Markus Andrews

PVWPS operationThe motor and the pump are built in together14 and the motor-pump set is submersed in the borehole under the water43. Control equipment is also installed between the PV modules and the motor-pump and/or integrated to the motor-pump set in the borehole14,17. This equipment allows the motor-pump to stop and also to operate the motor-pump and the PV modules at their best operating points14. Once the water is pumped, it might then be stored in a water tank to mitigate the variability of solar resources14,29. When pumping starts, a cone of depression of radius rc is formed and there is a drawdown Hb,d in the borehole (see Fig. 1). The higher the pumped flow rate, the higher the drawdown Hb,d and therefore the deeper the water in the borehole Hb. If Hb reaches the position of the motor-pump Hmp, the motor-pump automatically switches off, therefore preventing the motor-pump from running dry44. The motor-pump remains shut down during a period Δtshut, after which it makes an attempt to restart44.Input data processingWe observe in Table 1 that the datasets have varying spatial resolutions. In the article, we use the spatial resolution of the irradiance map, 0.2° (~22 km). Indeed, this resolution is sufficient for the purposes of this article and it allows to divide computing time and memory requirements by ~16 in comparison to the 0.05° resolution. At this 0.2° resolution, the total area of Africa of 30 million km2 is divided into 62,000 pixels. We apply this resolution of 0.2° to all datasets by nearest interpolation.No exact value of the static water depth Hb,s, transmissivity T and saturated thickness Hst are provided for each location by the original source but only a range of variation. For instance, for −15.8° (lat) & 21.9° (lon), the saturated thickness Hst is comprised between 25 and 100 m. In most cases, we consider the middle of the range (e.g., 62.5 m in the example). The only two exceptions are: when Hb,s is higher than 250 m, we consider 300 m (same for Hst); and, when Hb,s is between 0 and 7 m, we consider 7 m45. Due to the lack of available information, the input groundwater data provided in Table 1 are considered to remain constant over time.Reference46 provides complete irradiance data with a time step of 15 min from 2013 to 2020 across Africa. In this article, except mentioned otherwise, we use irradiance data from 2020 with a 30-min time step (by taking one point every two 15-min points), instead of all the available complete irradiance data. It divides computing time and memory requirements by ~16. Additionally, it produces reduced and acceptable deviations on the results. Indeed, for 100 randomly chosen locations, we simulated the pumped volume V, for the three considered PVWPS sizes, using (1) irradiance data from 2013 to 2020 with a 15-min time step and (2) irradiance data from 2020 with a 30-min time step. For these locations, the absolute error on volume V is systematically lower than 7.9% and the average absolute error is 2%. These results are coherent with the observed low influence of irradiance on the pumped volume in comparison to groundwater resources. Thanks to the consideration of this reduced irradiance vector, the random access memory (RAM) and the computing time required to obtain a map of final results (such as Fig. 5b) are respectively 38 Gb and 10 h (time for Intel Xeon E5-2643 3.3 GHz processors and 96 GB RAM, running on Debian 4.19.194-2), which is more reasonable.Atmospheric sub-modelFor each location, the irradiance on the plane of the PV modules Gpv at time t can be deduced from satellite data by47,48:$${G}_{{{{{{rm{pv}}}}}}}left(tright)={G}_{{{{{{rm{bn}}}}}}}left(tright){{cos }}left({{{{{rm{AOI}}}}}}left(t,theta ,alpha right)right)+{G}_{{{{{{rm{gh}}}}}}}left(tright)kappa frac{1-{{cos }}left(theta right)}{2}+{G}_{{{{{{rm{dh}}}}}}}left(tright)frac{1+{{cos }}left(theta right)}{2}$$
(1)
where κ is the albedo of the surrounding environment, θ and α are the tilt and azimuth of the PV modules and AOI is the angle of incidence between the sun’s rays and the PV modules. The albedo κ is taken equal to 0.2 because it corresponds to the albedo of cropland, which is a common environment in the rural areas considered49. In any case, additional simulations show that the value of the albedo has a negligible effect on the pumped volume V. AOI is computed using the MATLAB toolbox PVLIB developed by the Sandia National Laboratories50.For each location, the azimuth α and the tilt θ of the PV modules are chosen to maximize the irradiance on the plane of the PV modules Gpv. The azimuth α is taken equal to51:$$alpha =left{begin{array}{c}180^circ quad {{{{{rm{if}}}}}},phi , > ,0\ 0^circ quad {{{{{rm{if}}}}}},phi , < ,0end{array}right.$$ (2) where ϕ is the latitude of the location. The tilt is taken equal to51:$$theta =left{begin{array}{c}{{max }},(10,1.3793+(1.2011+(-0.014404+0.000080509phi )phi )phi )quad{{{{{rm{if}}}}}},phi > ,0\ {{min }},(-10,-0.41657+(1.4216+(0.024051+0.00021828phi )phi )phi )quad{{{{{rm{if}}}}}},phi , < ,0end{array}right.$$ (3) As evidenced by Eq. (3), the tilt should be higher than 10° or lower than −10°, so that the PV modules are tilted enough to be cleaned when it rains.Photovoltaic modules sub-modelConsidering that the maximum power point tracking of the PV modules is correctly performed, a simplified model to compute the power P produced by the modules is used:$$Pleft(tright)=frac{{G}_{{{{{{rm{pv}}}}}}}left(tright)}{{G}_{0}}{P}_{{{{{{rm{p}}}}}}}left(1-{c}_{{{{{{rm{pv}}}}}},{{{{{rm{loss}}}}}}}right)$$ (4) where G0 is the reference irradiance (1000 W m−2), Pp is the peak power of the PV modules in standard test conditions (STC) and cpv,loss is a coefficient that represents the losses (e.g., soiling, temperature, mismatch, wiring52,53) at the level of the PV modules. For the sake of simplicity, and as we consider a generic PVWPS, we consider that cpv,loss is independent of the operating point of the PV modules, of the time, and of the