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The numbers don't add up, with current technology, for a sustainable system.

Plants are the most efficient way to convert renewable energy into food, but "the most efficient" doesn't mean "efficient". The maximum power input from solar energy is around 1kW/m^2. Plants convert that energy into food with an efficiency of at best about 3%, and that assumes the entire plant is edible. That means plants are converting a maximum of 30W/m^2 - when the sun is shining and there are no clouds. Averaged over a year, the day length is 12 hours out of 24 which reduces the average "edible energy" to 15W/m^2. Factor in the influence of weather, and any other inefficiencies, and you might get a number like 5W/m^2 averaged over a year.

A sedentary human needs around 100W of power for survival, and more to actually "do stuff." So one human needs at least 20 square meters of "plant growing space" to stay alive. And if you try to feed yourself entirely from a 5-meter-square vegetable patch, you will soon discover that is a rather optimistic estimate!

The population density for New York City as a whole is one human per 100 square meters, though in the densest areas (e.g. Manhattan) that is reduced to one human per 30 square meters.

So the bottom line is that literally every available space in the entire city would have to be devoted to high-intensity farming, for self-sufficiency. No space available for basic infrastructure like roads - every available space would be needed for food production.

I'd probably lean towards something like aquaponics, a combination of hydroponic (or possibly aeroponic) plant farming with fish or crustacean aquaculture to give you a bit of protein and the plants a bit of fertiliser (by way of the fish poop).

When you're not tied to a conventional growth substrate, you can put your farms up all over the place, such as on the sides and tops of skyscrapers. It'll probably do the microclimate of the city of a world of good, too. The big problem at the moment is growing decent crops... leafy salads are easy, but what you really want is to do is fruits and vegetables and grains and so on. Clearing this technical hurdle doesn't obviously require super future ultratech, so it seems like it fits your needs.

I seem to recall that some existing scifi settings use this sort of setup... I think Gibson's sprawl trilogy references this way of farming, but I'm sure it appears elsewhere too.

You might consider recycling human waste to use as fertiliser but humans have an irritating tendency to use an awful lot of potentially quite hazardous pharmaceuticals and also tend to excrete quite a lot of unpleasant pathogens as well. Treating humanure so that it is safe without also removing its useful properties might be quite challenging. Have a look at the issues with milorganite, as well... it contains concerning levels of heavy metals so it is great for fertilising non-food plants but not so good if you're going to eat the end result. Poop purification may a scifi-step too far for you, but do bear it in mind.

For an even longer shot, consider farming seaweed and shellfish. You'd want the sea to be pretty clean for that sort of thing, but if you're ecologically minded enough to make cities self-sufficient and you're recycling all the poop you're producing, there is hope you can also sort out your polluting industries, too. New York has a lot of coastline, and whilst farming fish tends to be quite polluting, farming shellfish tends to make the sea a nicer place. You might do something like long line mussel farming, perhaps with floating seaweed racks above it. You can always use the mussels to help clean the water for future farming use, and the seaweed for biofuel, until the sea is one day clean enough to eat from again.

Good old Asimov, in his "The caves of steel", used engineered yeasts to feed the megalopolis crowding the under surface of planet Earth.

Normal yeast can be already used as food supplement:

Yeast is used in nutritional supplements, especially those marketed to vegans. It is often referred to as "nutritional yeast" when sold as a dietary supplement. Nutritional yeast is a deactivated yeast, usually S. cerevisiae. It is naturally low in fat and sodium as well as an excellent source of protein and vitamins, especially most B-complex vitamins (contrary to some claims, it contains little or no vitamin B12), as well as other minerals and cofactors required for growth. Some brands of nutritional yeast, though not all, are fortified with vitamin B12, which is produced separately by bacteria.

In 1920, the Fleischmann Yeast Company began to promote yeast cakes in a "Yeast for Health" campaign. They initially emphasized yeast as a source of vitamins, good for skin and digestion. Their later advertising claimed a much broader range of health benefits, and was censured as misleading by the Federal Trade Commission. The fad for yeast cakes lasted until the late 1930s.

