I
am developing on the same topic I have already highlighted in « Another
idea – urban wetlands », i.e. on urban wetlands. By the way, I have found a
similar, and interesting concept in the existing literature: the sponge city.
It is being particularly promoted by Chinese authors. I am going for a short
review of the literature on this specific topic, and I am starting with
correcting a mistake I made in my last update in French, « La
ville – éponge » when discussing the article by Shao
et al. (2018[1]). I got
confused in the conversion of square meters into square kilometres. I forgot
that **1 km2 = 10 ^{6} m2, not 10^{3}**. Thus, correcting
myself now, I rerun the corresponding calculations. The Chinese city of Xiamen,
population 3 500 000, covers an area of 1 865 km2, i.e.
1 865 000 000 m2. In that, 118 km2 = 118 000 000 m2 are
infrastructures of sponge city, or purposefully arranged urban wetlands. Annual
precipitations in Xiamen, according to Climate-Data.org,
are 1131 millimetres per year, thus 1131 m3 of water per 1 m2. Hence, the
entire city of Xiamen receives 1 865 000 000 m2 * 1 131
m3/m2 = 2 109 315 000 000 m3 of
precipitation a year, and the sole area of urban wetlands, those 118 square
kilometres, receives 118 000 000 m2 * 1 131 m3/m2 = 133 458 000 000 m3. The infrastructures of
sponge city in Xiamen have a target capacity of 2% regarding the retention of
rain water, which gives 2 669 160 000 m3.

Jiang et al. (2018[2]) present a large scale strategy for the development of sponge cities in China. The first takeaway I notice is the value of investment in sponge city infrastructures across a total of 30 cities in China. Those 30 cities are supposed to absorb $275,6 billions in the corresponding infrastructural investment, thus an average of $9,19 billion per city. The first on the list is Qian’an, population 300 000, are 3 522 km2, total investment planned I = $5,1 billion. That gives $17 000 per resident, and $1 448 041 per 1 km2 of urban area. The city of Xiamen, whose case is discussed by the previously cited Shao et al. (2018[3]), has already got $3,3 billion in investment, with a target at I = $14,14 billion, thus at $4800 per resident, and $7 721 180 per square kilometre. Generally, the intensity of investment, counted per capita or per unit of surface, is really disparate. This is, by the way, commented by the authors: they stress the fact that sponge cities are so novel a concept that local experimentation is norm, not exception.

Wu et al. (2019[4]) present another case study, from among the cities listed in Jiang et al. (2018), namely the city of Wuhan. Wuhan is probably the biggest project of sponge city in terms of capital invested: $20,04 billion, distributed across 293 detailed initiatives. Started after a catastrophic flood in 2016, the project has also proven its value in protecting the city from floods, and, apparently, it is working. As far as I could understand, the case of Wuhan was the first domino block in the chain, the one that triggered the whole, nation-wide programme of sponge cities.

Shao et al. (2016[5]) present an IT approach to organizing sponge-cities, focusing on the issue of data integration. The corresponding empirical field study had been apparently conducted in Fenghuang County, province Hunan. The main engineering challenge consists in integrating geographical data from geographic information systems (GIS) with data pertinent to urban infrastructures, mostly CAD-based, thus graphical. On the top of that, spatial data needs to be integrated with attribute data, i.e. with the characteristics of both infrastructural objects, and their natural counterparts. All that integrated data is supposed to serve efficient application of the so-called Low Impact Development (LID) technology. With the Fenghuang County, we can see the case of a relatively small area: 30,89 km2, 350 195 inhabitants, with a density of population of 200 people per 1 km2. The integrated data system was based on dividing that area into 417 sub-catchments, thus some 74 077 m2 per catchment.

