The simple answer is to look at average per-capita or household water use, average annual rainfall, and determine how much surface area (often a rooftop) is required to supply residential needs.
Example: 15" (380mm) of rainfall over a 3,000 ft^2 (280m^2) roof is 28,000 gallons (100k litre) per year. That's 75 gallons/day (290 l/day). And would be typical of amounts that a Northern California suburban household might expect.
Since rainfall is mostly in the winter months (November -- May or so), you'd likely want to have storage for at least half of that, which would be roughly the size of a typical backyard swimming pool (10' * 20' * 4' avg depth).
Keep in mind that in many parts of the world, high populations corresponde to very high population densities, and the actual land-surface area per person is low. There are also regions in which residences are ephemeral or unstable, such that long-term investment is not attractive or individually sensible.
Many high-population areas are also located in regions in which there is high rainfall (east, southeast, and southern Asia especially, also the Philippines and portions of South and Central America). Water may not be a limiting factor in those places.
Water availability and access tends to be highly localised. There is a lot of water on the planet, the problems are having it where people are, when people need it. Household usage is one question, but if you're looking at agricultural water, the quantities and other requirements (when and where irrigation is required) scale up tremendously.
Which is a long way of saying "it depends". Which is what I said at the beginning anyhow.
I think if we could catch a lot more water than we allow to evaporate, especially in places like Utah where we've been flooding lately and are STILL in a drought.. I can't wrap my head around that. Why aren't we trying to collect all that excess water like a rancher trying to catch stray cattle that wandered onto their ranch?
https://en.wikipedia.org/wiki/List_of_dams_and_reservoirs_in...
A fair amount is required to flow out of state due to laws and water treaties.
There are areas with highly permiable soil and scattered watersheds. Much of the rain that falls in such places either isn't captured by reservoirs, or is directed elsewhere (absorbed into the ground, perhaps refreshing aquifers or the water table, evaporation). Reservoirs themselves have evaporative losses (especially in dry and windy climates). At smaller scales, localised cisterns could make sense, especially as supplemental storage and when integrated into initial designs (the case for many traditional building styles in dry climates).
Considering that existing building styles already provide virtually all that's necessary for rainwater capture except the storage containment itself, the additional marginal costs are fairly modest.
What’s not obvious is how cheaply these things contain water. The hover dam for example can hold back back over 14,000 m3 of water per 1 m3 of concrete. Ignoring profit from hydroelectric power in 2020 money it cost about 1$ to store ~13,000 gallons for 85 years and counting. With the added upside of minimizing flooding and hydroelectric power.
Of course that water is stored a long way from where it initially fell, but that’s a different story.
Keep in mind that the comparsion shouldn't be against the largest and most efficient reservoir (e.g., Hoover Dam), but against the best incremental option (marginal cost) of providing alternative impoundment.
I'd already pointed at part of that issue above: there are only so many Hoover Dam / Lake Mead opportunities available. Most have been exploited, and the environmental externalities are high. Rainwater capture is generally proposed where alternatives aren't viable (few homeowners can build a Hoover Dam on their own property, or even as a collective community project), where the terrain and hydrology don't support buillding dams, where environmental concerns are to great, or (and probably realistically the most significant issue) where legal claims on water rights make stream impoundments nonviable.
How this maps out in dollars per gallon over time remains unclear, though again, it's a good question.
(Lifetime is another key consideration. The anticipated lifetime of structures is another question, and Hoover Dam faces challenges on several fronts here, with both siltation and drought limiting effectiveness of the structure).
Capitalist society, no profit = no initiative
There's a lot of variation there. If you look at off-grid and deep-back-packing sort of sites, they'll give you a good idea.
For me, it came to 500 gallons per person, for Central Texas, to "stay alive through the worst historical drought I know of". We don't have any natural place to get rid of sewage (we're on a solid limestone hill), so that really complicates things for us.
Ready.gov suggests one gallon (4 litres) per person per day (https://www.ready.gov/water)
It's helpful to look at actual empirical usage. Van Lifers often give their own usage statistics. This article gives a 6.15 gal/day (23 litre/day) figure: https://musingsonentropy.com/2014/10/07/motorhome-living-one...
Household-level usage might be closer to 60 gal/day (225 litre/day) (1996 New Mexico water usage report, table of estimated usage).
Keep in mind that individual usage varies, emergencies (heat, illness, freezing) may change patterns, and that there is discretionary and nondiscretionary usage.
Don't undercount sanitation requirements -- regular bathing and flushing toilets will keep you healthy. It's possible to reduce those demands, but entirely eliminating them (unless methods are changed) is likely a bad idea.
There are these earthship houses in New Mexico that are amazing. They stay 62-72 degrees year round. They have orange and banana trees in the atrium. They reuse all water, the water that goes down the sink/bathtub is used in the greenhouse/entry/atrium, then it goes to the toilet, then it goes outside to a kinda marshland or wetland area where they have all kinds of greenery or maybe vine-grown vegetables and fruits (don't want black water on root veggies).
Its a bit sad too see how the mainstream system pushes people way from this way of living. "It can be difficult to obtain a mortgage for an earthship home. Many banks are unwilling to lend money for earthship homes, since there are few (if any) comparable sales in the area the lender can use to determine the home’s value."
I'd first recognised this by an aside in James Burkes's Connections, where adoption of the latten-rigged sail was delayed by over 1,000 years in the west by the fact that the financiers and insurers of sailing ship voyages would not permit ships with this "new" (it had been used throughout the Arabian region for centuries) and "unproven" technology.
(It's worth considering that much of modern banking, finance, business, and insurance practices came directly from the shipping world.)
More recently you can look at redlining in mortgage and small commercial insurance markets. Paul Baran, one of the co-inventors of packet-switched networking in the 1960s wrote of this in one of his RAND publications on the ethics of computer-science and information applications in the 1960s.
Want to renovate your house, but might need to tap the bank for a bit more mortgage ... think twice before you rip out the last bathroom and the kitchen - To mortgage a house without a kitchen or bathroom, many lenders will see it as uninhabitable and won't consider it suitable security. But I need the money to do put in the kitchen and bathroom ...
There's the seasonality, which is to say, the expected duration of dry spells.
There's the variability, which is to say how much the total quantity varies year-to-year. There might be additional concerns such as bimodal or heavily-skewed averages --- a mix of very dry and very wet years, with few near the "average" arithmetic mean, for example, would change the calculus for how large collection and storage areas need be.
(I suspect that much of California might be subject to such patterns given the El Nino / La Nina ENSO cycle.)
There's also been an increasing amount of explicit exception to seniority rules for the specific purpose of rainwater collection, though this may include limitations, notably that the water be used only on the property in which it was originally collected. That is: you cannot collect rainwater, then sell it to others.