The mind-blowing hydro

My editorial on You Tube

There is that thing about me: I am a strange combination of consistency and ADHD. If you have ever read one of Terry Pratchett’s novels from the ‘Discworld’ series, you probably know the imaginary character of golems: made of clay, with a logical structure – a ‘chem’ – put in their heads, they can work on something endlessly. In my head, there are chems, which just push me to do things over and over and over again. Writing and publishing on that research blog is very much in those lines. I can stop whenever I want, I just don’t want right now. Yet, when I do a lot about one chem, I start craving for another one, like nearby but not quite in the same intellectual location.

Right now, I am working on two big things. Firstly, I feel like drawing a provisional bottom line under those two years of science writing on my blog. Secondly, I want to put together an investment project that would help my city, my country and my continent, thus Krakow, Poland, and Europe, to face one of the big challenges resulting from climate change: water management. Interestingly, I started to work on the latter first, and only then I began to phrase out the former. I explain. As I work on that project of water management, which I provisionally named « Energy Ponds » (see, for example, « All hope is not lost: the countryside is still exposed »), I use the « Project Navigator », made available by the courtesy of the International Renewable Energy Agency (IRENA). The logic built into the « Project Navigator » makes me return, over and over again, to one central question: ‘You, Krzysztof Wasniewski, with your science and your personal energy, how are you aligned with that idea of yours? How can you convince other people to put their money and their personal energy into developing on your concept?’.

And so I am asking myself: ‘What’s your science, bro? What can you get people interested in, with rational grounds and intelligible evidence?’.

As I think about it, my first basic claim is that we can do it together in a smart way. We can act as a collective intelligence. This statement can be considered as a manifestation of the so-called “Bignetti model” in cognitive sciences (Bignetti 2014 [1]; Bignetti et al. 2017 [2]; Bignetti 2018 [3]): for the last two years, I have been progressively centering my work around the topic of collective intelligence, without even being quite aware of it. As I was working on another book of mine, entitled “Capitalism and Political Power”, I came by that puzzling quantitative fact: as a civilization, we have more and more money per unit of real output[4], and, as I reviewed some literature, we seem not to understand why is that happening. Some scholars complain about the allegedly excessive ‘financialization of the economy’ (Krippner 2005 [5]; Foster 2007 [6]; Stockhammer 2010 [7]), yet, besides easy generalizations about ‘greed’, or ‘unhinged race for profit’, no scientifically coherent explanation is offered regarding this phenomenon.

As I was trying to understand this phenomenon, shades of correlations came into my focus. I could see, for example, that growing an amount of money per unit of real output has been accompanied by growing an amount of energy consumed per person per year, in the global economy[8]. Do we convert energy into money, or the other way around? How can it be happening? In 2008, the proportion between the global supply of broad money, and the global real output passed the magical threshold of 100%. Intriguingly, the same year, the share of urban population in the total human population passed the threshold of 50%[9], and the share of renewable energy in the total final consumption of energy, at the global scale, took off for the first time since 1999, and keeps growing since then[10]. I started having that diffuse feeling that, as a civilization, we are really up to something, right now, and money is acting like a social hormone, facilitating change.

We change as we learn, and we learn as we experiment with the things we invent. How can I represent, in a logically coherent way, collective learning through experimentation? When an individual, or a clearly organized group learns through experimentation, the sequence is pretty straightforward: we phrase out an intelligible definition of the problem to solve, we invent various solutions, we test them, we sum up the results, we select seemingly the best solution among those tested, and we repeat the whole sequence. As I kept digging the topic of energy, technological change, and the velocity of money, I started formulating the outline of a complex hypothesis: what if we, humans, are collectively intelligent about building, purposefully, and semi – consciously, social structures supposed to serve as vessels for future collective experiments?

My second claim is that one of the smartest things we can do about climate change is, besides reducing our carbon footprint, to take proper care of our food and energy base. In Europe, climate change is mostly visible as a complex disruption to our water system, and we can observe it in our local rivers. That’s the thing about Europe: we have built our civilization, on this tiny, mountainous continent, in close connection with rivers. Right, I can call them scientifically ‘inland waterways’, but I think that when I say ‘river’, anybody who reads it understands intuitively. Anyway, what we call today ‘the European heritage’ has grown next to EVENLY FLOWING rivers. Once again: evenly flowing. It means that we, Europeans, are used to see the neighbouring river as a steady flow. Streams and creeks can overflow after heavy rains, and rivers can swell, but all that stuff had been happening, for centuries, very recurrently.

Now, with the advent of climate change, we can observe three water-related phenomena. Firstly, as the English saying goes, it never rains but it pours. The steady rhythm and predictable volume of precipitations we are used to, in Europe (mostly in the Northern part), progressively gives ground to sudden downpours, interspersed with periods of drought, hardly predictable in their length. First moral of the fairy tale: if we have less and less of the kind of water that falls from the sky slowly and predictably, we need to learn how to capture and retain the kind of water that falls abruptly, unscheduled. Secondly, just as we have adapted somehow to the new kind of sudden floods, we have a big challenge ahead: droughts are already impacting, directly and indirectly, the food market in Europe, but we don’t have enough science yet to predict accurately neither their occurrence nor their local impact. Yet, there is already one emerging pattern: whatever happens, i.e. floods or droughts, rural populations in Europe suffer more than the urban ones (see my review of literature in « All hope is not lost: the countryside is still exposed »). Second moral of the fairy tale: whatever we do about water management in these new conditions, in Europe, we need to take care of agriculture first, and thus to create new infrastructures so as to shield farms against floods and droughts, cities coming next in line.