location. We take it constant, equal to a single value (see Table 2).Hydraulic sub-modelThe total dynamic head TDH between the motor-pump and the pipe output is given by54:$${TD}Hleft(tright)={H}_{{{{{{rm{b}}}}}}}(t)+{H}_{{{{{{rm{p}}}}}}}(t)$$ (5) where Hb is the water depth in the borehole and Hp is the additional head due to pressure losses in the pipe.The water depth in the borehole Hb is given by (see Fig. 1)42:$${H}_{{{{{{rm{b}}}}}}}(t)={H}_{{{{{{rm{b}}}}}},{{{{{rm{s}}}}}}}+{H}_{{{{{{rm{b}}}}}},{{{{{rm{d}}}}}}}(t)$$ (6) where Hb,s is the static water depth and Hb,d is the drawdown. The drawdown is composed of two parts:$${H}_{{{{{{rm{b}}}}}},{{{{{rm{d}}}}}}}(t)={H}_{{{{{{rm{b}}}}}},{{{{{rm{d}}}}}}}^{{{{{{rm{a}}}}}}}(t)+{H}_{{{{{{rm{b}}}}}},{{{{{rm{d}}}}}}}^{{{{{{rm{b}}}}}}}(t)$$ (7) where ({H}_{{{{{{rm{b}}}}}},{{{{{rm{d}}}}}}}^{{{{{{rm{a}}}}}}}(t)) is the head loss due to aquifer losses and ({H}_{{{{{{rm{b}}}}}},{{{{{rm{d}}}}}}}^{{{{{{rm{b}}}}}}}(t)) is the head loss due to borehole losses.The head loss due to aquifer losses ({H}_{{{{{{rm{b}}}}}},{{{{{rm{d}}}}}}}^{{{{{{rm{a}}}}}}}(t)) depends on the pumping flow rate Q, the aquifer transmissivity T, the borehole radius rb, and a length parameter rc representing the distance of water travel to replace the water pumped out. From dimensional analysis, we expect that (tfrac{{H}_{{{{{{rm{b}}}}}},{{{{{rm{d}}}}}}}^{{{{{{rm{a}}}}}}}left(tright)cdot T}{Qleft(tright)}) should be a function of (tfrac{{r}_{{{{{{rm{c}}}}}}}}{{r}_{{{{{{rm{b}}}}}}}}). We thus propose the following model for ({H}_{{{{{{rm{b}}}}}},{{{{{rm{d}}}}}}}^{{{{{{rm{a}}}}}}}), which is derived from Thiem equation55:$${H}_{{{{{{rm{b}}}}}},{{{{{rm{d}}}}}}}^{{{{{{rm{a}}}}}}}left(tright)=frac{{{{{{rm{ln}}}}}}left(frac{{r}_{{{{{{rm{c}}}}}}}}{{r}_{{{{{{rm{b}}}}}}}}right)}{2pi T}Qleft(tright)$$ (8) where rc can be considered the effective radius of the cone of depression. This model satisfies horizontal, radial and steady Darcy flow in a uniform, homogeneous and isotropic aquifer. It captures the essential features for aquifer losses: ({H}_{{{{{{rm{b}}}}}},{{{{{rm{d}}}}}}}^{{{{{{rm{a}}}}}}}(t)) proportional to pumped flow rate and inversely proportional to transmissivity45. Though the flow is transient, only simplified steady-state models, as the one of Eq. (8), can be applied with the available information as dynamic models would require pumping tests. Furthermore, we consider that the radius of the cone of depression rc is comprised between 100 and 1000 m and, to correlate it to a measured quantity, that it depends linearly on the groundwater recharge R: for the lowest recharge (0 m/year), rc is equal to 1000 m; for the highest one (0.2947 m year−1), rc is equal to 100 m; in-between, rc is obtained linearly from the recharge (rc = 1000–3054 · R). Thus, groundwater recharge R is used to constrain the size of the cone of depression.The head loss due to borehole losses ({H}_{{{{{{rm{b}}}}}},{{{{{rm{d}}}}}}}^{{{{{{rm{b}}}}}}}(t)) is given by56:$${H}_{{{{{{rm{b}}}}}},{{{{{rm{d}}}}}}}^{{{{{{rm{b}}}}}}}left(tright)=beta {Q}{left(tright)}^{2}$$ (9) where β is a coefficient related to the borehole design. For the yields considered in this article, ({H}_{{{{{{rm{b}}}}}},{{{{{rm{d}}}}}}}^{{{{{{rm{b}}}}}}}(t)) usually remains lower than a few meters but, as ({H}_{{{{{{rm{b}}}}}},{{{{{rm{d}}}}}}}^{{{{{{rm{b}}}}}}}(t)) depends on the square of the pumped flow rate, it may be more important for larger abstraction capacities.The additional head due to pipe losses Hp is given by57:$${H}_{{{{{{rm{p}}}}}}}left(tright)={H}_{{{{{{rm{p}}}}}},{{{{{rm{ma}}}}}}}left(tright)+{H}_{{{{{{rm{p}}}}}},{{{{{rm{mi}}}}}}}left(tright)$$ (10) where Hp,ma(t) corresponds to losses that occur along the pipe length (also called “major losses”) and Hp,mi(t) corresponds to losses at junctions such as elbows and curvatures (also called “minor losses”). Hp,ma(t) is given by57:$${H}_{{{{{{rm{p}}}}}},{{{{{rm{ma}}}}}}}left(tright)=frac{8f}{{pi }^{2}g{D}_{{{{{{rm{p}}}}}}}^{5}}{L}_{{{{{{rm{p}}}}}}}Q{left(tright)}^{2}$$ (11) where g is the gravitational acceleration (9.81 m s−2), Dp is the pipe diameter, Lp is the pipe length, Q is the pumped flow rate, and f is the friction coefficient between the water and the pipe. We approximate the pipe length Lp to be equal to the depth of the motor-pump Hmp (see Fig. 1). The expression of f depends on the value of the Reynolds number ({{{{{rm{Re}}}}}}=tfrac{4Q}{pi {D}_{{{{{{rm{p}}}}}}}w}), where w is the water kinematic viscosity (taken equal to 1 × 10−6 m2 s−1)57: for Re More

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Chasing Icebergs: How Frozen Freshwater Can Save the Planet Matthew H. Birkhold Viking (2023)The flavour of chilled Svalbarði-brand water, melted from an iceberg just 1,000 kilometres from the North Pole, is described by the company as “like catching snowflakes on the tongue”. Bottled in Longyearbyen, a tiny metropolis in Norway’s Svalbard archipelago, Svalbarði water is airlifted to luxury locales in London, Sydney, Florida and Macau. “Taste the Arctic to Save the Arctic,” its website croons, promoting the supposed carbon neutrality of the water, which sells online for €99.95 (US$107) for a 750-millilitre bottle.That price is far out of reach for most of the world’s people, including the one in four who lack safe drinking water. In Chasing Icebergs, Matthew Birkhold, a scholar of law, culture and the humanities, considers whether it’s possible to slake the world’s thirst with the two-thirds of global fresh water that is locked away in ice caps and glaciers — “stuck at the poles in gigantic fortresses of ice”, in his words.Some are already at it — and not just epicureans quaffing Svalbarði. In Newfoundland, Canada, Birkhold interviews “iceberg cowboy” Ed Kean, who wrangles bergs from the frigid sea, selling the water to cosmetics companies and breweries. In Qaanaaq, Greenland’s northernmost town, Birkhold notes, the public water supply includes filtered and treated iceberg melt.
