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Data for estimating drawdown areasThe calculation of drawdown areas was based on monthly time series of surface-area values for 6,818 reservoirs provided by GRSAD18. It comprises all reservoirs from the Global Reservoir and Dam dataset19 except of 45 reservoirs without reported geometric information. In accordance with ref. 1, we further removed 24 reservoirs classified as natural lakes that have been modified with water regulation structures (this includes lakes Victoria, Baikal and Ontario). The GRSAD dataset comprised entries from March 1984 to October 2015. To have a constant number of data points per year, we restricted our analysis to the period from January 1985 to December 2014.GRSAD was created by correcting the Global Surface Water dataset31 for images contaminated with clouds, cloud shadows and terrain shadows. With this correction, the number of effective images that can be used in each time series has been increased by 81% on average. Substantial improvements have been achieved for reservoirs located in regions with frequent cloud cover and high-latitude reservoirs in the Northern Hemisphere, where low illumination has previously resulted in missing area values during winter months.Calculation of drawdown areasWe calculated monthly drawdown areas for all reservoirs contained in GRSAD according to:$${rm{DA}}=left({{rm{Area}}}_{{rm{max }}}-{rm{Area}}right)/{{rm{Area}}}_{{rm{max }}}$$
(1)
where DA is the relative extent of the drawdown area for a given reservoir considering the current monthly surface area (Area) and the maximum area recorded during the period 1985–2015 (Areamax). We assumed that the maximum area of each reservoir recorded during the 30-year period is a valid representation of its nominal surface area (the area of the reservoir at maximum filling level).Complete filling of reservoirs was defined by a drawdown area smaller than 5% of Areamax. Because there is no uniform definition of ‘extreme drawdown’, we used the Cape Town water crisis 2018 as a reference21. The number of reservoirs experiencing extreme drawdown was estimated by averaging the number of reservoirs with drawdown areas exceeding 40%, 50%, 60% or 70% of Areamax at least once. To prevent initial filling of reservoirs being identified as extreme drawdown, 791 reservoirs built during the analysed period (year built ≥ 1985) were excluded from this analysis. The upper bound (70%) corresponds to the drawdown-area extent during the Cape Town water crisis 201821 (Fig. 1a). The lower bound (40%) corresponds to a reservoir capacity (storage water volume) of approximately 35%, as remained available during that water crisis, assuming an idealized, triangular reservoir shape (Extended Data Fig. 8). This was estimated according to:$$0.36=frac{{left(0.6times sqrt{2}right)}^{2}}{2}$$
(2)
For the calculation of total global drawdown area, used for the upscaling of GHG emissions, we combined data for reservoirs larger than 10 km2 with values derived from a Pareto model for smaller reservoirs. First, we estimated total reservoir surface area for nine size classes following a Pareto distribution. Subsequently, we estimated total drawdown area for each size class by multiplying the size-class-specific relative drawdown-area extent by the total reservoir surface area of each size class (Supplementary Table 3). Because the relative drawdown-area extent for reservoirs smaller than 0.001 km² is unknown and furthermore considered as being imprecise for reservoirs smaller than 10 km², we derived estimates for these size classes on the basis of four different statistical models (linear, square root, logarithmic, polynomial; Extended Data Fig. 9). Reservoirs larger than 10 km² were used to fit linear, square root and logarithmic models, whereas all available data were used for fitting a second-degree polynomial model to achieve a best representation of the available data. The four models all have a constant (linear model) or decreasing (square root, logarithmic, polynomial) slope. We have refrained from using models with increasing slopes (for example, exponential) to not overestimate the drawdown extent of small reservoirs and, thus, consider these estimates as conservative.Data analysisStatistical models to predict drawdown-area extent for each reservoir were developed using stepwise MLR. Climatic data (mean annual temperature, precipitation seasonality) for all reservoir locations were extracted from the Climatologies at High Resolution for the Earth’s Land Surface Areas climate dataset, which gives high-resolution (0.5 arcmin) climate information for global land areas over the period 1979–201332. Climate zones in the Köppen–Geiger system were determined from the high-resolution (5 arcmin) global climate map derived from long-term monthly precipitation and temperature time series representative for the period 1986–201033,34. Data on baseline water stress were extracted from Aqueduct 3.025. Baseline water stress measures the ratio of total water withdrawals to available renewable surface and groundwater supplies and is derived from high-resolution (5 arcmin) hydrological model outputs using the PCR-GLOBWB 2 model35,36.Dates were categorized into four seasons on the basis of their meteorological definition depending on hemisphere. Therefore, for the Northern Hemisphere, spring begins on 1 March, summer on 1 June, autumn on 1 September and winter on 1 December. For the Southern Hemisphere, spring begins on 1 