Thirdly, the most obviously observable manifestation of floods and droughts is variation in the flow of local rivers. By the way, that variation is already impacting the energy sector: when we have too little flow in European rivers, we need to scale down the output of power plants, as they have not enough water to cool themselves. Rivers are drainpipes of the neighbouring land. Steady flow in a river is closely correlated with steady a level of water in the ground, both in the soil, and in the mineral layers underneath. Third moral of the fairy tale: if we figure out workable ways of retaining as much rainfall in the ground as possible, we can prevent all the three disasters in the same time, i.e. local floods, droughts, and economically adverse variations in the flow of local rivers.

I keep thinking about that ownership-of-the-project thing I need to cope with when using the « Project Navigator » by IRENA. How to make local communities own, as much as possible, both the resources needed for the project, and its outcomes? Here, precisely, I need to use my science, whatever it is. People at IRENA have experience in such project, which I haven’t. I need to squeeze my brain and extract thereof any useful piece of coherent understanding, to replace experience. I am advancing step by step. I intuitively associate ownership with property rights, i.e. with a set of claims on something – things or rights – together with a set of liberties of action regarding the same things or rights. Ownership from the part of a local community means that claims and liberties should be sort of pooled, and the best idea that comes to my mind is an investment fund. Here, a word of explanation is due: an investment fund is a general concept, whose actual, institutional embodiment can take the shape of a strictly speaking investment fund, for one, and yet other legal forms are possible, such as a trust, a joint stock company, a crowdfunding platform, or even a cryptocurrency operating in a controlled network. The general concept of an investment fund consists in taking a population of investors and making them pool their capital resources over a set of entrepreneurial projects, via the general legal construct of participatory titles: equity-based securities, debt-based ones, insurance, futures contracts, and combinations thereof. Mind you, governments are investment funds too, as regards their capacity to move capital around. They somehow express the interest of their respective populations in a handful of investment projects, they take those populations’ tax money and spread it among said projects. That general concept of investment fund is a good expression of collective intelligence. That thing about social structure for collective experimentation, which I mentioned a few paragraphs ago, an investment fund is an excellent example. It allows spreading resources over a number of ventures considered as local experiments.

Now, I am dicing a few ideas for a financial scheme, based on the general concept of an investment fund, as collectively intelligent as possible, in order to face the new challenges of climate change, through new infrastructures for water management. I start with reformulating the basic technological concept. Water powered water pumps are immersed in the stream of a river. They use the kinetic energy of that stream to pump water up and further away, more specifically into elevated water towers, from which that water falls back to the ground level, as it flows down it powers relatively small hydroelectric turbines, and ends up in a network of ponds, vegetal complexes and channel-like ditches, all that made with a purpose of retaining as much water as possible. Those structures can be connected to others, destined directly to capture rainwater. I was thinking about two setups, respectively for rural environments and for the urban ones. In the rural landscape, those ponds and channels can be profiled so as to collect rainwater from the surface of the ground and conduct it into its deeper layers, through some system of inverted draining. I think it would be possible, under proper geological conditions, to reverse-drain rainwater into deep aquifers, which the neighbouring artesian wells can tap into. In the urban context, I would like to know more about those Chinese technologies used in their Sponge Cities programme (see Jiang et al. 2018 [11]).

The research I have done so far suggests that relatively small, local projects work better, for implementing this type of technologies, than big, like national scale endeavours. Of course, national investment programmes will be welcome as indirect support, but at the end of the day, we need a local community owning a project, possibly through an investment-fund-like institutional arrangement. The economic value conveyed by any kind of participatory title in such a capital structure sums up to the Net Present Value of three cash flows: net proceeds from selling hydroelectricity produced in small water turbines, reduction of the aggregate flood-related risk, as well as of the drought-related risk. I separate risks connected to floods from those associated with droughts, as they are different in nature. In economic and financial terms, floods are mostly a menace to property, whilst droughts materialize as more volatile prices of food and basic agricultural products.

In order to apprehend accurately the Net Present Value of any cash flow, we need to set a horizon in time. Very tentatively, by interpreting data from 2012, presented in a report published by IRENA (the same IRENA), I assume that relatively demanding investors in Europe expect to have a full return on their investment within 6,5 years, which I make 7 years, for the sake of simplicity. Now, I go a bit off the beaten tracks, at least those I have beaten so far. I am going to take the total atmospheric precipitations falling on various European countries, which means rainfall + snowfall, and then try to simulate what amount of ‘NPV = hydroelectricity + reduction of risk from floods and droughts’(7 years) could the retention of that water represent.