Towing icebergs to arid regions to reduce water scarcity
There’s more where that came from. By one estimate, some 2,300 cubic kilometres of ice breaks off from Antarctica every year. More than 100,000 Arctic and Antarctic icebergs melt into the ocean annually, according to a 2022 United Nations report. A relatively small, 113-million-tonne iceberg, says Birkhold, could be towed from Antarctica to Cape Town, South Africa, to supply 20% of the city’s water needs for a year. What’s not to like?Quite a lot, perhaps. “To write this book, I have talked to dozens of scientists,” Birkhold writes. “They are uniformly dubious.” Palaeoclimatologist Ellen Mosley-Thompson has led nine expeditions to Antarctica and six to Greenland to extract ice cores. “Make sure you write that I am skeptical of iceberg towing,” she instructs him.Less sceptical is master mariner Nick Sloane, the brains behind the Cape Town plan. Using satellite data to find the best berg, his “team of glaciologists, engineers and oceanographers” plans to catch it in a giant net and pull it by tugboat into the mighty Antarctic Circumpolar Current, and thence into the north-flowing Benguela Current towards South Africa.

Icebergs are sometimes towed to prevent damage to oil platforms.Credit: Greg Locke/Reuters

Sloane has estimated the cost at a cool $100 million, plus an extra $50 million or so to melt the ice and funnel the fresh water to land, if the iceberg hasn’t melted into the sea or fallen apart en route. In various interviews, Cape Town officials have expressed themselves as less than enthused.Sloane’s plans have yet to materialize. Meanwhile, POLEWATER, a Berlin-based company, has been working for almost a decade on a similar plan — to haul frozen fresh water to the western coast of Africa and the Caribbean, where the company intends to give it away to those in dire need. It, too, will use satellites to locate suitable bergs, but once it has relocated them, it plans to pump meltwater from pools on top into easily transportable gigantic bags.Then there’s the UAE Iceberg Project, the dream of Emirati inventor Abdulla Alshehhi to import an Antarctic iceberg to the Fujairah coast of the United Arab Emirates. An animated promotion features penguins and polar bears — species hailing from opposite poles — posing dolefully on the iceberg. Alshehhi has said that “it will be cheaper to bring in these icebergs” than to desalinate seawater — a common technique in the Middle East.
World’s largest ice sheet threatened by warm water surge
Desalination provides at least 35 trillion litres of drinking water globally every year. Birkhold notes that it is prohibitively expensive in many places. It also relies on fossil fuels for energy, and pollutes the ocean with excess salt. But he offers limited information on other, perhaps more effective, alternatives to iceberg towing, such as recycling municipal wastewater or tapping brackish water for crop irrigation. He offers no data on more esoteric sources of water, such as fog harvesting, used by remote communities in Chile, Morocco and South Africa. Nor does he address initiatives to reduce water waste or increase efficiency of use.Birkhold speculates that if iceberg harvesting succeeds, it might not remain the province of quixotic entrepreneurs — bigger, water-hungry enterprises might muscle in with their “deep coffers and profit-driven approach”. The race is largely unregulated: few national laws address iceberg use, and no international agreements clarify who can capture and sell these freshwater resources. If they are to be exploited fairly, the author concludes, “we need to decide who gets to use icebergs — and how and how many — in a way that is just and equitable”.Birkhold is engagingly honest about potential pitfalls. But if the enterprise could succeed, enormous quantities of fresh water that would otherwise melt into the ocean could be delivered to parched regions. Kudos to the author for diving in — whether or not it is ever realized.

Competing Interests
The author declares no competing interests. More

Study design and hypothesesThe encouragement of the Chinese central government to local governments to adopt the PPP model through the top-down procedure and build and operate WTI has created favourable external policy circumstances for the development of wastewater treatment PPP projects. However, the acceptance of the PPP model by both local governments and private capital is rooted in the positive effect of it on improving the UWTE. In China there is no completely private-owned WTI before. Compared to the original government monopoly on the construction and operation of the WTI, the introduction of private capital participation is equipped with conditions to improve the UWTE. The participation of private capital can donate sufficient funds, scientific management experience, and advanced technology to the construction and operation of the regional, quasi-natural monopoly, and public welfare WTI21, which are key elements that determine the UWTE. Furthermore, the urban wastewater treatment field was in a state of no market competition before the introduction of private capital, and the government’s early monopoly ensured that private capital could obtain both economic benefits and performance with exclusive agency rights after joining. Meanwhile, the government would conduct a performance assessment of the quality of wastewater treatment during construction and operation, and private capitals whose wastewater treatment efficiency failed to meet the requirements would be barred from obtaining performance benefits40. Therefore, private capital is inherently incentivised to ensure the UWTE and minimise profit loss. Most of the private capital involved in the construction and operation of WTI in China comes from state-owned enterprises, partly due to the remarkable cooperation between the local government and state-owned enterprises at the beginning of the market economy reform41. This is convenient for both sides in reducing the cost of supervising due to information asymmetry in the principal-agent relationship and to facilitate the unique advantages of state-owned capital to undertake social responsibility. Therefore, Hypothesis 1 is proposed:UWTE is high in prefecture-level cities that have introduced the PPP model compared to prefecture-level cities that have not adopted the PPP model for the construction and operation of WTI.The return mechanism is related to the risk sharing of the costs of WTI construction and operation. Part of the purpose of introducing private capital is to share the cost risk of the government’s monopoly on the construction and operation of infrastructure by exchanging the government’s appropriate concession of operating revenue42; however, excessive cost and risk sharing reduces the probability of private capital participation in the construction and operation of infrastructure43. In China, the return mechanisms of the public–private WTI include user payment, government payment, and feasibility gap subsidy, of which the cost risks of construction and operation under the first two return mechanisms are primarily borne unilaterally by the private capital and the government, respectively44, whereas the cost risks of construction and operation under the latter are borne by the government to fill the gap of user payment39. Accordingly, Hypothesis 2 is proposed:The return mechanism of the feasibility gap subsidy has a greater impact on improving the UWTE than the mechanisms of user payment and government payment.The way to choose private capital to cooperate with the government is related to the efficiency of the construction and operation of the WTI. Private capital selected through competitive procurement usually exhibits sufficient funds, scientific management experience, and innovative technology45. Cooperation between the government and this type of private partner helps obtain the optimal construction and operation plan at the lowest cost. The adoption of competitive procurement can improve efficiency while saving transaction costs, especially for infrastructures with large capital scale and long term and complicated operational systems, such as urban wastewater treatment38. In China, the competitive procurement mechanism of PPPs for WTI includes public bidding, competitive