|
|
| Fig. 1: Storm waves on the coast of Santa Cruz. (Source: Wikimedia Commons). |
Ocean waves are seemingly an endless source of energy, forming from geophysical phenomena that are not soon to run out. While an apparent solution to the increasingly strained supply of nonrenewable energy sources on Earth, it is difficult to effectively harness the power of ocean waves across a large enough coastline to have a dramatic effect on the distribution of global energy sources. Moreover, the power supplied to coastlines turns out to be much lower than what is required to support nearby cities, let alone landlocked areas. This work explores the potential for harnessing ocean waves along the California coastline. This is done by calculating the total power per meter delivered by ocean waves, which can be extrapolated to within 3 orders of magnitude to other coastlines across the world. This number is integrated over the length of the California coastline to determine the maximum possible energy that could be captured. The price and efficiency of emerging ocean wave technologies is compared to those of nonrenewable sources in order to provide context as to the limits of this apparently green source of energy.
The power per meter delivered to the California coastline by ocean waves can be calculated from the average wave height h ≃ 1.7 m, the speed of the incoming waves v ≃ 1-5 m/s, the density of water ρ = 1000 kg/m3, and the acceleration due to gravity g = 9.8 m/sec2 by [1]
| dP dx |
= | ½ρgvh2 |
| = | ½ × 1000 kg m-3 × 9.8 m sec-2 × 2.5 m sec-1 × (1.68 m)2 | |
| = | 3.5 × 104 Watts m-1 |
The above is likely an overestimate, as the velocity and height of waves are susceptible to great variability especially in recent years. For example, the average height of waves using the mean annual significant wave heights from 1948-1998 from Adams et al. was used in this calculation. [1] However, a study of the effect of climate change along the California coast found that the distribution of wave height depends heavily on location (ie. sea-level and, therefore, wave height fluctuations are much greater in north California). Moreover, wave heights are extremely sensitive to surge events, which in and of themselves are hugely variable. For example, a non-tidal event that draws the tide up by 17 cm corresponds to a peak wave height of about 4 m, but an event that results in a 2 cm increase has distribution centered at a peak height of around 2 m. [2] It should be noted also that both of these studies use only "significant" waves in their analysis, as the works focus on the trends of increasing extreme activity. For the purpose of this work, we would like to consider all activity, including insignificant waves that were not detected or not extreme enough to be reported in Adams et al. and Cayan et al.. [1,2] Accordingly, the above calculation gives an upper limit to the total potential power of around 62 GW that could ideally be harnessed off of California's coast (using the fact that California's coastline covers 1760 km. [3]
While much effort is being dedicated to creating renewable energy sources using the power of ocean waves, it is a science still very much in its infancy and will likely remain so. Any tool used to extract energy from water comes with a high installment and maintenance price tag relative to the maximum potential energy that could be harvested. Currently, the typical operation and maintenance cost of European wave energy converters (WEC) is around 21-37 $/MWh, comparable to that of US coal plants, which can range anywhere from 20-40 $/MWh. [4,5]
Based on the above maintenance costs and the fact that WECs are relatively efficient (see Table 9a in Astariz et al.), it is not obvious why wave energy is not more widely accepted as the next generation of renewable energy. [4] This can be encapsulated by details about the technology. First, many startups in this area emphasize efficiency over actual power output. This is a result of what was found in our calculation of the maximum possible power to be harnessed off the coast of California: ocean waves do not reliably generate enough power to build a competitive energy industry on them. The scale at which line magnets, point sources, and others, would have to be built on top of waves, on the ocean floor and in between, would need to be enormous. Some technologies take advantage of waves breaking while others would be situated further out from the coast. Considering the case of California once again, even with maximally built-in infrastructure and ideally powerful waves year-round, our power output of around 62 GW pales in comparison to the average yearly per capita consumption in California of around 478 GW in 2021. [6]
A second oft-unconsidered problem with fully implementing wave energy technology is the environmental effects it will have. Modern discussion of energy consumption is centered around CO2 emissions, often oversimplifying the negative effects of certain technologies on the environment. While wave technology is nowhere near the scale of harm, its effect on ocean ecosystems should be carefully researched. Kilometers of floating line magnets, or farms of ocean floor point sources are certain to, at the very least, disrupt local and potentially migratory wildlife. The effect is difficult to predict, as it is often the case that the needs of ecosystems are only understood once they are interrupted. Beyond the issue of wildlife, there would also likely to be great social opposition to placing what would appear to be thousands of floating orange rafts on a beautiful coastal view. (See Fig. 1.)
This work has been a case study on the maximum power output of ocean waves that reach the California shoreline. It has been found that the incoming power from the Pacific Ocean is highly insufficient to have a real impact on the energy sector in California alone, which explains the lack of global interest in this area as a whole. Technologies seeking to harness the energy of waves are often designed to be near the shore for maintenance and struggle in areas of efficiency and cost with respect to the total energy available. While WEC technology is promising to reduce small-scale emissions, the potential environmental impact resulting from its implementation should be preemptively studied.
© Maya Beleznay. The author warrants that the work is the author's own and that Stanford University provided no input other than typesetting and referencing guidelines. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.
[1] P. N. Adams, D. L. Inman, and N. E. Graham, "Southern California Deep-Water Wave Climate: Characterization and Application to Coastal Processes," J. Coast. Res. 24, 1022 (2008).
[2] D. R. Cayan et al., "Climate Change Projections of Sea Level Extremes Along the California coast," Clim. Change 87, 57 (2008).
[3] G. B. Griggs, L. Davar, and B. G. Reguero, "Documenting a Century of Coastline Change along Central California and Associated Challenges: From the Qualitative to the Quantitative," Water 11, 2648 (2019).
[4] S. Astariz and G. Iglesias, "The Economics of Wave Energy: A Review," Renew. Sustain. Energy Rev. 45, 397 (2015).
[5] "Generating Unit Annual Capital and Life Extension Costs Analysis," U.S. Energy Information Administration, SL-014201, May 2018.
[6] "State Energy Consumption Estimates 1960 Through 2021," US Energy Information Administration, DOE/EIA-0214(2021), June 2023.