Let’s walse. I take data from FAOSTAT regarding precipitations and water retention. As a matter of fact, I made a query of that data regarding a handful of European countries. You can have a look at the corresponding Excel file UNDER THIS LINK. I rearranged bit the data from this Excel file so as to have a better idea of what could happen, if those European countries I have on my list, my native Poland included, built infrastructures able to retain 2% of the annual rainfall. The coefficient of 2% is vaguely based on what Shao et al. (2018 [12]) give as the target retention coefficient for the city of Xiamen, China, and their Sponge-City-type investment. I used the formulas I had already phrased out in « Sponge Cities », and in « La marge opérationnelle de $1 539,60 par an par 1 kilowatt », to estimate the amount of electricity possible to produce out of those 2% of annual rainfall elevated, according to my idea, into 10-metres-high water towers. On the top of all that, I added, for each country, data regarding the already existing capacity to retain water. All those rearranged numbers, you can see them in the Excel file UNDER THIS OTHER LINK (a table would be too big for inserting into this update).

The first provisional conclusion I have to make is that I need to revise completely my provisional conclusion from « Sponge Cities », where I claimed that hydroelectricity would have no chance to pay for any significant investment in sponge-like structures for retaining water. The calculations I have just run show just the opposite: as soon as we consider whole countries as rain-retaining basins, the hydroelectric power, and the cash flow dormant in that water is just mind-blowing. I think I will need to get a night of sleep just to check on the accuracy of my calculations.

Deranging as they are, my calculations bear another facet. I compare the postulated 2% of retention in annual precipitations with the already existing capacity of these national basins to retain water. That capacity is measured, in that second Excel file, by the ‘Coefficient of retention’, which denominates the ‘Total internal renewable water resources (IRWR)’ over the annual precipitation, both in 10^9 m3/year. My basic observation is that European countries have a capacity to retain water very similar in disparity to the intensity of precipitations, measured in mm per year. Both coefficients vary in a similar proportion, i.e. their respective standard deviations make around 0,4 of their respective means, across the sample of 37 European countries. When I measure it with the Pearson coefficient of correlation between the intensity of rainfall and the capacity to retain it , it yields r = 0,63. In general, the more water falls from the sky per 1 m2, the greater percentage of that water is retained, as it seems. Another provisional conclusion I make is that the capacity to retain water, in a given country, is some kind of response, possibly both natural and man-engineered, to a relatively big amount of water falling from the sky. It looks as if our hydrological structures, in Europe, had been built to do something with water we have momentarily plenty of, possibly even too much of, and which we should save for later.

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, any amount you consider appropriate, to my PayPal account. You can also consider going to my Patreon page and become my patron. If you decide so, I will be grateful for suggesting me two things that Patreon suggests me to suggest you. Firstly, what kind of reward would you expect in exchange of supporting me? Secondly, what kind of phases would you like to see in the development of my research, and of the corresponding educational tools?

[1] Bignetti, E. (2014). The functional role of free-will illusion in cognition:“The Bignetti Model”. Cognitive Systems Research, 31, 45-60.

[2] Bignetti, E., Martuzzi, F., & Tartabini, A. (2017). A Psychophysical Approach to Test:“The Bignetti Model”. Psychol Cogn Sci Open J, 3(1), 24-35.

[3] Bignetti, E. (2018). New Insights into “The Bignetti Model” from Classic and Quantum Mechanics Perspectives. Perspective, 4(1), 24.

[4] https://data.worldbank.org/indicator/FM.LBL.BMNY.GD.ZS last access July 15th, 2019

[5] Krippner, G. R. (2005). The financialization of the American economy. Socio-economic review, 3(2), 173-208.

[6] Foster, J. B. (2007). The financialization of capitalism. Monthly Review, 58(11), 1-12.

[7] Stockhammer, E. (2010). Financialization and the global economy. Political Economy Research Institute Working Paper, 242, 40.

[8] https://data.worldbank.org/indicator/EG.USE.PCAP.KG.OE last access July 15th, 2019

[9] https://data.worldbank.org/indicator/SP.URB.TOTL.IN.ZS last access July 15th, 2019

[10] https://data.worldbank.org/indicator/EG.FEC.RNEW.ZS last access July 15th, 2019

[11] 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.

[12] 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.

All hope is not lost: the countryside is still exposed

My editorial on You Tube

I am focusing on the possible benefits of transforming urban structures of at least some European cities into sponge-like structures, such as described, for example, by Jiang et al. (2018) as well as in my recent updates on this blog (see Sponge Cities). In parallel to reporting my research on this blog, I am developing a corresponding project with the « Project Navigator », made available by the courtesy of the International Renewable Energy Agency (IRENA). Figuring out my way through the « Project Navigator » made me aware of the importance that social cohesion has in the implementation of such infrastructural projects. Social cohesion means a set of common goals, and an institutional context that allows the appropriation of outcomes. In « Sponge Cities », when studying the case of my hometown, Krakow, Poland, I came to the conclusion that sales of electricity from water turbines incorporated into the infrastructure of a sponge city could hardly pay off for the investment needed. On the other hand, significant reduction of the financially quantifiable risk connected to floods and droughts can be an argument. Especially the flood-related risks, in Europe, already amount to billions of euros, and we seem to be just at the beginning of the road (Alfieri et al. 2015 [1]). Shielding against such risks can possibly make a sound base for social coherence, as a common goal. Hence, as I am structuring the complex concept of « Energy Ponds », I start with assessing risks connected to climate change in European cities, and the possible reduction of those risks through sponge-city-type investments.