negotiation, invitational bidding, and competitive consultation, whereas the non-competitive procurement mechanism mainly refers to single-source procurement46. In accordance with this, Hypothesis 3 is proposed:The competitive procurement mechanism has a greater impact on improving the UWTE than the single-source procurement mechanism.The PPP is ultimately a contract between the principal and the agent that specifies how risks are shared and how benefits are distributed40. Construction and operation of WTI under the PPP model usually require long-term contracts. This means that contracts are often incomplete, and the allocation of remaining control rights has a significant impact on the incentives for private capital parties to participate. Existing research suggests that the greater the remaining control the private capital receives, the stronger their incentive to participate in the construction and operation of infrastructure, and the more they pursue innovation and efficiency47. The remaining control right is related to the manner in which the infrastructure is operated48. In China, PPPs for WTI operate through outsourcing (e.g. Operation and Maintenance [OM], Management Contract [MC], and Build-Transfer [BT]), franchising (e.g. Build-Operate-Transfer [BOT], Build-Own-Operate-Transfer [BOOT], Transfer-Operate-Transfer [TOT], and Rehabilitate-Operate-Transfer [ROT]), and privatisation (e.g. Build-Own-Operate [BOO] and Buy-Build-Operate [BBO]). Therefore, Hypothesis 4 is proposed:Privatised operations have a greater impact on improving UWTE than outsourcing and franchising.Promotion after demonstration has long been a feature of public policy formulation and implementation by the Chinese government, and this is also true for the construction and operation of wastewater treatment PPP projects. Selecting a portion of these projects for demonstration can facilitate pre-judgement of the issues encountered in the construction and operation of infrastructure and improve efficiency49. The demonstration of WTI is prioritised for various government policies and funding support and is subject to stringent monitoring by the government50. Therefore, to obtain priority support from the government, WTIs that have not entered the demonstration have greater motivation to perform higher quality wastewater treatment. In this case, Hypothesis 5 is proposed:Wastewater treatment PPP projects that have not yet entered the demonstration have a UWTE higher than those that have been in the demonstration.Quantifying the UWTE using DEAIn order to measure the efficiency represented by the capacity to increase output at a given input, two methods have been proposed. One is the estimation method based on parameters. The common method is stochastic frontier analysis (SFA). The other is based on the nonparametric estimation method, and the DEA is the most widely used. Although SFA can consider the influence of random factors on output, it needs to determine the specific form of production frontier as the condition when measuring efficiency. This means that if the pre-set production function form is inconsistent with the reality, the efficiency of the measure is not accurate. In contrast, the advantage of DEA is that there is no need to presuppose a specific production function form. It is based on a number of input and output indicators, using the method of linear programming, with the data envelope frontier as the comparison base, the decision making unit (DMU) of the same type of relative evaluation to determine the efficiency. In addition, DEA can also give the improvement space of each DMU in terms of input and output, which is convenient to give optimisation suggestions. Thus, DEA is widely used to assess the efficiency of public services, the environment, and natural resources fields51. With different settings of comparative DMUs, DEA can be divided into the CCR model, which assumes that the comparative DMUs meet the condition of constant returns to scale, and the BCC model, which assumes that the comparative DMUs meet the condition of variable returns to scale, and Shephard distance function introduced to distinguish pure technical efficiency from scale efficiency and determine whether the DMU production is optimal. Most studies have concluded that the BCC model is more consistent with the reality of production52; therefore, it is widely accepted and adopted compared to the CCR model. In this study, DEA based on the BCC model was used to measure the UWTE. The length of the urban wastewater network and the daily treatment capacity of urban wastewater treatment plants are established as input indicators, and the total amount of urban wastewater treatment is established as the output indicator53. The efficiency for each DMU is measured by solving the following linear programming of the BCC model, shown in Eq. (1):$$begin{array}{l}max theta \ s.t.mathop {sum }limits_{i = 1}^{283} lambda _i cdot lwn_i le lwn_{i_0}\ mathop {sum }limits_{i = 1}^{283} lambda _i cdot dtc_i le dtc_{i_0}\ mathop {sum }limits_{i = 1}^{283} lambda _i cdot tawt_i le theta tawt_{i_0}\ lambda _i ge 0\ mathop {sum }limits_{i = 1}^{283} lambda _i = 1end{array}$$
(1)
where subscript θ denotes the evaluated DMU. lwni and dtci represent the inputs, i.e. length of the wastewater network and the daily treatment capacity of urban wastewater treatment plants in prefecture-level city i, respectively, and the output is tawti, the total amount of wastewater treatment of each prefecture-level city. is a λ vector of intensity variable, and θ represents the efficiency score based on the input-output calculation. This is the UWTE to be calculated in this study.Causal linking the PPPs to the UWTE using DEA-Tobit regression modelThe DEA-Tobit regression model was used to empirically test the causal relationship between the PPPs and the UWTE. It is meaningful to use DEA to measure the UWTE, because the measured relative efficiency can be used to evaluate the capacity of urban wastewater treatment, and make it possible to compare the capacity of urban wastewater treatment between prefecture-level cities, and also creates conditions for finding the factors affecting the UWTE. As the range of UWTE measured by DEA is between 0 and 1, it does not obey the normal distribution and violates the classical assumption of ordinary least squares estimation. Therefore, in order to avoid the bias caused by OLS estimation, the restricted dependent variable model, also known as the Tobit regression model, is usually adopted in previous studies. The regression model which combines DEA and the Tobit regression model is also called the DEA-Tobit regression model. This study employs a DEA-Tobit regression model based on panel data, shown in Eq. (2).$$uwte_{it} = beta _0 + beta _1 cdot PPP_{it} + X^prime cdot gamma + varepsilon _{it}$$
(2)
where uwte denotes the efficiency of urban wastewater treatment. PPP denotes the degree of development of urban wastewater treatment PPP projects, which is measured in three calibres by determining the presence or absence of wastewater treatment PPP projects, the number of wastewater treatment PPP projects, and the investment amount of wastewater treatment PPP projects. X′ denotes other main control variables that potentially affect UWTE including population density, urbanisation rate, GDP per capita, industrialisation rate, openness, and green innovations. i and t represent prefecture-level city and year, respectively. β0 and εit denote the intercept term and the random disturbance term, respectively. β1 and γ are both parameters to be estimated, and β1 is significantly positive, indicating that the PPP model has a significant positive effect on the UWTE. Because the DEA-Tobit regression model with panel data does not have consistent and unbiased parameter estimates obtained under the fixed effects, the random effects estimation method is used in this study, referring to the parameter estimation recommendations presented by Liu et al.54Measurements of dependent, explanatory and control variablesThe dependent variable in this study is the UWTE. As mentioned above, we use DEA based on the BCC model to measure the UWTE. The closer the value of UWTE is to 1, the higher the efficiency is; the closer it is to 0, the lower the efficiency is.The degree of PPP development is