Models Built With Water

Before powerful computing, water was used to model both projects and economies.


A couple of years ago I wrote a post using the famous quote by statistician George Box: All Models Are Wrong; Some Are Useful. In that post, I discussed paper and plastic airplanes, but mostly I talked about modeling in computers, and especially what I call the “digital illusion.” The digital illusion is the idea that signals in digital chips are ones and zeros, with timing, and not analog voltages. It is the effectiveness of this illusion that enables us to build billion-gate chips. If we had to worry about the analog behavior of each signal, it would be intractable to design a microcontroller, let alone a multicore processor. What would we do if we didn’t have computers?

One way to answer that question is simply to go back in time to the dawn of computing in the 1940s and 1950s.

Bay model

In the late 1940s and early 1950s, there were various proposals to build dams on San Francisco Bay to capture water coming down the Sacramento River for drinking water and irrigation. There would also be about 30 square miles of the bay reclaimed. This was originally known as the San Francisco Bay Project, but was also called The Reber Plan, named after John Reber, who created it. He was a “former schoolteacher and theatrical producer,” which hardly seems like the perfect background for hydrological engineering.

In one telling of the story:

Reber argued the bay was “a geographic mistake,” interfering with the efficient operation of the surrounding metropolis. Because of the bay, the transcontinental railroad ended in Oakland instead of its natural destination, San Francisco. Reber initially favored an earthen causeway to bring the rails directly into the city.

By 1929 his proposal included two large earth-filled dams, one located just south of the current Bay Bridge and the other at the approximate location of today’s Richmond-San Rafael Bridge. While the tops of the structures would serve as transportation corridors for rail and auto traffic, the dams would also block saltwater intrusion into both the north and south bays, creating two massive freshwater lakes. Under the Reber Plan, only about 15 percent of the present bay would have remained subject to ocean tides. Reber estimated the lakes would store about 10 million acre-feet of water, more than twice the capacity of Lake Shasta, California’s largest reservoir. The water would have been available for residential and industrial use around the bay and for irrigation in regional agricultural areas such as the Santa Clara Valley.

According to UC Berkeley’s “Bridging the Bay”:

The Reber Plan claimed it would provide 20,000 acres of additional filled land, increase the deep-water harbor by 50 miles, and conserve 2,400,000 acre-feet of fresh water annually. Critics pointed out the plan’s destruction of commercial fisheries, increased sewage disposal problems, adverse effects on the ports of Oakland, Stockton, and Sacramento, and flooding potential. Although it attracted considerable attention, even that of the editors of the Saturday Evening Post, the Reber Plan was opposed by the State of California, the Bureau of Reclamation, and the Army Corps of Engineers and was never adopted. 

It’s true that it was never adopted, and it was opposed by the State and the Army Corps of Engineers. But that wasn’t just because they simply didn’t like the idea. They made a model of it to see whether it would work. Remember, this is in 1957, so it is not feasible to build a computer model. Computers existed by then, of course, but they had very limited power. For example, in RAMAC Park and the Origin of the Disk Drive, I wrote about the first computer with disk drives that dated from around that period. A typical instruction took 30ms, so it ran about 30 instructions per second (0.00003 MIPS). You are not going to do large-scale fluid dynamic modeling with that.

What the Army Corps of Engineers did was to build a physical model of the Bay in Sausalito. The model is at a scale of 1:1000 horizontally and 1:100 vertically. It covers the whole Bay, including much of the delta, and going out through the Golden Gate for nearly 20 miles into the Pacific Ocean. I say “covers” in the present tense, since although the model was built in 1957 it still exists today. It is no longer used for real work on simulating the hydrography of the Bay, that is all done on computers now. It is currently described as an:

education center administered by the U.S. Army Corps of Engineers which hosts a working hydraulic model of the San Francisco Bay and Sacramento – San Joaquin River Delta System.

Last time I was there, the tides in the Pacific were running, the model pumps water into or out of the ocean and then it flows through the Golden Gate. In addition to having an exaggerated vertical scale, the model also compresses time and an entire half-day (one tide cycle) is compressed into, if I remember right, about 30 minutes.

It is currently closed, like everything else, but normally it is open to the public and anyone can visit (it’s free). It is just a couple of minutes’ drive from the 101 freeway so I recommend a visit if you ever find yourself driving through Marin. It is also close to the normal cycle route over the Golden Gate Bridge to Tiburon (where you can get a ferry back to San Francisco), another trip that I also recommend.

Fellow Brit Tom Scott visited in 2016 and made a video “Stopping a Disastrous Plan with Science: the Bay Model.”


This is not the only model using water. In The Science Museum (in London), they have a model of the British economy that used water as money, and flows as water to represent the flows of finance through the economy. The model is called MONIAC for MOnetary National Income Analogue Computer. It was built for the London School of Economics (LSE) in 1952. It’s quite large so it is hard to get a good photograph of it (and somehow taking pictures through glass never comes out as clearly as it looks to the eye).

As it says on the descriptive panel:

This machine modeled the British economy using the flow of water to represent money. It was made for the London School of Economics in 1952 by Bill Philips, an engineer turned economist. Economists such as Philips used mathematical equations to describe economic behavior, and this machine solved them in a visual way. The lower tank represented the nation’s stock of money, which emerged as spending, saving, taxes, and international trade. It was sophisticated but many economists now believe that the economy is more complicated than the simple equations that this machine is based on.

The MONIAC in The Science Museum is no longer operational, but the Reserve Bank of New Zealand built one, too, and you can see it operating in this video.


The Netherlands is even more dependent on water engineering than the San Francisco Bay area since about 15% of the country is below sea level and only about 50% higher than one meter. They, too, used physical modeling to simulate the effect of building dikes and other structures to hold back the sea. I’ve never been there but here is Tom Scott back again with a video “How The Netherlands Simulated The Sea Before Computers: The Waterloopbos.”

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