Myself I am a chemical engineer working in agricultural research. We are working on aquaponics and also test vertical growbeds. Vertical growbeds underperform significantly unless you put expensive light on them.
Generating the electricity for light through PV uses about ten times the area compared to using direct sunlight. No way to counter that by using the full spectrum.
Not saying it's a good idea, just that it seems there are some offsetting concerns.
* 25% PV efficiency best case * 75% transport efficiency * 50% LED light efficiency best case
This amounts to a total area efficiency of 9.5%. So artificial light has a ten times worse area efficiency compared to using direct sunlight.
Transport energy consumption for the product on the other hand is often over estimated. Transporting amounts to something between 1% - 5% of the total energy cost of produce, depending on type and distance of course.
The vertical farm fallacy lies in the assumption that area is the scarce resource. This is simply not true if you move outside the city borders. Area within the city is very valuable and incredibly expensive. Even if you only pay a comparably low rent, lets say 2.5$/sqm (25ct/sqft), that amounts to ~30.000$ rent per year (for a 1000sqm indoor farm). You can buy farmland for this amount of money and forward from that the cost for area is not there any more.
In my (our faculty) opinion the sweet spot for urban farming ist in the peri urban part around the city. Area is still cheap, you can use direct sunlight with little or no artificial light and transportation cost and energy can be slashed by 90%.
Depending on the industry in that area there may even be some synergy potentials with residual heat and other materials (eg. compostable stuff from near by production).
Dutch Prof. P. Smeets proposes argoparks as a sustainable urban agriculture concept. We are in favour of that.
Edit: Clarified on indoor farm area.
Plants actually _do_ use the green light of the spectrum, just not as much, thus leaves appear in green color. How high would you estimate the efficiency gain by using a better spectrum? My guess would be that this gain would be below 50%. So area efficiency of artificial light would still be below 20%. And the calculation has been made "best case". 25% photovoltaic efficiency are lab figures for the very best cells possible. Installed base is lower still, monocrystallin cells 20 - 22 %, polycrystallin 15 - 20 %.
Theoretically, an infinite-junction solar cell can achieve up to 68.7% efficiency under non-concentrated sunlight. The best demonstrated so far is about half of that: https://www.sciencedaily.com/releases/2016/05/160517121811.h...
Efficiency under concentrated illumination is higher but concentrating designs require direct illumination and have their performance fall off a cliff under even partially cloudy conditions.
Spectral tuning of the light sources can make illumination more photosynthetically efficient, and so can evening out the illumination intensity. If you could get lights and multi-junction solar cells that operated at the theoretical limit it might be more efficient than natural sunlight growing, but that's a tall order to achieve in practice. To achieve a net environmental benefit not only does it have to be more efficient than single-story natural illuminated structures, it has to be enough more efficient to pay back the environmental costs of manufacturing the extra equipment required up-front in the vertical case.
Or is cooling horizontal greenhouses easy enough, even in deserts?
Artificial illumination farming of course does make sense for crewed deep space missions because there's not any other option. That's actually how I first started thinking about this problem -- "what if you wanted to feed a crewed nuclear powered outpost in orbit around Neptune?" It turns out that it takes a lot of electricity to feed people that way because our food crops suck at turning light-energy into human-edible energy. Having a rough idea of the enormous electricity expenditures, I started doing double-takes when vertical farm enthusiasm started spreading a few years ago.
[1] http://www.abc.net.au/news/2016-10-01/sundrop-farms-opens-so...
What if we are talking theoretical limits instead of what is practical today?
Couldn't capturing the full spectrum of sunlight (e.g. through multi-junction cells) and then emitting an optimized spectrum for plants to absorb boost efficiency?
Photosynthesis efficiency is also affected by temperature. So at least in hot climates having the plants indoors while capturing the sunlight outside could yield increased efficiency when compared to fields exposed to direct sunlight.