I start with comparative a review of Alfieri et al. 2015 [2] as regards flood-related risks, on the one hand, and Naumann et al. (2015 [3]) as well as Vogt et al. (2018 [4]) regarding the drought-related risks. As a society, in Europe, we seem to be more at home with floods than with droughts. The former is something we kind of know historically, and with the advent of climate change we just acknowledge more trouble in that department, whilst the latter had been, until recently, something that happens essentially to other people on other continents. The very acknowledgement of droughts as a recurrent risk is a challenge.

Risk is a quantity: this is what I teach my students. It is the probability of occurrence multiplied by the magnitude of damage, should the s**t really hit the fan. Why adopting such an approach? Why not to assume that risk is just the likelihood of something bad happening? Well, because risk management is practical. There is any point in bothering about risk if we can do something about it: insure and cover, hedge, prevent etc. The interesting thing about it is that all human societies show a recurrent pattern: as soon as we organise somehow, we create something like a reserve of resources, supposed to provide for risk. We are exposed to a possible famine? Good, we make a reserve of food. We risk to be invaded by a foreign nation/tribe/village/alien civilisation? Good, we make an army, i.e. a group of people, trained and equipped for actions with no immediate utility, just in case. The nearby river can possibly overflow? Good, we dig and move dirt, stone, wood and whatnot so as to build stopbanks. In each case, we move along the same path: we create a pooled reserve of something, in order to minimize the long-term damage from adverse events.

Now, if we wonder how much food we need to have in stock in case of famine, sooner or later we come to the conclusion that it is individual need for food multiplied by the number of people likely to be starving. That likelihood is not evenly distributed across the population: some people are more exposed than others. A farmer, with a few pigs and some potatoes in cultivation is less likely to be starving than a stonemason, busy to build something and not having time or energy to care for producing food. Providing for the risk of flood works according to the same scheme: some structures and some people are more likely to suffer than others.

We apprehend flood and drought-related risks in a similar way: those risks amount to a quantity of resources we put aside, in order to provide for the corresponding losses, in various ways. That quantity is the arithmetical product of probability times magnitude of loss.

Total risk is a complex quantity, resulting from events happening in causal, heterogeneous chains. A river overflows and destroys some property: this is direct damage, the first occurrence in the causal chain. Among the property damaged, there are garbage yards. As water floods them, it washes away and further into the surrounding civilisation all kinds of crap, properly spoken crap included. The surrounding civilisation gets contaminated, and decontamination costs money: this is indirect damage, the second tier of the causal chain. Chemical and biological contamination by floodwater causes disruptions in the businesses involved, and those disruptions are costly, too: here goes the third tier in the causal chain etc.

I found some interesting insights, regarding the exposure to flood and drought-related risks in Europe, with Paprotny et al. (2018 [5]). Firstly, this piece of research made me realized that floods and droughts do damage in very different ways. Floods are disasters in the most intuitive sense of the term: they are violent, and they physically destroy man-made structures. The magnitude of damage from floods results from two basic variables: the violence and recurrence of floods themselves, on the one hand, and the value of human structures affected. In a city, a flood does much more damage because there is much more property to destroy. Out there, in the countryside, damages inflicted by floods change from the disaster-type destruction into more lingering, long-term impediments to farming (e.g. contamination of farmed soil), as the density of man-made structures subsides. Droughts work insidiously. There is no spectacular disaster to be afraid of. Adverse outcomes build up progressively, sometimes even year after year. Droughts affect directly the countryside much more than the cities, too. It is rivers drying out first, and only in a second step, cities experiencing disruptions in the supply of water, or of the rivers-dependent electricity. It is farm soil drying out progressively, and farmers suffering some damage due to lower crops or increased costs of irrigation, and only then the city dwellers experiencing higher prices for their average carrot or an organic cereal bar. Mind you, there is one type of drought-related disaster, which sometimes can directly affect our towns and cities: forest fires.

Paprotny et al. (2018) give some detailed insights into the magnitude, type, and geographical distribution of flood-related risks in Europe. Firstly, the ‘where exactly?’. France, Spain, Italy, and Germany are the most affected, with Portugal, England, Scotland, Poland, Czech Republic, Hungary, Romania and Portugal following closely behind. As to the type of floods, France, Spain, and Italy are exposed mostly to flash floods, i.e. too much rain falling and not knowing where to go. Germany and virtually all of Central Europe, my native Poland included, are mostly exposed to river floods. As for the incidence of human fatalities, flash-floods are definitely the most dangerous, and their impact seems to be the most serious in the second half of the calendar year, from July on.