the key explanatory variable of this study. It can be measured in various ways. The most common approach is determining the presence or absence of PPP projects, the number of PPP projects, and the investment amount of PPP projects31,33. To assess the impact of PPP on the UWTE in a comprehensive and reliable manner, this study uses all three metrics simultaneously.The endogeneity of mutual causation must be addressed when investigating the causal relationship between PPPs and the UWTE. This is because prefecture-level cities that use PPP models to build and operate WTI may consider wastewater treatment to be important, for example, the promotion of local government officials is closely related to the quality of public services in their jurisdictions during their tenure. To obtain a higher promotion probability, these prefecture-level cities focus on the efficiency of urban public services, including wastewater treatment, and the higher UWTE determines their willingness to adopt PPPs. Therefore, this study uses instrumental variables to eliminate the endogeneity problem in the regression analysis.Exogenous and correlation conditions are required for suitable instrumental variables. Waste treatment PPP development measured by determining the presence or absence and the number of waste treatment PPP projects is an instrumental variable for the degree of wastewater treatment PPP projects. This is because waste treatment and wastewater treatment are both urban environmental protection infrastructures. Furthermore, prefecture-level cities that consider wastewater treatment are highly likely to consider waste treatment, which are highly correlated. The PPP development for waste treatment does not directly affect the UWTE. Furthermore, the mean number of wastewater PPP projects in neighbouring prefecture-level cities in the prefecture-level city’s province was an instrumental variable for wastewater treatment PPP projects there. This is because, on the one hand, local government officials proactively follow the practices of other neighbouring prefecture-level cities in the province55. Assuming that other neighbouring prefecture-level cities in the province are inclined to promote wastewater treatment PPP projects, the prefecture-level city is highly likely to adopt a PPP model for the construction and operation of WTI. However, the mean number of wastewater treatment PPP projects in other neighbouring prefecture-level cities in the province will not directly affect UWTE in the prefecture-level city.Control variables: based on IPAT theory56, population density, urbanisation rate, GDP per capita, industrialisation rate, openness, and green innovations were selected in this study to measure the influence of three dimensions of population, wealth, and technology on the UWTE. The population density is measured as the urban population divided by the urban area. The higher the population density, the greater the need for an urban wastewater treatment capacity. The urbanisation rate is calculated as the share of urban population in the total population of the prefecture-level city. The higher the urbanisation rate, the higher the population in urban areas and the higher the demand for urban wastewater treatment capacity. Meanwhile, the urban population produces relatively more wastewater.GDP per capita is measured as GDP divided by population. The higher the GDP per capita, the higher the level of economic development of the prefecture-level city, and the more the government can regulate urban wastewater35, thus affecting the UWTE. The industrialisation rate is obtained by calculating the ratio of the output value of the secondary industry to GDP. The higher the industrialisation rate, the greater the demand for urban water resources, and more wastewater discharges are generated2, which affects the UWTE. Openness is measured by the proportion of imports and exports to GDP. The higher the openness, the more likely it is to attract companies with advanced environmental technologies57, reducing the amount of wastewater discharged from the prefecture-level city’s production sector. The ‘pollution heaven’ hypothesis may attract additional pollution discharge enterprises to the prefecture-level city58, affecting the prefecture-level city’s UWTE. Green innovations are measured using the number of green patents for wastewater treatment. Green patents for wastewater treatment are obtained from the Green List of International Patent Classification provided by the World Intellectual Property Organization (WIPO). If there are green patents for wastewater treatment, the reduction of wastewater discharge from enterprises is more likely, and thus the UWTE is improved59. This study considers the logarithm of the number of green patents for wastewater treatment to avoid the influence of data heteroscedasticity on the regression estimation results.DataThe research sample in this study comprised 1303 wastewater treatment PPP projects in 283 prefecture-level cities in China from 2014 to 2019, excluding Hong Kong, Macao, and Taiwan. To estimate the impact of PPPs on the UWTE, we needed data on the length of urban wastewater network, daily treatment capacity of urban wastewater treatment plants, total amount of urban wastewater treatment, wastewater treatment PPP projects, population density, urbanisation rate, GDP per capita, industrialisation rate, openness, and green innovations. Data on the length of the urban wastewater network, the daily treatment capacity of urban wastewater treatment plants, and the total amount of urban wastewater treatment were obtained from the China Urban Construction Statistical Yearbook 2014–201960. The PPP data were obtained from the Ministry of Finance’s Public–Private Partnerships Center61 and were captured by python technology. Data on population density, urbanisation rate, GDP per capita, industrialisation rate, and openness were obtained from China City Statistical Yearbook 2015–202062, and data on green patents were obtained from China National Intellectual Property Administration63. Supplementary Table 1 presents the descriptive statistics of the main variables, and Supplementary Fig. 1 reports the UWTE of 283 prefecture-level cities in China from 2014 to 2019. More

Overview of paper search outcomeA general overview of the 231 general water consumption-related and 48 framework analysis scientific publications reviewed in this study (Fig. 3) shows that the number of papers published per year from the general water consumption-related set has been increasing, particularly since the early 2000s. Peaks of more than 10 papers per year in this category emerge since 2011, with a maximum peak of 34 papers recorded in 2018. This increasing trend in time can be attributed to the increasing development of smart metering studies, which have been increasingly allowing detailed household water demand/consumption and behavioral analysis20,47. As a selected subset of the general water consumption-related papers set, the number of framework analysis papers has also increased in the last decade, compared to the ’80s and ’90s, constituting up to 5 papers per year. The final set of papers includes small-case studies comprising only a few units (11 individual households are considered as a minimum in48), as well as large-scale studies comprising several thousands of households (e.g., more than 8000 individual households are considered in49), or entire communities/towns50.Fig. 3: Temporal development of the literature on the determinants of household water consumption.The yearly count of the 231 general water consumption-related (blue) and 48 framework analysis (orange) scientific publications reviewed in this study is represented for the last forty years.Full size imageFigure 4 shows the locations of the studies from the framework analysis set, with larger blue dots indicating more studies. The geographical distribution of the reviewed studies indicates that the interest in the determinants of water use is worldwide. Prominent interest emerges in particular areas, such as the US west coast, the east coast of Australia, and the Mediterranean area in Europe, perhaps reflecting the combination of areas more prone to drought and/or having the higher economic capacity to undertake water use related research.Fig. 4: Geographical