The size and intensity of waves are dependent on many factors. Some can be measured and predicted. Others are affected by shifting weather factors. In the case of tsunami like waves, events can align in once in a lifetime combinations.
Measuring waves can be described in scientific or surfing terms. In surfing, there are three popular ways to measure wave height.
The first is called the Bascom Method. Popular in California, it was created by Willard Newell Bascom. He was a pioneer oceanographer and ocean treasure hunter. He proposed that waves could be measured by standing on the beach and aligning your eyes with the wave crest and horizon. The wave is measured from the crest point to the average sea level. In boating terms this is also called the wave height–the distance from the trough to the crest. Some surfers feel the result is an overestimation.
The second method originated in Hawaii–aptly named the Hawaiian Method. The waves are measured from the back, which is just after the crest, as the wave begins to curl down. This measurement is usually about 1/2 the size of the Bascom results. Using this format, can be difficult because small dense waves are hard to gauge. In nautical terms this is called Wave Amplitude is the distance top where the water is undisturbed to the trough–the bottom undisturbed water surface.
The final, more balanced approach is based on an the actual area ridden by a surfer. This is called the Surfable Wave Method. Right when the wave begins to barrel, you measure. This matches well with the Hawaiian Method.
Of course, measuring the height of a wave is more important to surfers who are not riding waist high waves. Once waves are neck high or higher, the competition for catching and riding the perfect wave becomes greater and the bragging rights are more serious. The use of the Bascom method in California leads the surfing world to view their claims to nuclear rides to be questionable as this way of measuring tends to inflate the height of the wave.
Expert surfers who travel to find the most challenging conditions take wave height seriously. They are not going to be showing up for 10 or 15 foot waves, unless they are there for the beach, friends, or happen to be traveling through.