Good, so this is like a cursory review of literature on the Chinese concept of sponge city. Now, I am trying to combine it with another concept, which I first read about in a history book, namely Civilisation and Capitalism by Fernand Braudel, volume 1: The Structures of Everyday Life[6]: the technology of lifting and pumping water from a river with the help of kinetic energy of waterwheels propelled by the same river. Apparently, back in the day, in cities like Paris, that technology was commonly used to pump river water onto the upper storeys of buildings next to the river, and even to the further-standing buildings. Today, we are used to water supply powered by big pumps located in strategic nodes of large networks, and we are used to seeing waterwheels as hydroelectric turbines. Still, that old concept of using directly the kinetic energy of water seems to pop up again, here and there. Basically, it has been preserved in a slightly different form. Do you know that image in movies, with that windmill in the middle of a desert? What is the point of putting a windmill in the middle of a desert? To pump water from a well. Now, let’s make a little jump from wind power to water power. If we can use the force of wind to pump water from underground, we can use the force of water in a river to pump water from that river.

In
scientific literature, I found just one article making reference to it, namely Yannopoulos
et al. (2015[7]). Still,
in the less formal areas, I found some more stuff. I found that U.S. patent,
from 1951, for a water-wheel-driven
brush. I found more modern a technology
of the spiral pump, created by a company called PreScouter.
Something similar is being proposed by the Dutch company Aqysta.
Here are some graphics to give you an idea:

Now, I put together the infrastructure of a sponge city, and the technology of pumping water uphill using the energy of the water. I have provisionally named the thing « **Energy Ponds** ». Water wheels power water pumps, which convey water to elevated tanks, like water towers. From water towers, water falls back down to the ground level, passes through small hydroelectric turbines on its way down, and lands in the infrastructures of a sponge city, where it is being stored. Here below, I am trying to make a coherent picture of it. The general concept can be extended, which I present graphically further below: infrastructure of the sponge city collects excess water from rainfall or floods, and partly conducts it to the local river(s). What limits the river from overflowing or limits the degree of overflowing is precisely the basic concept of Energy Ponds, i.e. those water-powered water pumps that pump water into elevated tanks. The more water flows in the river – case of flood or immediate threat thereof – the more power in those pumps, the more flow through the elevated tanks, and the more flow through hydroelectric turbines, hence the more electricity. As long as the whole infrastructure physically holds the environmental pressure of heavy rainfall and flood waves, it can work and serve.

My
next step is to outline the business and financial framework of the « **Energy
Ponds** » concept, taking the data provided by Jiang
et al. (2018)
about 29 sponge city projects in China, squeezing as much information as I can
from it, and adding the component of hydroelectricity. I transcribed their data
into an Excel file, and added some calculations of my own, together with data
about demographics and annual rainfall. Here
comes the Excel file with data as of July 5^{th} 2019.
A pattern emerges. All the 29 local clusters of projects display quite an even
coefficient of capital invested per 1 km2 of construction area in those
projects: it is $320 402 571,51 on average, with quite a low standard
deviation, namely $101 484 206,43. Interestingly, that coefficient is not
significantly correlated neither with the local amount of rainfall per 1 m2,
nor with the density of population. It looks like quite an autonomous variable,
and yet as a recurrent proportion.

Another
interesting pattern is to find in the percentage of the total surface, in each
of the cities studied, devoted to being filled with the sponge-type infrastructure.
The average value of that percentage is 0,61% and is accompanied by quite big a
standard deviation: 0,63%. It gives an overall variability of 1,046. Still,
that percentage is correlated with two other variables: annual rainfall, in
millimetres per square meter, as well as with the density of population, i.e.
average number of people per square kilometre. Measured with the Pearson
coefficient of correlation, the former yields ** r = 0,45**, and the
latter is

**: not very much, yet respectable, as correlations come.**

*r = 0,43*From underneath those coefficients of correlation, common sense pokes its head. The more rainfall per unit of surface, the more water there is to retain, and thus the more can we gain by installing the sponge-type infrastructure. The more people per unit of surface, the more people can directly benefit from installing that infrastructure, per 1 km2. This one stands to reason, too.

There
is an interesting lack of correlations in that lot of data taken from Jiang
et al. (2018).
The number of local projects, i.e. projects per one city, is virtually not
correlated with anything else, and, intriguingly, is negatively correlated, at
Pearson ** r = – 0,44**, with the size of local populations. The more
people in the city, the less local projects of sponge city are there.