locations of the 48 framework analysis papers.The location of the 48 framework analysis papers reviewed in this study is represented with blue markers. Marker size is proportional to the amount of studies in a specific location.Full size imageDeterminant representation by classFrom the analysis of the 48 framework analysis papers, we identified a range of heterogeneous determinants and quantified different combinations of determinant classes, namely observable, latent, and external (see Determinant classification). Figure 5 shows an overview of the representation for the different classes of determinants over the 48 analyzed papers. Observable determinants were the most popular (47 total studies, i.e., 98% representation), with latent and external having lower representation of 52% and 56%, respectively. The values represented in the figure confirm our hypotheses that observable determinants are more common in literature than latent determinants, due to their availability in public databases, either at the household level or at coarser spatial sub-urban scales (e.g., census data collected at the block group-level, such as those used in49). The slightly higher representation of external determinants, compared to latent determinants, is also as expected due to the widespread availability of weather records (e.g., temperature, rainfall) from national or international environmental agencies. While there is no full consensus in the literature on the effect of weather or price variables on water consumption51,52,53, the high degree of representation of external determinants demonstrates that they are considered in more than half of the studies.Fig. 5: Venn diagram of household water consumption determinants representation.The representation of different classes of determinants (observable, latent, and external) in the 48 reviewed framework analysis papers is represented with coloured circles. Intersections are also visualized. The size of each circle and the numerical labels indicate the number of studies in which each combination of determinant classes appeared.Full size imageIt is worth observing that multiple classes of determinants are simultaneously analyzed in most of the reviewed studies, with fewer than 20% analyzing observable variables alone. Further, almost every time external or latent variables are considered, they appear in combination with observable variables. Only one study specifically focused on analyzing the motivations for using and conserving water based on only latent determinants42, while no studies exclusively considered external variables. In contrast, nearly 30% of the studies included both observable and external variables, approximately 23% of the studies considered latent and external variables simultaneously, and 27% of the studies included all three types of determinant classes.The high representation of observable determinants (Fig. 5) suggests that observable variables are widespread in the literature on modelling and forecasting of household water consumption. The prevalence of this class of determinants seems also to confirm the findings from previous studies, which demonstrated that meteorological variables have a greater influence on medium-term prediction and urban/suburban scales, but socio-demographics become more relevant when household-scale and short-term water demand models are developed54,55.Individual determinant representation, impact, and effortTo facilitate interpretation of the numerical values we obtained for the three determinant assessment criteria (i.e., representation, impact, and effort) we defined some regions of interest for each criterion based on thresholds (see the regions labelled as low/high/very high in Fig. 6). We selected the threshold values used to delimit the above regions of interest based on visual inspection of the empirical distribution of the representation, impact, and effort values. This simplification is carried out to facilitate the inference of general qualitative conclusions, while accounting for the low number of papers and, at the same time, high number of determinants. As a result, representation values above/below 30% are considered high/low. Impact values below 75% are considered low, values between 75% and 90% are considered high, and values above 90% are considered very high. Effort rate values above/below 8 are considered high/low.Fig. 6: Individual analysis of representation, impact, and effort.The three criteria to perform determinant analysis, i.e., representation (top), impact (middle), and effort rate (bottom) are associated with individual determinants. Observable determinant class is shown in green, latent class in blue, and external in orange. Shaded background indicates different levels of intensity for each analysis criterion. See Tables 1–3 for determinant acronyms definition (the determinants included in the categories marked as “Other” in the tables are not represented for better clarity).Full size imageFrom the resulting data visualized in Fig. 6, we can infer the following insights about determinant representation, impact, and effort. First, the determinants with the highest representation (top plot in Fig. 6) were household income ( > 70%), family size ( > 60%), and age ( > 45%). As already suggested by the outcomes of class representation (Fig. 5), all the above determinants with high representation are observable. One exception is the awareness determinant, which is the only non-observable determinant we found with high representation. The majority of the other determinants had a representation rate of 10% to 30%.Second, the number of determinants with a high or very high impact (middle plot in Fig. 6) is much larger than the number of determinants with high representation. It must be noted that a high impact does not necessarily mean that a determinant was found to have a high influence on water consumption, but rather that it was found to have some influence on water consumption in many publications. Interestingly, some determinants from all classes achieve high or very high levels of impact. Observable determinants with very high impact include socio-demographic information (number of occupants), house characteristics (house age, value), and outdoor characteristics (garden size, and presence of rainwater tanks). While these latter attributes related to gardens ranked among those with the highest impact, garden composition was found to have one of the lowest impact rates across the analyzed studies. Also, the observable determinants related to the education level of occupants was found to have low impact. A latent variable that emerges as very important (GARD_C) is also related to garden characteristics, but, rather than representing any physical variable, it accounts for the psychological value given by occupants’ attitudes and habits towards gardening. Finally, all external variables were found to have high or very high impact, with rainfall and water price emerging as the two with impact above 90%.The bottom plot of Fig. 6 shows that there was a wide variability in the effort rate for each individual determinant. Data on most of the observable determinants can be generally gathered with low effort, but some (e.g., appliance inventory and irrigation system) require house visits, and thus require high effort. In turn, all latent variables display an effort rate higher than 6, and three out of four are classified as high-effort. Conversely, data on all external determinants can be retrieved with low effort, as they are usually available from national agencies (weather data) and water utilities (water price). Obtaining information on higher effort determinants likely requires getting in contact with individual householders, via phone/online surveys, or house visits.Overall, the results reported in Fig. 6 suggest that there are trade-offs between representation, impact, and effort. In the next section, we perform a joint analysis of the three criteria and their trade-off to infer the implications of the outcomes of this study for researchers and practitioners.Trade-off analysis and implications for researchers and practitionersFigure 7 shows the interaction between the representation, impact, and effort criteria. The distribution of blue and orange points in the figure demonstrates that there are different