September, summer on 1 December, autumn on 1 March and winter on 1 June.For the analyses of reservoir use types, we used the information provided in the column ‘MAIN_USE’ of the Global Reservoir and Dam dataset. Reservoirs where the main use was not specified (n = 1,554) were combined with those having MAIN_USE = ‘Other’ (n = 205).To identify the magnitude of trends in time series, we used the non-parametric Theil–Sen estimator and the Mann–Kendall test because they do not require prior assumptions of statistical distribution for the data and are resistant to outliers. The Theil–Sen estimator was used to compute the linear rate of change, and the Mann–Kendall test was used to determine the level of significance. We analysed differences between groups using the Kruskal–Wallis test and Dunn’s post hoc test. The threshold to assess statistical significance was 0.05 for all analyses, The statistical analyses were performed using R 3.4.437.Upscaling of GHG emissions and OC burialBecause the global reservoir area derived in this study differed from the area used in previous studies, we recalculated the published global estimates for both OC burial6 in and GHG emissions1 from reservoirs to allow for comparison (Extended Data Fig. 10). We fitted empirical distributions to CO2 emission data from drawdown areas (Supplementary Table 2 and Extended Data Fig. 7) as well as the published OC burial rates6 and published GHG emission data1 from water surfaces of reservoirs. For CO2 emissions from drawdown areas, we used a gamma distribution to account for non-normality of the data (Extended Data Fig. 7). For CO2 and N2O emissions from the water surface, we fitted a skewed normal distribution because of the occurrence of negative values (Extended Data Fig. 7). For CH4 emissions from the water surface, we fitted a log-normal distribution (Extended Data Fig. 7). Because the global estimate of OC burial was derived using geostatistical modelling, we fitted a gamma distribution to the published moments of OC burial rate6 (mean ± s.d. = 144 ± 75.83 gC m−2 yr−1) where the s.d. is calculated as the s.d. of the four scenarios used in that study. The final global empirical distributions for all fluxes were estimated by multiplying average emission and burial rates derived from resampling the preceding distributions times the total water surface area and drawdown area of reservoirs, resulting also from resampling their distributions after uncertainty propagation (see Treatment of uncertainty).Treatment of uncertaintyAs in all upscaling exercises, the global analysis conducted in this study is subject to substantial uncertainty. In our case, the uncertainty results from both the quantification of water surface and drawdown area of reservoirs and the estimation of global rates for GHG emission and OC burial. To comprehensively take all sources of uncertainty into account, we propagated all uncertainty throughout the whole analysis using a combination of Taylor series expansion and Monte Carlo simulations (Extended Data Fig. 10). In brief, we applied customary equations for uncertainty propagation derived from the Taylor series expansion method when propagating uncertainty of moments (for example, mean) or simple arithmetic calculations (for example, multiplication). For more-complex situations or when non-normality was conspicuous, we used Monte Carlo propagation. To obtain global estimates and standard error of water surface and drawdown area of reservoirs, both the systematic (bias) and random uncertainties of the remote-sensing-derived dataset18 as well as the uncertainty induced by our Pareto modelling for reservoirs More

Global value of controlling eutrophicationThe substantial emissions from lakes and reservoirs and the potential for increased emissions suggest that there is considerable value in improving water quality in lakes and reservoirs and in preventing further deterioration. We calculated the global climate damages from CH4 emissions and the avoided damages from preventing increased emissions from 2015 to 2050 using well-accepted integrated assessment models (IAMs) (see “Methods”). Because GHGs rapidly become well mixed in the atmosphere, the global social costs of GHG emissions do not depend on where they are emitted. Because GHGs can persist for many years in the atmosphere, the effect of emissions of today will be felt for many years in the future, which means that the rate used to discount future economic damages to the present exerts a strong influence on the social cost of GHG (SC-GHG) estimates. Following the U.S. Government Interagency Working Group (IWG), we report all results using three discount rates: 2.5%, 3%, and 5% yr−1.The estimated present value of the global climate change costs of CH4 emissions from lakes and reservoirs for 2015–2050 range from $7.5 to 81 trillion (2015$; top half of Table 1). Low-end estimates assume a high discount rate (5% yr−1), low current emissions (4.8 Pg CO2-eq yr−1), and no emission growth. High-end estimates assume a low discount rate (2.5% yr−1), high current emissions (8.4 Pg CO2-eq yr−1), and high growth in emissions from lakes (100%). It will not be possible to avoid all emissions from lakes and reservoirs, but with concerted effort it may be possible to prevent increased emissions. The present value of avoided damages from holding emissions constant at current levels rather than increasing by 20–100% by 2050 from increasing eutrophication is $0.66–24 trillion (2015$).Although it has