Besides, the research by Paprotny et al. (2018) indicates that in Europe, we seem to be already on the path of adaptation to floods. Both the currently observed losses –human and financial – and their 10-year, moving average had their peaks between 1960 and 2000. After 2000, Europe seems to have been progressively acquiring the capacity to minimize the adverse impact of floods, and this capacity seems to have developed in cities more than in the countryside. It truly gives a man a blow, to their ego, when they learn the problem they want to invent a revolutionary solution to does not really exist. I need to return on that claim I made in the « Project Navigator », namely that European cities are perfectly adapted to a climate that does no longer exist. Apparently, I was wrong: European cities seem to be adapting quite well to the adverse effects of climate change. Yet, all hope is not lost. The countryside is still exposed. Now, seriously. Whilst Europe seem to be adapting to greater an occurrence of floods, said occurrence is most likely to increase, as suggested, for example, in the research by Alfieri et al. (2017 [6]). That sends us to the issue of limits to adaptation and the cost thereof.

Let’s rummage through more literature. As I study the article by Lu et al. (2019 [7]), which compares the relative exposure to future droughts in various regions of the world, I find, first of all, the same uncertainty which I know from Naumann et al. (2015), and Vogt et al. (2018): the economically and socially important drought is a phenomenon we just start to understand, and we are still far from understanding it sufficiently to assess the related risks with precision. I know that special look that empirical research has when we don’t really have a clue what we are observing. You can see it in the multitude of analytical takes on the same empirical data. There are different metrics for detecting drought, and by Lu et al. (2019) demonstrate that assessment of drought-related losses heavily depends on the metric used. Once we account for those methodological disparities, some trends emerge. Europe in general seems to be more and more exposed to long-term drought, and this growing exposure seems to be pretty consistent across various scenarios of climate change. Exposure to short-term episodes of drought seems to be growing mostly under the RCP 4.5 and RCP 6.0 climate change scenarios, a little bit less under the RCP 8.5 scenario. In practical terms it means that even if we, as a civilisation, manage to cut down our total carbon emissions, as in the RCP 4.5. climate change scenario, the incidence of drought in Europe will be still increasing. Stagge et al. (2017 [8]) point out that exposure to drought in Europe diverges significantly between the Mediterranean South, on the one hand, and the relatively colder North. The former is definitely exposed to an increasing occurrence of droughts, whilst the latter is likely to experience less frequent episodes. What makes the difference is evapotranspiration (loos of water) rather than precipitation. If we accounted just for the latter, we would actually have more water

I move towards more practical an approach to drought, this time as an agricultural phenomenon, and I scroll across the article on the environmental stress on winter wheat and maize, in Europe, by Webber et al. (2018 [9]). Once again, I can see a lot of uncertainty. The authors put it plainly: models that serve to assess the impact of climate change on agriculture violate, by necessity, one of the main principles of statistical hypotheses-testing, namely that error terms are random and independent. In these precise models, error terms are not random, and not mutually independent. This is interesting for me, as I have that (recent) little obsession with applying artificial intelligence – a modest perceptron of my own make – to simulate social change. Non-random and dependent error terms are precisely what a perceptron likes to have for lunch. With that methodological bulwark, Webber et al. (2018) claim that regardless the degree of the so-called CO₂ fertilization (i.e. plants being more active due to the presence of more carbon dioxide in the air), maize in Europe seems to be doomed to something like a 20% decline in yield, by 2050. Winter wheat seems to be rowing on a different boat. Without the effect of CO₂ fertilization, a 9% decline in yield is to expect, whilst with the plants being sort of restless, and high on carbon, a 4% increase is in view. With Toreti et al. (2019 [10]), more global a take is to find on the concurrence between climate extremes, and wheat production. It appears that Europe has been experiencing increasing an incidence of extreme heat events since 1989, and until 2015 it didn’t seem to affect adversely the yield of wheat. Still, since 2015 on, there is a visible drop in the output of wheat. Even stiller, if I may say, less wheat is apparently compensated by more of other cereals (Eurostat [11], Schills et al. 2018 [12]), and accompanied by less potatoes and beets.

When I first started to develop on that concept, which I baptised “Energy Ponds”, I mostly thought about it as a way to store water in rural areas, in swamp-and-meadow-like structures, to prevent droughts. It was only after I read a few articles about the Sponge Cities programme in China that I sort of drifted towards that more urban take on the thing. Maybe I was wrong? Maybe the initial concept of rural, hydrological structures was correct? Mind you, whatever we do in Europe, it always costs less if done in the countryside, especially regarding the acquisition of land.

Even in economics, sometimes we need to face reality, and reality presents itself as a choice between developing “Energy Ponds” in urban environment, or in rural one. On the other hand, I am rethinking the idea of electricity generated in water turbines paying off for the investment. In « Sponge Cities », I presented a provisional conclusion that it is a bad idea. Still, I was considering the size of investment that Jiang et al. (2018) talk about in the context of the Chinese Sponge-Cities programme. Maybe it is reasonable to downsize a bit the investment, and to make it sort of lean and adaptable to the cash flow possible to generate out of selling hydropower.

[1] Alfieri, L., Feyen, L., Dottori, F., & Bianchi, A. (2015). Ensemble flood risk assessment in Europe under high end climate scenarios. Global Environmental Change, 35, 199-212.

[2] Alfieri, L., Feyen, L., Dottori, F., & Bianchi, A. (2015). Ensemble flood risk assessment in Europe under high end climate scenarios. Global Environmental Change, 35, 199-212.

