One Planet Living

Joe Wallwork

Joe Wallwork

As a student of MPE CDT, based at Imperial College, I am currently working on adaptive numerical methods in ocean dynamics, with particular interest in application to tidal power generation and tsunami modelling. I am passionate about finding solutions to the enormous problems posed by climate change and its consequences, and try to incorporate this into my lifestyle as much as possible.
Joe Wallwork

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If everyone in the world lived as the average UK resident, three planets’ worth of natural resources would be required to support humanity. By no means is this a responsible example of sustainability. But any such negative statement is useless unless accompanied with a proposed better alternative. Are there countries on Earth which pose as a model society, whereby extrapolation of their consumption rates would give true sustainability?



Last month, a fellow MPE CDT student and I volunteered on a project with the Nuffield Foundation, which saw six maths students spend 2 weeks at Imperial College London during the summer between their A-level years. Together, we brainstormed some ideas about important aspects of mathematics (such as geometry, calculus and numerical methods) and important elements of Planet Earth (such as the atmosphere, oceans, flora and fauna).

Following their brainstorming, the students ranked by importance and urgency some related problems, such as predicting temperature rise due to climate change, analysing the way in which glacier melt leads to sea level rise and trying to estimate how many years’ worth of natural resources remain for humanity’s usage. In the end, the students decided they were most interested in the latter problem and set to work trying to figure out how they could use their mathematical abilities to tackle this problem and what the implications of their findings might mean.

The students decided to consider two developed countries (Japan and South Africa) and two developing countries (Cuba and Uganda), in order to see the range of impacts being made across the world. Assuming the birth rate and death rate of these countries to be constant, the students considered two simple models of population growth: the Malthus model and the Logistic model

The former model prescribes an exponential growth or exponential decline of population, with the rate of increase or decline determined by the birth rate and death rate.  For the logistic model, a so-called carrying capacity must be specified, beyond which a population could not be sustained by the planet whatsoever. Demographers estimate this value to be around 10 billion, which we are not so far away from at the present time. From these simple models, the students could make basic predictions of the future populations of the countries considered, and indeed, the world population if everyone gave birth and died at a constant rate.

As well as birth and death rate data, the students collected information regarding the biomass, coal, gas and oil stocks and consumption rates of their chosen countries. Using the previously estimated population curves, the students were able to approximate the associated usage of the four fuels. The latter three models are fairly simple, since a constant rate of consumption per citizen is assumed, and there is effectively no return rate of the fuel stocks. In the case of biomass, however, the students had to consider the fact that trees grow back over a few years, and so the resulting equations are a little more difficult to solve.

Having forecasted the diminishing of the fuel reserves, the students were able to go on to say how much CO2 would be released into the atmosphere by each country, estimate the consequent concentration in the atmosphere and provide a first approximation to the associated temperature increase to the planet. Here they made a major assumption that CO2 is not re-absorbed, which is of course not true in reality. However the project centred on making a first approximation to what is going on, so many simplifications must be made.


Rather than copying their results, I have considered similar calculations for four other countries which pose as markedly different examples in their approaches to environmental protection and resource consumption. Consider India, China, UK and USA. As can be seen in the map above, the One Planet Living initiative claims these countries fall into the categories of using less than 1, 1-2, 2-4 and more than 4 planets when their trends are projected onto the worldwide populace, respectively. That is, if the entire world were to behave in the same way as these countries in terms of population change and resource usage, the number of planets’ worth of resources needed would be as indicated. Python code is available for how I calculated these projections on GitHub.*


In the following plots, only the contributions of domestic coal, natural gas and oil are considered. As has been mentioned, the Nuffield project students also considered biomass, but they discovered that it is rather difficult to get data on the consumption thereof and the mass to CO2 conversion varies depending on the particular biomass fuel used. Of course, there are plenty of other resources (such as food, clean water and rare earth materials) and plenty of other sources of pollution (such as emissions from livestock, waste and aviation) which could be considered, but here we focus on the three main fossil fuels since they make contributions in both categories.

For an example of the predictions relating to one resource, if the whole world acted as the USA, the graph above indicates that oil reserves would drop dramatically, completely drying up after 70 years. Similar plots can be made for the other fuels, through which we can get a picture of the total resources used, and hence the total carbon emissions. Subject to a number of assumptions both stated here and neglected, the associated additional mean warming to the atmosphere would look as displayed in the plot below. From this plot, if the whole world acted as the UK or India in terms of its population change and fuel usage, we should expect an extra warming contribution of around 2°C after one century has passed. In the case of China, this would be more like 4°C and in the case of the USA 10°C.

temp_change_Malthus_g=OFF_trees=OFFThese are very rough estimates, as has already been mentioned, but there seems to be significant evidence to suggest that we shouldn’t only be concerned with using the resources of one planet, but also which resources we choose to use, and at what rate. This is especially true when taking into consideration that the international agreement made at COP21 aims to keep warming below 2°C above pre-industrial levels. UK Met Office research indicates the world has already warmed 1°C since then.

Calculations above were performed in the Malthusian case. In the case of the Logistic model, predictions are more conservative, due to the world population being unable to breach 10 billion. The resulting plot is indicated below. There the range of additional temperature increases is approximately 0.3-3°C. Even under this more conservative approach, it doesn’t look likely that we could meet the cumulative 2°C target in any case.

temp_change_Logistic_g=OFF_trees=OFFNot only are there some countries which use ‘more than one planet’ and some which use ‘less than one planet’, the average taken across all of humanity is currently actually about 1.6 planets. The interpretation of this claim is not that we are generating resources out of nothing or collecting them from space, but that we are consuming resources faster than they can regenerate naturally. Resources are being used at such an alarming rate, and the natural environment is being damaged so badly, that the regenerative ability of the planet has been significantly reduced.