Nutritional yeast has a nutty, cheesy flavor and is often used as an ingredient in cheese substitutes. Another popular use is as a topping for popcorn. It can also be used in mashed and fried potatoes, as well as in scrambled eggs. It comes in the form of flakes, or as a yellow powder similar in texture to cornmeal. In Australia, it is sometimes sold as "savoury yeast flakes". Though "nutritional yeast" usually refers to commercial products, inadequately fed prisoners have used "home-grown" yeast to prevent vitamin deficiency.

With some genetic engineering one can overcome the shortcomings.

You need to factor in a new energy source. Like @alephzero explains in their answer, if you take all the sunlight falling on New York and let plants convert it into food, it's not enough. You need a source of electricity and then grow food on every floor and on walls in high-rises, like how @cyn describes in their answer.

Extrapolating from hydrophonics that exist in the real world should be taken with a grain of salt. True, there are high density cities in the world where hydrophonic farming of salads take place, but this is for logistical optimization. The food is grown in the city so that premium salads can be delivered to customers the same day they are picked. This is a small niche market and you need a big city to get enough customers. Growing grains requires a lot more space and a lot more energy. Illumination would have to be nearly free for hydroponics to produce all our food at a reasonable price.

So what energy can be harvested locally? Heat from the earth. Worldwide, "geothermal" electricity is produced when hot steam from deep wells drive turbines. New York state is not a particularly good spot for this, having a lukewarm subsurface, but if you drill deep enough you can always find heat. In New York, the wells will have to be 6 kilometres deep or more to get to the really high temperatures. In a science fiction setting, you can arbitrarily elongate these wells and extend them out under the ocean, providing you with as much energy as you like.

As other answers have pointed out, optimal use of rooftop gardens and roofs over roads and parking lots could suffice. The urban moties in The Mote in God's Eye used this technology as a backup plan for when their transportation networks inevitably collapsed, cutting off food from their rural farmlands.

But suppose you want to use only a portion of a coastal city for farms? The following technologies allow having some buildings specialize in farming, while keeping the rest of the cityscape you know and love.

1. Extract uranium from seawater. (In the prototype stage now.)


2. Process the uranium to get nuclear fuel. (Proven technology, but has security and geopolitical risks.)


3. Use inherently stable nuclear power plant designs. (Prevents melt-downs.
   Successfully prototyped 15 years ago, but still tied up in red-tape.)


4. Glassify the nuclear waste. (Proven technology. Also tied up in red-tape.)


5. Desalinate seawater to make irrigation water. (Proven technology.)


6. Use waste heat from the nuclear power plants to heat each farming building to the optimal temperature(s) for growing the plants and animals inside it. (Proven technology.)


7. Put the farms in multi-story, low-rise buildings. (Proven technology.)


8. Use hydroponics to minimize soil weight and optimize the number of crops per year. (Proven technology.)


9. Use high-efficiency lighting for producing the color(s) of light that are optimal for growing the desired crops. Avoid headache-producing lighting, because driving your workers crazy is not optimal. (Near-future technology. Will likely need to be upgraded as lighting technology becomes more efficient.)


10. Figure out uses for the waste heat from lighting the indoor farms.


11. Have sewage-treatment plants to eliminate pollution from livestock farming. (Proven technology.)


12. Sterilize the sewage-treatment waste, and use it as fertilizer for animal feed-crops. (Safer in this application than for use with sewage that contains hazardous wastes.)


13. Fix nitrogen from the air, to supplement the fertilizer. (Proven technology.)


14. Optionally, extract sodium, potassium, calcium, magnesium, chlorides, and sulfates from seawater. The extraction of these elements (and the uranium) can be done from the concentrated waste water from the desalination plants.

These technologies assume that plenty of carbon dioxide is available from the air.
There would still be a need to import fertilizers containing phosphates, iron, and less-common elements like manganese.

What you're basically describing is called 'closed loop agriculture'. The idea is that you're capturing all the waste products from creating AND consuming food and recycling them back into the system. Matt Damon's potatoes from 'The Martian' are a perfect example. You're envisioning something on a much larger scale, but the principle in the same.

There are two really critical components to making this idea work for heavily urbanized place.

First: You need to be VERY rigorous in your recycling program. Nothing gets dumped in the Hudson, every bit of water and organic waste your population generates needs to be captured, processed, and cycled back into your food production.

Second: You'd still need a lot of space devoted to food production. Hydroponics and so forth give you ways to concentrate that space, but it only goes so far. This previous article right here from Worldbulding gives some great information on that topic.