trade-offs among the three criteria. Each trade-off can have a different set of implications to derive recommendations for researchers and also practitioners. We identified the three groups of determinants marked with (A), (B), and (C) to illustrate the different needs of research and practice. Group A is characterized by high impact, high representation, and low effort. Determinants in this group include household family size, occupants’ age, and occupants’ income. This group of well-studied determinants with proven impact might be particularly interesting for practitioners aiming to gather knowledge on household water consumption with budget constraints. Group (B), which includes, among others, information on the household irrigation system, appliance efficiency, and occupant gender, is characterized by medium-to-high impact, but low representation, and a range of low to high effort. While this group might not be very appealing for practitioners due to low representation, researchers might be interested in focusing on these determinants to increase their representation and, thus, validate or contrast the limited findings on these determinants that appear in the literature. Finally, Group C refers to determinants with low representation and, compared to those in groups A and B, lower impact. As they also might require high gathering efforts, these determinants should be treated with caution until more research is performed to prove their potential impact on a larger sample of studies.Fig. 7: Trade-off analysis of determinant representation, impact, and effort.Impact (x-axis) vs Representation (y-axis) vs Effort (color) of each determinant. Each point refers to a specific determinant. See Tables 1–3 for determinant acronyms definition. The determinants classified as “High effort” are those with an effort value larger than 8.0, vice-versa for the “Low effort” determinants. Determinants are organized in three groups: Group A – high impact, high representation, and low effort; Group B – medium-to-high impact, low representation, and mixed low and high effort; Group C – low representation, low impact, mixed effort.Full size imageAccounting for similar trade-offs across the entire sample of determinants that we have identified from the review of the literature enables determinant-specific recommendations to be derived for practitioners and researchers. In the last step of this review and determinant classification effort we thus develop a trade-off analysis framework that considers different combinations of representation, effort, and impact to formulate such recommendations. In keeping with the goal of this study, our trade-off analysis aims at identifying groups of determinants that have proven cost-effective impact via extensive research and, thus, can be recommended for use in practice, compared with groups of determinants that require more research to address open questions related to representation, impact, and effort. The proposed trade-off analysis framework includes four main recommendation categories:UIn this category, we include determinants characterized by high representation, high/very high impact, and low effort. We consider these determinants as determinants that practitioners can “definitely use” (U), as they have been extensively researched and have been shown to have an impact in most cases, while being affordable. For the same reasons, higher levels of research priority should be devoted to less explored determinants, while these can serve as references. The determinants included in box (A) in Fig. 7 belong to this group.IR-UCIn this category, we classify those determinants characterized by low representation, high/very high impact, and low effort. Given their promising, but not extensively proven, impact, and overall affordability, further research on these determinants should be prioritized to increase their representation (IR). We consider these determinants as determinants that practitioners can “use with caution” (UC), as they have not been extensively researched, but at the same time might have high impact at low-cost. The determinants included in box (B) in Fig. 7 and classified as low effort (blue color) belong to this group.LE/IR-UCIn this category, we include determinants characterized by generally low representation, high/very high impact, and high effort. Similarly to the previous category, we believe that practitioners can use these determinants “with caution” (UC), as they have not been extensively researched and require high effort for data collection, but at the same time might have high/very high impact. Given their promising, but not extensively proven, impact, and high cost, further research on these determinants should be prioritized, primarily to lower the effort (LE) needed to collect them and, thus, facilitate their consideration in more studies (increased representation – IR). The determinants included in box (B) in Fig. 7 and classified as high effort (orange color) belong to this group.IR/LE/AI-NPIn this category, we include determinants characterized by low representation, low impact, and mainly high effort. Given the limited knowledge on these determinants, we suggest that these determinants are “not prioritized” (NP) for use by practitioners unless further research demonstrates that the effort required to collect these determinants is worth the benefit of considering them. Further research should then aim at increasing their representation (IR), lowering the effort needed to obtain data on these determinants (LE), and further assessing their impact (AI) to acquire better knowledge on their actual value. The determinants included in box (C) in Fig. 7 belong to this group.Summary information on the above categories is reported in Table 5. Based on the proposed trade-off analysis framework and the threshold values defined in Fig. 6, we associated each of the different determinants identified in the framework analysis papers with a level of recommendation (see Fig. 8). Some relevant insights for researchers and practitioners emerge. First, only observable determinants are classified as “U”. At present, there are some socio-demographic determinants (i.e., number of occupants, income level, and occupant age) that can be reliably used by practitioners in most cases to model household water consumption and can be easily and affordably retrieved.Table 5 Framework for trade-off analysis, based on representation, impact, and effort.Full size tableFig. 8: Household water consumption determinant classification and associated recommendations for practitioners and researchers based on individual determinants.Each household water consumption determinant identified in the framework analysis papers is associated with a level of recommendation. Determinants are classified according to the three defined classes (columns), i.e., observable, latent, and external. Four levels of recommendation (rows) are formulated for practitioners and researchers. They are sorted in decreasing order of representation and proven impact in research, as well as confidence for use in practical applications. Confidence for use in practical applications decreases going from green (“U” level of recommendation) to orange (“IR/LE/AI-NP” level of recommendation).Full size imageSecond, all external variables (i.e., average rainfall, temperature, and water price) are classified as IR-UC. Consequently, they have a proven impact, but have been used sporadically in connection with household water consumption (while they have been used more often at larger, urban scales), thus results might be case-specific and further research is needed to assess their impact on a larger number of studies.Third, a mix of observable and latent external variables deserves further research to lower effort (e.g., by improving technology/data gathering practices or identifying lower-effort proxies for the same type of information) and increase representation. These variables are either observable determinants, the collection of which requires significant effort and house visits/calls to occupants (e.g., to build an inventory of appliance efficiency or storing information on irrigation systems), or latent variables the impact of which is still not proven due to low representation. The increasing availability of high-resolution metering