By the way, I have some concurrent information on the topic. According to a press release by Voith, this company has recently acquired a contract with the city of Xiamen, one of the sponge-cities, for the supply of large hydroelectric turbines in the technology of pumped storage, i.e. almost exactly the thing I have in mind.

Now, the Chines programme of sponge cities is a starting point for me to reverse engineer my own concept of « Energy Ponds ». I assume that four economic aggregates pay off for the corresponding investment: a) the Net Present Value of proceedings from producing electricity in water turbines b) the Net Present Value of savings on losses connected to floods c) the opportunity cost of tap water available from the retained precipitations, and d) incremental change in the market value of the real estate involved.

There
is a city, with ** N** inhabitants, who consume

**m3 of water per year,**

*R***per person per year, and they consume**

*R/N***kWh of energy per year,**

*E***per person per year.**

*E/N***divided by 8760 hours in a year (**

*R***) is the approximate amount of water the local population needs to have in current constant supply. Same for energy:**

*R/8760***is a good approximation of power, in kW, that the local population needs to have standing and offered for immediate use.**

*E/8760*The
city collects ** F** millimetres of precipitation a year. Note that

**. With a density of population**

*F mm = F m*^{3}/m^{2}**people per 1 km**

*D*^{2}, the average square kilometre has what I call the

**sponge function**:

**. Each square kilometre collects**

*D*(R/N) = f(F*10*^{6})**cubic meters of precipitation a year, and this amount remains is a recurrent proportion to the aggregate amount of water that**

*F*10*^{6}**people living on that square kilometre consume per year.**

*D*The
population of ** N** residents spend an aggregate

**on energy, and an aggregate**

*P*_{E}*E**on water, where**

*P*_{R}*R**and**

*P*_{E}**are the respective prices of energy and water. The supply of water and energy happens at levelized costs per unit. The reference math here is the standard calculation of**

*P*_{R}**, or Levelized Cost of Energy in an interval of time**

*LCOE***, measured as**

*t***, where**

*LCOE(t) = [I*_{E}(t) + M_{E}(t) + U_{E}(t)] / E**is the amount of capital invested in the fixed assets of the corresponding power installations,**

*I*_{E}**is their necessary cost of current maintenance, and**

*M*_{E}**is the cost of fuel used to generate energy. Per analogy, the levelized cost of water can be calculated as**

*U*_{E}**, with the same logic: investment in fixed assets plus cost of current maintenance plus cost of water strictly speaking, all that divided by the quantity of water consumed. Mind you, in the case of water, the**

*LCOR(t) = [I*_{R}(t) + M_{R}(t) + U_{R}(t)] / R**part could be easily zero, and yet it does not have to be. Imagine a general municipal provider of water, who buys rainwater collected in private, local installations of the sponge type, at**

*U*_{R}(t)**per cubic metre, that sort of thing.**

*U*_{R}(t)The
supply of water and energy generates gross margins: ** E(t)*(P_{E}(t)
– LCOE(t)) **and

**(**

*R(t)****. These margins are possible to rephrase as, respectively,**

*P*_{R}(t) – LCOR(t))**–**

*P*_{E}(t)*E(t)**, and**

*I*_{E}(t) – M_{E}(t) – U_{E}(t)**. Gross margins are gross cash flows, which finance organisations (jobs) attached to the supply of, respectively, water and energy, and generate some net surplus. Here comes a little difficulty with appraising the net surplus from the supply of water and energy. Long story short: the levelized values of the «**

*R(t)*P*_{R}(t) – I_{R}(t) – M_{R}(t) – U_{R}(t)*LCO-whatever follows*» type explicitly incorporate the yield on capital investment. Each unit of output is supposed to yield a return on investment

**. Still, this is not how classical accounting defines a cost. The amounts assigned to costs, both variable and fixed, correspond to the strictly speaking current expenditures, i.e. to payments for the current services of people and things, without any residual value sedimenting over time. It is only after I account for those strictly current outlays that I can calculate the current margin, and a fraction of that margin can be considered as direct yield on my investment. In standard, basic accounting, the return on investment is the net income divided by the capital invested. The net income is calculated as**

