraction for the given incident deep water swell H1/3, direction, and period. During extra-large or higher surf on the north shore of Oahu, this refers to outer reefs, while breakers near shore are at least 30% lower.

This scheme emphasizes the smaller percent of larger waves, which are the ones that pose the greatest risk to safety. Even on the largest days of surf, breakers can be low during lulls and in the divergent wave energy regions between zones of high refraction. This elusive nature of surf height variability gives false security to novices, and makes surf the number one weather-related killer in Hawaii.

Questions or comments: Mr. Patrick Caldwell, patrick.caldwell@noaa.gov

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