been noted that it might result in underestimation, especially when assuming a high discount rate15, an alternative approach to estimating the climate change damages from non-CO2 GHGs involves first converting the emissions to CO2-equivalents (CO2-eq)16 and then multiplying these by the social cost of carbon dioxide (SC-CO2)15. This approach is less accurate than direct application of the social cost of CH4 (SC-CH4)15, but it has been frequently used in previous studies. To facilitate comparison to other estimates of climate damages in the literature, we also used the CO2-e × SC-CO2 approach with otherwise equivalent assumptions to value eutrophication emissions. Results using this approach are reported in the bottom half of Table 1. The cost of CH4 emissions from lakes and reservoirs from 2015 to 2050 is estimated to be $5.4–95 trillion (2015$), and the associated avoided damages from keeping emissions constant are $0.46–27 trillion (2015$).These estimates consider only the cost of CH4 emissions, but lakes and reservoirs also emit CO2 and N2O. Adding current CO2 and N2O emission estimates10, the SC-GHG emissions increases by 27–51% above those for CH4 alone. Although mounting evidence suggests poor water quality also influences emissions of CO2 and N2O, global analyses of future scenarios for altered emissions of CO2 and N2O from lakes have not yet been published, so we do not monetize these damages. Nevertheless, even our partial estimates suggest that reducing eutrophication is an important means of avoiding climate change damages with a large benefit when measured in monetary terms.Comparison to other economic damages from water pollutionHow do these estimated global climate damages from eutrophication compare to the local and regional benefits of water pollution control typically included in assessments of the benefits and costs of water pollution policies? To help put our results in context, we consider the case of Lake Erie, where eutrophication and associated harmful algal blooms (HABs), primarily due to excess P from agricultural sources, have caused considerable economic damage since the mid-1990s7. Local values of eutrophication abatement vary among lakes, but Lake Erie is a salient example because reliable estimates of local value are available, and Lake Erie’s GHG emissions were included in the global emission analysis9,10 that we used to compute our global estimates presented in Table 1. Recent work using a stated preference survey of Ohio residents estimates that a 40% reduction in total P loading to the western Lake Erie basin from the Maumee River watershed would lead to a $4.0–6.0 million annual welfare gain to Ohio recreational anglers17,18. Assuming constant annual benefits from 2015 to 2050 and using a 3% yr−1 discount rate, this amounts to a present value of $0.087–0.12 billion in total recreational fishing benefits.Table 1 Present value (PV) of global social costs of CH4 emissions from lakes and reservoirs, 2015–2050 (billion 2015 US$).Full size tableApplying our methods to this case, a 40% reduction in total P loading to Lake Erie would yield a 0.079 Tg yr−1 reduction in CH4 emissions (2.7 Tg CO2-eq yr−1). If the P-loading reduction began in 2015 and was maintained through 2050, we estimate that the resulting water quality improvement would generate present value economic benefits (avoided climate damages) of $3.1 billion using the SC-CH4 ($3.3 billion using CO2-e × SC-CO2) and a 3% yr−1 discount rate (Table 2). Thus, the global climate benefits of achieving the targeted 40% reduction in P loading are well over an order of magnitude larger than the estimated recreational benefits to Ohio anglers (Fig. 1).Table 2 Present value (PV) of avoided global social costs of CH4 emissions, 2015–2050 (billion 2015 US$), from a 40% reduction in total P loading in the western Lake Erie basina.Full size tableFig. 1: Comparison of the recreational vs. climate implications of eutrophication.A The welfare gain, 2015–2050, from a 40% reduction in phosphorus (P) loading to western Lake Erie reducing the frequency and extent of harmful algal blooms (HABs). The range of economic impact on recreational angling was estimated from the annual welfare gain17 assuming constant annual benefits and a 3% yr−1 discount rate. The welfare gain from this same total P loading to Lake Erie was estimated from the corresponding reduction in CH4 emissions (and CO2-equivalent emissions) through 2050, using estimates and methods reported in Table 2. B The welfare cost of seasonal Lake Erie HABs sufficient to close beaches, 2015–2050. Benefit transfer work20 estimates the 95% confidence interval of daily recreational losses from the closure of all 67 Lake Erie beaches in Ohio and Michigan. We aggregate to seasonal (115 day)39 HABs occurring annually, 2015–2050, using a 3% yr−1 discount rate. Methane cost estimates are derived from methane emissions under nutrient concentrations that would lead to closure of all of these beaches due to high chlorophyll from HABs as well as from chlorophyll levels that would lead to moderate risk of adverse health effects from beach use.Full size imagePublished estimates suggest that the 40% reduction in total P loading to Lake Erie that we model here could be achieved with a fertilizer tax or a tax-and-rebate policy with rebates funding agricultural best management practices at an annual cost to taxpayers of about $16–17 million19. Note that these cost estimates are conservative, as they do not include yield