I believe there is a concept of vertical farming, in which skyscraper like buildings would have farms on each floor instead of offices.

Using hydroponics or aeroponics a lot more food could be grown per unit of surface area than in traditional dirt farming, and vertical farming would multiply the surface area available for food production in a city. Combining those two should make it possible to grow enough food in a metropolitan area to feed its population.

In a base on an alien planet or a space habitat everything, including wastes, would be recycled. So each atom of carbon, hydrogen, oxygen, nitrogen, etc., would be used over and over again to produce food. And it would certainly be possible to do the same in a city on Earth.

There have been a few questions here about the greatest possible production of food per unit of land surface using various techniques.

See here: Giving Tolkien Architecture a Reality Check: Dwarvish Kingdoms1

and here: How can Dwarves produce honey underground?2

And here: How many people can you feed per square-kilometer of farmland?3

You gave us New York metropolis which gives us a lot of options. If you listen to the government, the New York MSA has 19.9 million people in 17,405 sq.km. or 1143 people per sq.km, or 874 sq.metres per person.

As Alephzero's math shows, you need 20 square metres of land to grow plants simply to stay alive. Even if we shrink our definition of "urban area", reducing the square metres per person, we can still endure a lot of shrink before we're really in trouble.

Sun worshipping

1000 watts/sq.metre is too valuable to waste. Artificial lighting will never cut the mustard, you can't get anywhere near the efficiency you need with any foreseeable tech. I'm talking Future. Right now it's in the "fuggedaboutit" category. You have

 174,050,000,000,000 Wh/day of sunlight on the MSA, and you cannot replace that with a

      30,000,000,000 Wh/day nuclear plant.  Not even close.

You have to use the sun, and you have to make the most of it.

Again, it depends just what you define the metro area to be. The smaller you define the metro, the more extremes you'll need to go to place every square metre of solar exposure into service growing food. Roughly in order of intensity/commitment/cost:

• Maximize the yield of the farmland already inside the metro, using tactics like Polyface Farm (read The Omnivore's Dilemma section 2), and paradoxically, treeing up suburban homes to be the "forest" part of that design.




• Require all residences with yards to have victory gardens.




• Or better, greenhouses, as done in this town in Ukraine (within 10 miles of a nuclear and coal power plant complex, where waste heat unusable by the power turbines is sent over to heat the greenhouses).

The long, narrow greenhouses could be partially automated, by having machines on "railroad tracks" run up and down the length of the greenhouse, with tool-heads that do mechanized farming, or simply providing the farmers access to all crops without needing to waste square footage on aisleways. The greenhouses could be linked so a valuable machine could use a transfer table to move laterally from greenhouse to greenhouse.

• Push into waterways with landfill to grow crops


• Require homes with yards to use effectively all yard space for crops, removing ornamental trees etc.


• Nuclear power for power generation, and waste heat for above greenhouses for year-round crop growth


• make people park at the end of their block, reduce street capacity/width to exactly the width of a delivery truck, and recovered land and driveways are re-tasked for growing crops


• Improve transit, significantly curtail driving (probably need to happen anyway since cars need big energy), deprecate many roads and convert to growing crops.


• Deck over roadways and railways to grow crops


• Require all single-family homes to be rebuilt as earth-sheltered, so 100% of the yard is now farmable.


• A bunch of engineering happens in the tall-building City proper, to catch every single ray. Existing buildings get their roofs extended (widthwise). Very tall buildings are altered to turn every east, south and west exposure into garden beds. Building interiors are turned into effective greenhouses.

Every scrap of solarization lands somewhere it's used.

At the extreme settings, artificial lighting (possibly powered by solar) is used to light human-occupied spaces just enough for living, turning them dim and gloomy, akin to the old Kowloon Walled City.

If you're willing to accept nanotechnology "magic" as an answer, then Feed (or later, Seed) technology as shown in Neal Stephenson's "Diamond Age" can do it. The premises are :

1 ) Nanotech building techniques allow you to create diamond shapes from pure carbon input. Shapes and mixtures of all other elements and compounds can be made given time, energy, templates for the building plans, computation, and other infrastructure considerations.