This summer’s Nuffield Project was not the first time I considered mathematical problems related to One Planet Living. On Open Data Day in March this year, I attended a hackathon at the European Centre for Medium-range Weather Forecasts (ECMWF) in Reading. There, a team of us attempted to create an app which enables the user to calculate their carbon footprint and thereby to find out whether or not their contribution is greater or smaller than the average for their country of origin. Whilst in the Nuffield Project we only had time to consider fuel usage, in this project only road, rail, bus and aviation transportation was taken into consideration.

Sadly, the app we worked on in the hackathon never came to a particularly user friendly stage, due to tight time constraints and a lack of app developing experience. However, the Bioregional initiative provides a calculator for finding out how many planets would be required to sustain a planet of Yous, covering far more aspects than we could ever have hoped to consider. Even if you produce zero waste, cycle everywhere and never fly or drive, it is fiendishly difficult to become a One Planet Citizen. My output is shown below, and I clearly have some progress to make.

Screen Shot 2017-09-23 at 09.23.36.png

The different coloured sections on the bottom bar correspond to energy generation, transport, food, goods, government, capital assets and services, respectively. I’m not going to start making excuses for why the calculator tells me I use more than one planet, but I will just make a few comments on its output:

  • Notice that at least 28% of my footprint is purely due to the government, dispelling the myth that individuals can tackle climate change, resource conservation and ecology deprivation completely on their own. Authorities have to make an effort, too.
  • Goods, food and services have extra footprint included because there is a large implicit contribution in supply chains. This factor points out that businesses have an environmental responsibility, as well as governments. Personal impact in this case can be reduced by shopping at second hand shops, charity shops and local markets.
  • Finally, it is difficult to improve on the energy contribution if you live in rented accommodation, since it is up to your landlord to install things like loft insulation, condensing boilers, cavity wall insulation and solar panels. However, if you get on with them you could maybe consider suggesting these.



Last month I attended a symposium of talks at Imperial College entitled ‘Balancing sustainability and development: cities in the 21st century’ on the need to adapt future cities to the omnicrisis of issues faced by present and future citizens, such as overpopulation, rising temperatures, inequality, resource scarcity and overstressed infrastructures. The symposium was opened by a talk by David Thorpe, author of ‘The One Planet Life: a Blueprint for Low Impact Living’. He claims the world’s ‘biocapacity’ was breached in the early 1970’s and since then we have been running on ‘borrowed time’. The World Wildlife Foundation (WWF) lists nine ‘planetary boundaries’, four of which have already been passed: climate change, biosphere integrity, soil quality and nitrate pollution.

slide.5planetintroThorpe claims, with the present population, the only way to ‘get back on track’ is for the entire world to have a ecological footprint as in Central Africa. This does not, imply the reduction in living standards one might expect for more privileged citizens, as in the West. For instance, whilst research by the One Planet Living initiative indicates that residents of the USA use ‘two more planets’ worth of resources than the average European (see diagram opposite), there are many metrics by which one might claim Europeans are better off than Americans.** Does all that extra resource and carbon impact really make for a happier, more fulfilled life? Who says the UK couldn’t reduce its impact and maintain the same quality of life or, indeed, improve it?

Thorpe works on a One Planet Living initiative in Wales, where the word ‘sustainability’ has been made equivalent to the ‘well-being of future generations’. His motto,

“if it gets measured, it gets saved”

motivates the reduction of ecological footprint in line with closer control on consumption levels and methods. Thorpe’s thinking recently influenced a public advice spreadsheet available on the Welsh government website. In principle, the creation of a One Planet society is not an enormous undertaking. All that is required is some careful planning of how waste is to be dealt with, how electricity is to be generated and which materials are to be used for construction and packaging (if any). What is difficult, on the other hand, is converting a currently damaging society to a One Planet one.

Model cities do exist. Thorpe points to Freiburg, Germany, which has been heralded by many as a leading example, through its restrictions on polluting traffic, energy saving schemes and use of efficient technology. Perhaps unexpectedly, China also provides an example in terms of its recent efforts to develop vertical farming, which requires less space, water and effort and can bring impressively increased yields of staple foods.

One conclusion of the symposium was that there are very real limits to growth, to quote the Club of Rome (1972). This is something discussed by John Burnside in his once-three-weekly Nature column in New Statesman this January. There he pointed out the inherent contradictions between the growth modern countries are fixated on and the very clear bounds enforced by the forces of nature. That we can continue as we have in the past decades indefinitely and with little to no consequence for the residents (human and otherwise) of this planet is an utter lie.

Can you take up the One Planet challenge? In a way it is the least you can do.


[Also posted on my personal blog Cut Waste, Not Trees Down]



*: References for resource consumption data used:

**: In a New York Review of Books article, Europe vs. America, Tony Judt points to the following statistics:

  • “[T]he EU has 87 prisoners per 100,000 people; America has 685.”
  • “[A]ccording to the OECD a typical employed American put in 1,877 hours in 2000, compared to 1,562 for his or her French counterpart.”
  • “Whereas Swedes get more than thirty paid days off work per year and even the Brits get an average of twenty-three, Americans can hope for something between four and ten, depending on where they live.”
  • “45 million Americans have no health insurance at all.”

[Image sources: headermap, plots (and Python code), calculatorplanets]

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