[3] Gustavo Naumann et al. , 2015, Assessment of drought damages and their uncertainties in Europe, Environmental Research Letters, vol. 10, 124013, DOI https://doi.org/10.1088/1748-9326/10/12/124013

[4] Vogt, J.V., Naumann, G., Masante, D., Spinoni, J., Cammalleri, C., Erian, W., Pischke, F., Pulwarty, R., Barbosa, P., Drought Risk Assessment. A conceptual Framework. EUR 29464 EN, Publications Office of the European Union, Luxembourg, 2018. ISBN 978-92-79-97469-4, doi:10.2760/057223, JRC113937

[5] Paprotny, D., Sebastian, A., Morales-Nápoles, O., & Jonkman, S. N. (2018). Trends in flood losses in Europe over the past 150 years. Nature communications, 9(1), 1985.

[6] Alfieri, L., Bisselink, B., Dottori, F., Naumann, G., de Roo, A., Salamon, P., … & Feyen, L. (2017). Global projections of river flood risk in a warmer world. Earth’s Future, 5(2), 171-182.

[7] Lu, J., Carbone, G. J., & Grego, J. M. (2019). Uncertainty and hotspots in 21st century projections of agricultural drought from CMIP5 models. Scientific reports, 9(1), 4922.

[8] Stagge, J. H., Kingston, D. G., Tallaksen, L. M., & Hannah, D. M. (2017). Observed drought indices show increasing divergence across Europe. Scientific reports, 7(1), 14045.

[9] Webber, H., Ewert, F., Olesen, J. E., Müller, C., Fronzek, S., Ruane, A. C., … & Ferrise, R. (2018). Diverging importance of drought stress for maize and winter wheat in Europe. Nature communications, 9(1), 4249.

[10] Toreti, A., Cronie, O., & Zampieri, M. (2019). Concurrent climate extremes in the key wheat producing regions of the world. Scientific reports, 9(1), 5493.

[11] https://ec.europa.eu/eurostat/statistics-explained/index.php/Agricultural_production_-_crops last access July 14th, 2019

[12] Schils, R., Olesen, J. E., Kersebaum, K. C., Rijk, B., Oberforster, M., Kalyada, V., … & Manolov, I. (2018). Cereal yield gaps across Europe. European journal of agronomy, 101, 109-120.

Sponge cities

My editorial on You Tube

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 = 10⁶ m2, not 10³. 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 r = 0,43: not very much, yet respectable, as correlations come.

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 R m3 of water per year, R/N per person per year, and they consume E kWh of energy per year, E/N per person per year. R divided by 8760 hours in a year (R/8760) is the approximate amount of water the local population needs to have in current constant supply. Same for energy: E/8760 is a good approximation of power, in kW, that the local population needs to have standing and offered for immediate use.

The city collects F millimetres of precipitation a year. Note that F mm = F m³/m². With a density of population D people per 1 km², the average square kilometre has what I call the sponge function: D*(R/N) = f(F*10⁶). Each square kilometre collects F*10⁶ cubic meters of precipitation a year, and this amount remains is a recurrent proportion to the aggregate amount of water that D people living on that square kilometre consume per year.

The population of N residents spend an aggregate P_E*E on energy, and an aggregate P_R*R on water, where P_E and P_R 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 LCOE, or Levelized Cost of Energy in an interval of time t, measured as LCOE(t) = [I_E(t) + M_E(t) + U_E(t)] / E, where I_E is the amount of capital invested in the fixed assets of the corresponding power installations, M_E is their necessary cost of current maintenance, and U_E is the cost of fuel used to generate energy. Per analogy, the levelized cost of water can be calculated as LCOR(t) = [I_R(t) + M_R(t) + U_R(t)] / R, 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 U_R(t) 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.

The supply of water and energy generates gross margins: E(t)*(P_E(t) – LCOE(t)) and R(t)*(P_R(t) – LCOR(t)). These margins are possible to rephrase as, respectively, P_E(t)*E(t) – I_E(t) – M_E(t) – U_E(t), and R(t)*P_R(t) – I_R(t) – M_R(t) – U_R(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 « LCO-whatever follows » type explicitly incorporate the yield on capital investment. Each unit of output is supposed to yield a return on investment I. 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 π = Q*P – Q*VC – FC – r*I – T, where Q and P are quantity and price, VC is the variable cost per unit of output Q, FC stands for the fixed costs, r is the price of capital (interest rate) on the capital I invested in the given business, and T represents taxes. In the same standard accounting, Thus calculated net income π is then put into the formula of internal rate of return on investment: 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 P_E = $0,21 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 $816 189 ≤ Q*P_E ≤ $952 220 a year from the city area, and $2 555 485 ≤ Q*P_E ≤ $2 981 400 a year from the metropolitan area.

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 $16 516 646 ≤ NPV(Q*P_E ; 8 years) ≤ $19 269 421 for the metropolitan area.

When 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.

[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.