2 ) Perfect decomposition of garbage, sewage, and random seawater into perfectly segregated elemental lumps. For dangerous elements like fluorine, combine them into safe compounds. A sphere of diamond is probably the safest, most reliable carrying container.

3 ) Perfect pumping system of these lumps. Use spheres instead of cubes, for better pumping. Use pure, clean water as the carrying medium and heat sink. Tag each sphere with its payload lump, track it, and send it out from the decomposition center. Or, have a bunch of decomposition centers and use a system like TCP/IP to send lumps where needed. Either way, it looks like a vascular system pumping out in a Feed.

4 ) Matter compilers in every home, business, and street corner. These request data, power, and lumps of atoms from the Feed. The matter compiler builds physical objects according to the templates in memory or that it fetches from the Internet.

5 ) Each home, business, and street corner has a waste system. If the decomposition machines can be made small, then just have one in every home. If you need a big one, then have a traditional sewage system, which flushes every away to the decomposition machine.

6 ) Power generation from nuclear, geothermal, solar, wind, and/or other sources. Perfect decomposition can also be applied to mining, or seawater, so Uranium is easy to get and refine.

In this city, the population can be extremely dense, only limited by the heat generation of the machinery and people. If people decompose and compile the same atoms with minimal movement every day (food, drink, and clothes can be created from the same atoms discarded as waste earlier in the same building or even room) , then there's relatively little waste from transportation.

This may seem a little disgusting - yesterday's feces, urine, breath, skin flakes, clothes, etc, are all spun into today's consumption. But it's been what we've each been doing since before we were born. We're already part of the water cycle, carbon cycle, nitrogen cycle, and many other cycles of biology. If you're eating a strawberry today, some portion of it was manure a month ago.

The Decomposer/Feed/Compiler system merely speeds it up, minimizes movement of dumb atoms, and applies the idea of perfectly recreating the template that you want. If they figure out how to perfectly recreate the Best Strawberry, then you get that one whenever you want, without blemish, insect, or age since it was harvested. Better yet, given that scanning an object for a template takes time, and templates can be manually reviewed to take out imperfections, you can having a really perfect strawberry, something that could never be enjoyed in a real city.

Each city now resembles a flower taking in power from the Sun and other sources, and endlessly recycling and rejuvenating itself.

Self-sufficient cities will look very different from the cities we know. It is probably a good idea to brainstorm a bunch of different tactics for localizing food production and think through how those will change the face of the city. You might also want to do some napkin math on populations, minimum caloric intake, statistical spread of caloric intake across levels of society.

There are also many different circumstances that could lead to needing or wanting to do it. It might be beneficial to think through those too (increased transportation costs, restrictions on travel for one reason or another)

Below are some suggestions for tactics for localizing food production in cities. Use your napkin math to pick the mix that works for the world you're building.

Farm central park. Nothing changes priorities like hunger. Public spaces might go from lawn to food really fast given the right incentives.
https://modernfarmer.com/2014/02/central-parks-sheeps-meadow/

Underground farming. Don't need sunlight if you have power. Don't need fields if you have plentiful underground space (repurpose subway stations?)
https://www.sciencealert.com/world-s-first-underground-urban-farm-opens-for-business-in-london

Oyster beds everywhere (this also protects the city from storm surges and cleans the water)
https://observer.com/2016/07/how-a-billion-oysters-are-set-to-change-new-yorks-harbor/

Aquaculture (fish farming)
http://www.cityfarmer.org/fish.html

Rooftop gardens (maybe not a huge part of the mix but strikingly visible one)
https://www.timeout.com/newyork/things-to-do/the-best-rooftop-gardens-in-nyc

Window boxes on every apartment (decentralize your food production, everyone contributes like the victory gardens of WWII, remember canning then becomes much more prevelant in daily life and conversation)
https://nutrigift.com/grow-endless-supply-cancer-fighting-food-window-boxes/

Lab grown meat. Meat production takes a lot of space and resources. Lab meat will probably be a great source of protein in the near future.
https://www.wired.com/story/lab-grown-meat/

As someone calculated before, we need about 20m2 to feed one human. Roughly 5x5 meters if we assume some wasted space.

New York has close to 9 million people - let's make it 10 million for tourists and other visitors.

Also, we want some space for other purposes, like generating energy, to be fully self-sufficient.

