The principle that the net energy delivered by a tidal pool can be increased by pumping extra water into the pool at high tide or by pumping extra water out of the pool at low tide is well known in the industry. On paper, pumping can potentially enhance the net power delivered by a factor of about four. However, pumping seems generally to be viewed as a minor optional extra, delivering only a modest power enhancement. Two possible reasons why pumping is not emphasized in tidal designs are that increasing the vertical water range introduces additional costs (for example, higher walls), and that alternating between pumping and generating worsens the intermittency-of-supply problem from which simple tide pools suffer.
The intermittency-of-supply problem also causes problems for wind. How can we switch to wind power if the wind might stop blowing for two days at a time? Storage systems are an economical way to smooth out the fluctuations of wind power on a time-scale of minutes, but what about hours and days?
Perhaps a shift of perspective on tidal lagoons is helpful. I sketch designs for a large pumped-storage system located at sea-level with a dual purpose: first, it can turn power that is poorly matched to demand into high-value demand-following power; and second, it can simultaneously serve as a tidal power station. Large designs with a capacity of several gigawatts are the most economical.