Yes in principle …using photovoltaic energy

There is no reason why electrolysis could not be used as you suggest. The real issue becomes the efficiency of this process… how large of a solar collector is needed to generate the power to make significant quantities of oxygen and hydrogen? This would require some extensive chemical engineering calculations.

However, to break the O-H bond of water, its rather expensive energetically. Why do electrolysis when you could just effect the phase change. That is use distillation?

Boiling sea water requires less energy than splitting the O-H bond

Another possibility would be to use photovoltaic energy to distill sea water. That is, boil sea water and capture and condense the fresh water. Then the issue becomes getting the fresh water to where you want it.

You could do this on land with solar collectors. Pump sea water to a facility and then use solar power to boil the sea water and condense the fresh water. Again the issue is the efficiency and power available given a size of the solar energy collection apparatus… once you have the power from that, then its easy to determine how much sea water can be boiled per unit time to make the fresh water that is desired. Is this rate of pure water generation enough to make it competitive with other methods of fresh water production?

If you want 1000 kg (one ton) of fresh water per minute --> that is one ton per minute or 16.7 kg/s. So you need to condense 16.7 kg of boiling sea water per second. That is, you need to add sufficient energy to 16.7 kg of sea water each second to get the sea water to a flash.

Since the enthalpy of vaporization of sea water is roughly 40,000 Joules / 0.018 kg = 2.2 MJ/kg, that is 2.2 Megajoules per kg. This is the amount of energy needed to boil 1 kg of sea water(approximately)

One would also have to add in the heat required to go from 20 C to 100 C… that is another 50%.

So allowing for that ONE NEEDS roughly 3 MJ/kg per second from the power source to make a ton of fresh water per minute.

So you now need to see what size photovolatic system is needed to generate roughly 3 MJ per second, or 3 MW (3 Mega Watts).

You need to go to the literature and read about photovoltaic systems… you need one that can deliver > 3MW

To allow for heat loss and other irreversibilities you probably need a PhVolt. generator of say 10 MW.

So, study this and see what size collection areas are needed given solar insolation in Southern California. Then send me your musing at spera@geol.ucsb.edu

This proposal is not technologically impossible, but is almost certainly economically inviable. Using electricity to split water into oxygen and hydrogen (a process called electrolysis) can be performed with electricity produced by any means, provided the voltage is high enough (~1.23 V for perfect conditions, but higher in practice because of losses). While a single solar cell does not produce a large enough voltage, a solar panel has many cells connected in series to increase the output voltage to 12+ V. So a solar panel could be used to provide the electricity for electrolysis. [Side note: the rate at which water is split will depend on the current supplied for electrolysis, which depends on the number of solar panels, their efficiency, side reactions during splitting, etc.]

Both hydrogen and oxygen can be transported via pipelines much like natural gas (though, like natural gas, they would likely be compressed and liquefied to improve efficiency, so technically the gases would not be transported to the desert). Realize, however, that oxygen is abundant in the atmosphere and could simply be taken up at the end site; capturing and transporting the O₂ from electrolysis would only increase costs. Once at the final destination (a water production plant in this scenario), hydrogen and oxygen could easily be reacted to produce water. The amount of hydrogen needed to produce a given quantity of water can be calculated from the molecular weights of the various species (see here for an example in reverse). The water would then need to be transported from the desert to locations which need water, which would further increase costs of this endeavor. While I did not find specific numbers for the costs associated with each of these steps, the existence of other methods of producing clean water from sea water indicates that electrolysis is not an efficient approach to producing potable water.

There are several other methods of purifying undrinkable water (such as sea water) to make it suitable for consumption as well.

Although the scheme proposed in the question is not viable for water production, the production of hydrogen for fuel is an active area of research. This is due to interest in hydrogen as an alternative to fossil fuels and as a way to store energy from intermittent renewable sources (i.e., solar and wind). In fact, there is an interesting project to use nearly the same approach as in this question to do just that: a floating rig uses solar cells to split water and captures the hydrogen, effectively storing the energy from the sun for a time or place without sunlight. Hydrogen is currently used for (backup) energy production and some vehicles. In these cases, the water is essentially a waste product. If drought conditions became extreme enough, storing and distributing this water may become economically viable.

The scheme that you are describing is a variant of what is called desalinization, and yes, people do it. The way that it is usually practiced is to have the desalinization plant be on the coast instead of on a barge. The problem with your idea is that evaporating seawater from sunlight uses the same energy that the sun naturally shines into the ocean, which means that the amount of water you get from this is roughly comparable as what you get from ordinary rainfall.

You could use more area to collect solar energy and use it to evaporate only a smaller amount of water, but that would require more solar panels. I suspect that sooner or later something like this will indeed be done, unless nuclear fission becomes more accepted as a means of deriving power in the future.