Another idea – urban wetlands

My editorial on You Tube

I have just come with an idea. One of those big ones, the kind that pushes you to write a business plan and some scientific stuff as well. Here is the idea: a network of ponds and waterways, made in the close vicinity of a river, being both a reservoir of water – mostly the excess rainwater from big downpours – and a location for a network of small water turbines. The idea comes from a few observations, as well as other ideas, that I had over the last two years. Firstly. in Central Europe, we have less and less water from the melting snow – as there is almost no snow anymore in winter – and more and more water from sudden, heavy rain. We need to learn how to retain rainwater in the most efficient way. Secondly, as we have local floods due to heavy rains, some sort of spontaneous formation of floodplains happens. Even if there is no visible pond, the ground gets a bit spongy and soaked, flood after flood. We have more and more mosquitoes. If it is happening anyway, let’s use it creatively. This particular point is visualised in the map below, with the example of Central and Southern Europe. Thus, my idea is to utilise purposefully a naturally happening phenomenon, component of climate change.

Source: https://www.eea.europa.eu/data-and-maps/figures/floodplain-distribution last access June 20^th, 2019

Thirdly, there is some sort of new generation in water turbines: a whole range of small devices, simple and versatile, has come to the market. You can have a look at what those guys at Blue Freedom are doing. Really interesting. Hydroelectricity can now be approached in an apparently much less capital-intensive way. Thus, the idea I have is to arrange purposefully the floodplains we have in Europe into as energy-efficient and carbon-efficient places as possible. I give the general idea graphically in the picture below.

I am approaching the whole thing from the economics’ point of view, i.e. I want a piece of floodplain arranged into this particular concept to have more value, financial value included, than the same piece of floodplain just being ignored in its inherent potential. I can see two distinct avenues for developing the concept: that of a generally wild, uninhabited floodplain, like public land, as opposed to an inhabited floodplain, under incumbent or ongoing construction, residential or other. The latter is precisely what I want to focus on. I want to study, and possibly to develop a business plan for a human habitat combined with a semi-aquatic ecosystem, i.e. a network of ponds, waterways and water turbines in places where people live and work. Hence, from the geographic point of view, I am focusing on places where the secondary formation of floodplain-type of terrain already occurs in towns and cities, or in the immediate vicinity thereof. For more than one century, the growth of urban habitats has been accompanied by the entrenching of waterways in strictly defined, concrete-reinforced beds. I want to go the other way, and let those rivers spill around their waters, into wetlands, in a manner beneficial to human dwelling.

My initial approach to the underlying environmental concept is market based. Can we create urban wetlands, in flood-threatened areas, where the presence of the explicitly and purposefully arranged aquatic structures increases the value of property so as to top the investment required? I start with the most fundamental marks in the environment. I imagine a piece of land in an urban area. It has its present market value, and I want to study its possible value in the future.

I imagine a piece of land located in an urban area with the characteristics of a floodplain, i.e. recurrently threatened by local floods or the secondary effects thereof. At the moment ‘t’, that piece of land has a market value M(t) = S * m(t), being the product of its total surface S, constant over time, and the market price m(t) per unit of surface, changing over time. There are two moments in time, i.e. the initial moment t₀, and the subsequent moment t₁, after the development into urban wetland. Said development requires a stream of investment I(t₀ -> t₁). I want to study the conditions for M(t₁) – M(t₀) > I(t₀ -> t₁). As surface S is constant over time, my problem breaks down into units of surface, whence the aggregate investment I(t₀ -> t₁) being decomposed into I(t₀ -> t₁) = S * i(t₀ -> t₁), and the problem restated as m(t₁) – m(t₀) > i(t₀ -> t₁).

I assume the market price m(t) is based on two types of characteristics: those directly measurable as financials, for one, e.g. the average wage a resident can expect from a locally based job, and those more diffuse ones, whose translation into financial variables is subtler, and sometimes pointless. I allow myself to call the latter ones ‘environmental services’. They cover quite a broad range of phenomena, ranging from the access to clean water outside the public water supply system, all the way to subjectively perceived happiness and well-being. All in all, mathematically, I say m(t) = f(x₁, x₂, …, x_k) : the market price of construction land in cities is a function of k variables. Consistently with the above, I assume that f[t₁; (x₁, x₂, …, x_k)] – f[t₀; (x₁, x₂, …, x_k)] > i(t₀ -> t₁).

It is intellectually honest to tackle those characteristics of urban land that make its market price. There is a useful observation about cities: anything that impacts the value of urban real estate, sooner or later translates into rent that people are willing to pay for being able to stay there. Please, notice that even when we own a piece of real estate, i.e. when we have property rights to it, we usually pay to someone some kind of periodic allowance for being able to execute our property rights fully: the real estate tax, the maintenance fee paid to the management of residential condominiums, the fee for sanitation service (e.g. garbage collection) etc. Any urban piece of land has a rent tag attached. Even those characteristics of a place, which pertain mostly to the subjectively experienced pleasure and well-being derived out of staying there have a rent-like price attached to them, at the end of the day.

Good. I have made a sketch of the thing. Now, I am going to pass in review some published research, in order to set my landmarks. I start with some literature regarding urban planning, and as soon as I do so, I discover an application for artificial intelligence, a topic of interest for me, those last months. Lyu et al. (2017 [1]) present a method for procedural modelling of urban layout, and in their work, I can spot something similar to the equations I have just come up with: complex analysis of land-suitability. It starts with dividing the total areal of urban land at hand, in a given city, into standard units of surface. Geometrically, they look nice when they are equisized squares. Each unit ‘i’ can be potentially used for many alternative purposes. Lyu et al. distinguish 5 typical uses of urban land: residential, industrial, commercial, official, and open & green. Each such surface unit ‘i’ is endowed with a certain suitability for different purposes, and this suitability is the function of a finite number of factors. Formally, the suitability s_ik of land unit i for use k is a weighted average over a vector of factors, where w_kj is the weight of factor j for land use k, and r_ij is the rating of land unit i on factor j. Below, I am trying to reproduce graphically the general logic of this approach.