*I***, where**

*π = Q*P – Q*VC – FC – r*I – T***and**

*Q***are quantity and price,**

*P***is the variable cost per unit of output**

*VC***,**

*Q***stands for the fixed costs,**

*FC***is the price of capital (interest rate) on the capital**

*r***invested in the given business, and**

*I***represents taxes. In the same standard accounting, Thus calculated net income**

*T***is then put into the formula of internal rate of return on investment:**

*π***.**

*IRR = π / I*When I calculate my margin of profit on the sales of energy or water, I have those two angles of approach. Angle #1 consists in using the levelized cost, and then the margin generated over that cost, i.e. P – LC (price minus levelized cost) can be accounted for other purposes than the return on investment. Angle #2 comes from traditional accounting: I calculate my margin without reference to the capital invested, and only then I use some residual part of that margin as return on investment. I guess that levelized costs work well in the accounting of infrastructural systems with nicely predictable output. When the quantity demanded, and offered, in the market of energy or water is like really recurrent and easy to predict, thus in well-established infrastructures with stable populations around, the LCO method yields accurate estimations of costs and margins. On the other hand, when the infrastructures in question are developing quickly and/or when their host populations change substantially, classical accounting seems more appropriate, with its sharp distinction between current costs and capital outlays.

Anyway,
I start modelling the first component of the possible payoff on investment in the
infrastructures of « Energy Ponds », i.e.
**the Net Present Value of proceedings from producing electricity in
water turbines**. As I generally like staying close to real life (well, most
of the times), I will be wrapping my thinking around my hometown, where I still
live, i.e. Krakow, Poland, area of the city: 326,8 km2, area of the metropolitan
area: 1023,21 km2. As for annual precipitations, data from Climate-Data.org[1] tells me
that it is a bit more than the general Polish average of 600 mm a year. Apparently,
Krakow receives an annual rainfall of 678 mm, which, when translated into
litres received by the whole area, makes a total rainfall on the city of 221 570 400 000 litres, and, when enlarged to
the whole metropolitan area, makes

693 736 380 000 litres.

In
the generation of electricity from hydro turbines, what counts is the flow,
measured in litres per second. The above-calculated total rainfall is now to be
divided by 365 days, then by 24 hours, and then by 3600 seconds in an hour.
Long story short, you divide the annual rainfall in litres by the constant of **31
536 000 seconds in one year**. Mind you, on odd years, it will be **31
622 400** seconds. This step leads me to an estimate total flow of 7 026
litres per second in the city area, and 21 998 litres per second in the
metropolitan area. Question: what amount of electric power can I get with that
flow? I am using a formula I found at Renewables
First.co.uk[2] : flow per
second, in kgs per second multiplied by the gravitational constant a = 9,81, multiplied
by the average efficiency of a hydro turbine equal to 75,1%, further multiplied
by the net head – or net difference in height – of the water flow. All that
gives me electric power in watts. All in all, when you want to calculate the
electric power dormant in your local rainfall, take the total amount of said rainfall,
in litres falling on the entire place where you can possibly collect that rainwater
from, and **multiply it by 0,076346*Head of the waterflow**. You will get
power in kilowatts, with that implied efficiency of 75,1% in your technology.

For
the sake of simplicity, I assume that, in those installations of elevated water
tanks, the average elevation, thus the head of the subsequent water flow
through hydro turbines, will be H = 10 m. That leads me to **P = 518 kW**
available from the annual rainfall on the city of Krakow, when elevated to H =
10 m, and, accordingly, **P = 1 621 kW** for the rainfall received over
the entire metropolitan area.

In
the next step, I want to calculate the market value of that electric power, in
terms of revenues from its possible sales. I take the power, and I multiply it
by 8760 in a year (8784 hours in an odd year). I get the amount of electricity
for sale equal to **E = 4 534 383 kWh** from the rainfall received over
the city of Krakow strictly spoken, and **E = 14 197 142 kWh** if we
hypothetically collect rainwater from the entire metro area.