That makes a block of 25*20km, or 500km2. The city of NY (not the state) has around 780km2, so we can even keep some parks and major traffic arteries, and produce some extra plants for organic items like plates, packaging and so on. Ideally mostly resuseable, to save on farming space.

Most of the city-area is build up with a green house or a hydroponic garden on top, maybe a green house with plants which need less light a floor below, the working and living areas, the utility levels (with streets, machines and so on), and where needed some underground levels.

All in all, around 5..10 levels should be enough to provide lots of living and office space, lots of space for walkways and transport systems.

The top levels are flush, so they don't put resistance to wind turbines or stand in the way of neighboring lower green houses or solar panels.

The remaining parks and such are used intensively for edible plants, wood production and so on, so they also stay productive.

All waste (including dead humans) gets composted in suitable ways (including mushroom production and such), then used as fertiliser for the green houses or fish tanks. This will also provide biogas to keep temperatures up in winter, among others. Not much more than current modern canalisation and sewage treatment plants needed for that.

People of significance or who were on too much medicine at the end of their life may get proper burials in the parks or outside of the city. Some may get cremated, with the exhaust being fed into green houses and the ashes being taken care of by the relatives.

All in all, it is easily doable w/o any future tech, and it's only our cultural norms which keep it from happening.

Archaea are a lesser known and very interesting domain of life that could plausibly be modified to create a previously unused (directly via agriculture) sources of energy and molecular building blocks for a complicated metropolitan food chain.

Some thrive in extreme conditions such as very high temperatures or high salinity. Maybe you could have some sort of geothermal process involving modified archaea that adds another source of energy to your food chain rather than directly from sunlight.

They also could be used in the ocean to collect useful organics/inorganics from the ocean in a place like NYC. They also have mutualistic and commensural relationships with other species which might provide some inspiration for maximizing available resources into human consumable energy.

They also might be helpful in recycling waste products from humans and other parts of the food production process.

There's no modern technology that you need. 100 years ago, the population of NYC was 3 million. Before mass refrigeration, cars, or transportation, all of its food was grown within a one mile radius, carted in the early morning by donkey and mule, sold in the marketplaces, then cooked and eaten fresh that day... as has been done around the world for thousands of years.

Even today, many of the megalopolises around the world still have a considerable amount of fresh produce and meet being sold and consumed the same day.

The only thing modern technology brought was cheaper food from places further away.

So all you need is perhaps more farmland. You might have to go out two or three miles. And you would need more people farming. Food would cost more than industrially produced and transported food.

In similar over-crowded worlds or ones where meat production has been banned, I have seen plant-based substitutes being used. Namely, they grow some hand-wavy plant-stuff in big vats underneath the city that also double as CO2 scrubbers. This plant is probably some form of algae, such as Nori or Wakame, genetically modified to increase the protein content.

As is, even just one cup contains 376 calories, at 14% fat, 40% carbs, 47% protein. (www.fatsecret.com/calories-nutrition/generic/algae-dried). A quick image search show that algae vats can easily be 3ft radius by 10 ft tall is roughly 270 cubic feet or 32316 cups of liquid. Even if algae can only grow at 10% density, that's still 3232 cups of algae, or enough for 646.6 people at 2,000 calories a day.

If we assume that the population of New York City doubles when we reach the point you're talking about, then we need to feed 20 million people by this method. This means we need roughly 31,000 vats of algae. Assuming it as a 310 x 100 array of vats with three feet on either side of each, the necessary area is 2790 ft x 900 feet, or about 0.02% the area of New York City.

As for "cheap", I know I can buy some at the market for pretty cheap. Scaled production would lower the costs even further.

I'm not sure what the growth medium requires but Cultured Meat and cellular agriculture is becoming more viable each year. It's only a matter of time before the processes are improved to the point that higher volumes could be cultured.

Pass a law that every building over "x" (3-5) stories has to be built with the outer 15' leased to a farm. The buildings are already temperature controlled and have water in them. Executives lose their view of the city for a view through a farm to the city with a glass wall separating the corporate workers from the farm. The farm environment will be completely self contained so crops needing special seasons and temperatures can all be accommodated. Each corporation will need to partner with a farm on building expansions.

Every skyscraper built also contributes to the food production for the city. In conjunction with other ideas presented in other answers this could significantly increase food production.