In a city approached analytically with the general method presented above, Lyu et al. (2017 [1]) distribute three layers of urban layout: population, road network, and land use. It starts with an initial state (input state) of population, land use, and available area. In a first step of the procedure, a simulation of highways and arterial transport connections is made. The transportation grid suggests some kind of division of urban space into districts. As far as I understand it, Lyu et al. define districts as functional units with the quantitative dominance of certain land uses, i.e. residential vs. industrial rather than rich folks’ estate vs. losers’ end, sort of.

As a first sketch of district division is made, it allows simulating a first distribution of population in the city, and a first draft of land use. The distribution of population is largely a distribution of density in population, and the corresponding transportation grid is strongly correlated with it. Some modes of urban transport work only above some critical thresholds in the density of population. This is an important point: density of population is a critical variable in social sciences.

Then, some kind of planning freedom can be allowed inside districts, which results in a second draft of spatial distribution in population, where a new type of unit – a neighbourhood – appears. Lyu et al. do not explain in detail the concept of neighbourhood, and yet it is interesting. It suggests the importance of spontaneous settlement vs. that of planned spatial arrangement.

I am strongly attached to that notion of spontaneous settlement. I am firmly convinced that on the long run people live where they want to live, and urban planning can just make that process somehow smoother and more efficient. Thus comes another article in my review of literature, by Mahmoud & Divigalpitiya (2019 [2]). By the way, I have an interesting meta-observation: most recent literature about urban development is based on empirical research in emerging economies and in developing countries, with the U.S. coming next, and Europe lagging far behind. In Europe, we do very little research about our own social structures, whilst them Egyptians or Thais are constantly studying the way they live collectively.

Anyway, back to by Mahmoud & Divigalpitiya (2019 [3]), the article is interesting from my point of view because its authors study the development of new towns and cities. For me, it is an insight into how the radically new urban structures sink into the incumbent spatial distribution of population. The specific background of this particular study is a public policy of the Egyptian government to establish, in a planned manner, new cities some distance away from the Nile, and do it so as to minimize the encroachment on agricultural land. Thus, we have scarce space and people to fit into, with optimal use of land.

As I study that paper by Mahmoud & Divigalpitiya, some kind of extension to my initial idea emerges. Those researchers report that with proper water and energy management, more specifically with the creation of irrigative structures like those which I came up with – networks of ponds and waterways – paired with a network of small hydropower units, it is possible both to accommodate an increase of 90% in local urban population, and create 3,75% more of agricultural land. Another important finding about those new urban communities in Egypt is that they tend to grow by sprawl rather than by distant settlement. New city dwellers tend to settle close to the incumbent residents, rather than in more remote locations. In simple words: it is bloody hard to create a new city from scratch. Habits and social links are like a tangible expanse of matter, which opposes resistance to distortions.

I switch to another paper based on Egyptian research, namely that by Hatata et al. 2019 [4], relative to the use of small hydropower generators. The paper is rich in technicalities, and therefore I note to come back to it many times when I will be going more into the details of my concept. For now, I have a few general takeaways. Firstly, it is wise to combine small hydro off grid with that connected to the power grid, and more generally, small hydro looks like a good complementary source of power, next to a regular grid, rather than a 100% autonomous power base. Still, full autonomy is possible, mostly with the technology of Permanent Magnet Synchronous Generator. Secondly, Hatata et al. present a calculation of economic value in hydropower projects, based on their Net Present Value, which, in turn, is calculated on the grounds of a basic assumption that hydropower installations carry some residual capital value V_r over their entire lifetime, and additionally can generate a current cash flow determined by: a) the revenue Rt from the sales of energy b) the locally needed investment I_t c) the operating cost O_t and d) the maintenance cost M_t, all that in the presence of a periodic discount rate r.

[1] Lyu, X., Han, Q., & de Vries, B. (2017). Procedural modeling of urban layout: population, land use, and road network. Transportation research procedia, 25, 3333-3342.

[2] Mahmoud, H., & Divigalpitiya, P. (2019). Spatiotemporal variation analysis of urban land expansion in the establishment of new communities in Upper Egypt: A case study of New Asyut city. The Egyptian Journal of Remote Sensing and Space Science, 22(1), 59-66.

[3] Mahmoud, H., & Divigalpitiya, P. (2019). Spatiotemporal variation analysis of urban land expansion in the establishment of new communities in Upper Egypt: A case study of New Asyut city. The Egyptian Journal of Remote Sensing and Space Science, 22(1), 59-66.

[4] Hatata, A. Y., El-Saadawi, M. M., & Saad, S. (2019). A feasibility study of small hydro power for selected locations in Egypt. Energy Strategy Reviews, 24, 300-313.

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