Now,
the pricing. According to data available at GlobalPetrolPrices.com[3], the average price of
electricity in Poland is ** P_{E} = $0,18** per kWh. Still,
when I get, more humbly, to my own electricity bill, and I crudely divide the
amount billed in Polish zlotys by the amount used in kWh, I get to something like

**per kWh. The discrepancy might be coming from the complexity of that price: it is the actual price per kWh used plus all sorts of constant stuff per kW of power made available. With those prices, the market value of the corresponding revenues from selling electricity from rainfall used smartly would be like**

*P*_{E}= $0,21**$816 189 ≤**from the city area, and

*Q*P*$952 220 a year_{E}≤**$2 555 485 ≤**from the metropolitan area.

*Q*P*$2 981 400 a year_{E}≤I
transform those revenues, even before accounting for any current costs, into a
stream, spread over 8 years of average lifecycle in an average investment
project. Those 8 years are what is usually expected as the time of full return
on investment in those more long-term, infrastructure-like projects. With a technological
lifecycle around 20 years, those projects are supposed to pay for themselves
over the first 8 years, the following 12 years bringing a net overhead to
investors. Depending on the pricing of electricity, and with a discount rate of
r = 5% a year, it gives something like ** $5 275 203 ≤ NPV(Q*P_{E}
; 8 years) ≤ $6 154 403** for the city area, and

**for the metropolitan area.**

*$16 516 646 ≤ NPV(Q*P*_{E}; 8 years) ≤ $19 269 421When I compare that stream of revenue to what is being actually done in the Chinese sponge cities, discussed a few paragraphs earlier, one thing jumps to the eye: even with the most optimistic assumption of capturing 100% of rainwater, so as to make it flow through local hydroelectric turbines, there is no way that selling electricity from those turbines pays off for the entire investment. This is a difference in the orders of magnitude, when we compare investment to revenues from electricity.

I
am consistently delivering good, almost new science to my readers, and love
doing it, and I am working on crowdfunding this activity of mine. You can
communicate with me directly, via the mailbox of this blog: goodscience@discoversocialsciences.com.
As we talk business plans, I remind you that you can download, from the library
of my blog, the business
plan I prepared for my semi-scientific project Befund (and you can access
the French version as well). You can also get a free e-copy of my book ‘Capitalism
and Political Power’ You can support my research by donating directly,
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[1] https://en.climate-data.org/europe/poland/lesser-poland-voivodeship/krakow-715022/ last access July 7^{th}
2019

[2] https://www.renewablesfirst.co.uk/hydropower/hydropower-learning-centre/how-much-power-could-i-generate-from-a-hydro-turbine/ last access July 7^{th},
2019

[3] https://www.globalpetrolprices.com/electricity_prices/
last access July 8^{th} 2019

[1] Shao, W., Liu, J., Yang, Z., Yang, Z., Yu, Y., & Li, W. (2018). Carbon Reduction Effects of Sponge City Construction: A Case Study of the City of Xiamen. Energy Procedia, 152, 1145-1151.

[2] Jiang, Y., Zevenbergen, C., & Ma, Y. (2018). Urban pluvial flooding and stormwater management: A contemporary review of China’s challenges and “sponge cities” strategy. Environmental science & policy, 80, 132-143.

[3] Shao, W., Liu, J., Yang, Z., Yang, Z., Yu, Y., & Li, W. (2018). Carbon Reduction Effects of Sponge City Construction: A Case Study of the City of Xiamen. Energy Procedia, 152, 1145-1151.

[4] Wu, H. L., Cheng, W. C., Shen, S. L., Lin, M. Y., & Arulrajah, A. (2019). Variation of hydro-environment during past four decades with underground sponge city planning to control flash floods in Wuhan, China: An overview. Underground Space, article in press

[5] Shao, W., Zhang, H., Liu, J., Yang, G., Chen, X., Yang, Z., & Huang, H. (2016). Data integration and its application in the sponge city construction of China. Procedia Engineering, 154, 779-786.

[6] Braudel, F., & Reynolds, S. (1979). Civilization and capitalism 15th-18th Century, vol. 1, The structures of everyday life. Civilization, 10(25), 50.

[7] Yannopoulos, S., Lyberatos, G., Theodossiou, N., Li, W., Valipour, M., Tamburrino, A., & Angelakis, A. (2015). Evolution of water lifting devices (pumps) over the centuries worldwide. Water, 7(9), 5031-5060.

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