and behavioral studies fostered by smart metering development is likely to contribute more knowledge on these determinants and more complete guidelines for use by practitioners in the coming years7,17,20.Fourth, we would like to stress that the recommendation “Do not favor adoption until further research” for the determinants classified as IR/LE/AI-NP does not mean that they should not be considered in future applications or no research should be done on them. Conversely, we recognize that many existing studies are based on limited data or data with coarser spatio-temporal resolutions, thus conclusive statements on the impact of such determinants would require further validation. Since large uncertainty about their impact remains, more studies are actually needed to increase the representation of these determinants and increase the statistical significance and generality of their impact assessment. Joint research that also includes other determinants with higher levels of representation could be beneficial to discover more information on the determinants in this group and better understand whether practitioners should eventually include one/more of these determinants in their analysis. Further research could be also developed to assess the degree to which these determinants are correlated with others, and hence redundant, and to which extent these and other determinants can relate to particular characteristics of water consumption (e.g., demand peaks, end use components).Finally, some of the determinants that we recommend to use with caution (UC) in practice, and that should be prioritized for research, might become determinants to definitely use (U) in the future. Two limitations currently prevent us to recommend “definitely use” for these determinants, i.e., generally low representation and high effort for data collection. Low representation indicates that the determinant has not been well-studied in the literature. Hence it might not be generalizable to a wide range of locations. To address the disadvantages of low representation, the following is recommended for practitioners:

Check the literature and if there are studies with similar context (location/climate/application) to the practitioners’ required application, and the impact of the determinant is high, then the determinant could be considered for use.

Continue to monitor the literature, to see if new studies appear using that determinant.

The other limitation, high effort, means that in the reviewed past studies it has been costly for practitioners to collect some of the required determinants. With the advent and widespread use of new technologies, the effort required to collect some of the required high-effort determinants may be substantially reduced. Lowering the effort related to some high-impact, yet also high-effort, determinants (see, e.g., those indicated with orange color in Group B in Fig. 7) would have a two-fold benefit. The direct reduction of the costs required to collect information on those determinants will also enable wider consideration of these determinants in a larger number of studies, thus increasing their representation. As technology enhances the capture of such determinants, there is an opportunity to revisit past studies/datasets and increase the representation of these determinants, which might then transition to determinant group A in in Fig. 7. To address the current limitations and disadvantages of high effort, the following is recommended for practitioners:

Monitor the use of emerging technologies that provide an opportunity to lower the cost required to collect the determinant. For example, there is an opportunity for analysis of high resolution satellite maps/photos to provide automated estimates of observable determinants such as garden size (GSZE) over large number of households, which would lower the cost substantially56. Similarly, latent determinants such as water consumption awareness (AWARE_C) could be based on the uptake of user-friendly smart metering and phone apps on water consumption if they were widely available17,57.

Evaluate overall costs vs benefits based on preliminary experiments on small sample data (to evaluate benefits while avoiding high costs), and consider the use of lower cost proxy data for the “high effort” determinant.

These recommendations provide some guidance for practitioners to handle determinants classified as “use with caution”.Limitations and future researchThis work provides evidence and a quantitative framework for the analysis of household water consumption determinants, yet several limitations and questions remain for further research. First, alternative formulations of determinant representations, impact, and effort could lead to different results. This also stands for the subjective thresholds we adopted to distinguish between high and low representation, impact, and effort. Such thresholds and criteria formulation could be changed based on needs and subjective judgement.Second, in this review we focused on the analysis of individual determinants of household water consumption. However, some determinants could be correlated, present redundant information, or be accounted for in alternative ways to build models for forecasting water demand (e.g., rainfall amount versus rainfall occurrence53). Input feature engineering, variable redundancy, and data accuracy can substantially affect the performance of water demand models. Future studies focused on comparative analysis of alternative determinant formulations and inter-links/dependencies among different determinants can help define non-redundant determinant sets to train models of water demand and recommendations for variable pre-processing.Third, the findings of this study are consistent with previous review papers that identified both observable and latent variables as the most important with respect to domestic water consumption58. Yet, other meta-analyses and review studies found partly contradictory results. Differently from our study26, found that the most important determinants of water use behaviour are related to individual opportunities and motivations, gender, income, and education level. In turn59, formulated a model that accounted for a wide range of variables including demographics, dwelling characteristics, household composition, conservation intention, trust, perceptions, habits, and perceived behavioral control. It must be noted that the above studies do not consider household water consumption per se as we do here, but relate potential determinants of water consumption also to individual consumption or behavior changes (i.e., changes in water consumption over time). Future, potentially contrasting, studies could then expand the scope of this work and relax the exclusion criteria we adopted here to achieve more inclusive comparative analyses that investigate the effect of different determinants in relation to quantified intervals of total household water consumption, and other heterogeneous aspects of domestic water demand, including statistics on end use components (e.g., flow rate, duration, or frequency of individual appliances)60 and temporal changes of water consumption levels due to external stressors such as droughts, or demand management interventions39,49, for example.Fourth, the set of framework analysis papers includes case studies primarily located in the United States, Australia, and Europe (see Fig. 4). Geographical coverage is thus skewed. There is a need for more studies from other geographical regions (including countries with low-income economies) in order to obtain a more balanced picture and consolidate/expand the results obtained so far.Finally, recent works have highlighted that urban and household water demands have been modelled at different spatial and temporal resolutions47. The choice of the temporal and spatial resolution of interest is determined both by data availability and the specific modelling and management purpose. Multi-scale studies combining different levels of spatial and temporal aggregation of water demands and potential determinants would further advance our analysis and contextualize specific recommendations for data collection and processing at the different spatial and temporal scales of interest. More

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