losses or other agricultural compliance costs19. These annual costs would exceed the estimated annual recreational fishing benefits of the policy goal18 but are still smaller than the climate benefits.Economists have also used benefit transfer techniques to extrapolate from individual estimates of the value of water quality changes for a specific location to estimates for an entire region. For example, recent work20 using a function transfer approach estimates that the closure of all 67 Lake Erie beaches in Ohio and Michigan due to a large HAB in Lake Erie would generate daily recreational losses of $2.39 million (95% confidence interval $1.81–3.11 million). Assuming an extreme case that the HAB season lasts continuously for 115 days20, this implies an annual welfare loss of about $280 million. If a severe HAB that closed all 67 Lake Erie beaches in the two states occurs annually from 2015 to 2050 and annual damages are constant, the present value of total damages, derived from the definition of the present value of a constant stream of benefits, using a 3% yr−1 discount rate, would be about $6.1 billion using the central estimate of the cost of beach closure20, or a range of $4.4–7.7 billion, using their 95% confidence interval20.The CH4 emissions from a HAB event in Lake Erie large enough to close all 67 beaches in Ohio and Michigan would depend on the severity of the triggering water quality impairment. We use two approaches to make a comparable estimate of CH4 emission damages. First, if the chlorophyll a concentration exceeds 30 ppb, the risk of Cyanobacteria blooms is 80–100%, gauged by the risk of Cyanobacteria biomass exceeding 50%21. This level would exceed statutory thresholds that trigger beach closures or health advisories and would yield an emission increase of 1.0 Tg CH4 yr−1 (34 Tg CO2-eq yr−1). These emissions would create a present value of damages of $39 billion using the SC-CH4 ($42 billion using CO2-e × SC-CO2) at a 3% yr−1 discount rate (Table 3), roughly seven times larger than the estimated recreational damages from a HAB severe enough to close all Lake Erie beaches in Michigan and Ohio for 35 years.Table 3 Present value (PV) of global social costs of CH4 emissions, 2015–2050 (billion 2015 US$), from a harmful algal bloom sufficient to close all MI and OH beaches on Lake Erie.Full size tableAs a second approach to making this comparison, we use the World Health Organization guideline for chlorophyll a concentration yielding a moderate probability of adverse health effects in recreational waters (50 ppb)22. Because the assumed triggering concentration for beach closures is higher, both the estimated emissions associated with the closure events (1.7 Tg CH4 yr−1 or 59 Tg CO2-eq yr−1) and the economic damages using a 3% yr−1 discount rate ($69 and $73 billion) are higher (Table 3). With this approach, the global climate costs of HABs severe enough to close all MI and OH beaches on Lake Erie from 2015 to 2050 are an order of magnitude larger than the estimated recreational damages from beach closures (Fig. 1).We cannot say how our CH4 damage estimates would compare with a full estimate of other damages from Lake Erie eutrophication. The literature demonstrates that important water quality benefits are difficult to value2. A single-season HAB similar to the 2014 event that resulted in the issuance of a do not drink/do not boil order for the public water system in the City of Toledo created damages of about $1.3 billion, including impacts on property values, water treatment costs, and tourism23. Estimates of damages to fishing activity at Lake Erie’s Canadian coast are also substantial24. An earlier study estimates damages from eutrophication of all U.S. rivers and lakes25, omitting the climate damage estimates we calculate here; an assessment of the methods used to obtain these estimates is outside the scope of our paper. Notably, recent work links HABs in Gull Lake, Michigan (not far from Lake Erie) with increased likelihood of low birth weight and shorter gestation among infants born to exposed mothers26.Given that the full gamut of potential damages is difficult to monetize, a comprehensive estimate of the non-climate damages from eutrophication and HABs—especially if human health impacts are significant—could exceed our damage estimates for CH4 emissions. However, our estimates of the global CH4 emission damages from eutrophication in Lake Erie exceed all published estimates of other damages, to the extent that we can compare them. Smaller lakes than Erie may show even greater differences between global and local values of eutrophication because, on average, people have greater willingness to pay for recreation on large lakes27, and CH4 emissions per unit area do not vary with lake size10. These results suggest that global climate impacts are a substantial omission from benefit–cost assessments of policies targeting eutrophication, in Lake Erie and elsewhere.Eutrophication is a local and global problemDegraded water quality is often considered a local or regional problem. We show that water quality has important implications for global climate, through emissions of CH4 and other GHGs. These emissions are likely to increase substantially unless action is taken to prevent further eutrophication. The damage from eutrophication-related GHG emissions is likely to be in trillions of dollars, and appears to be far larger than other monetized damages from poor water quality that economists have so far been able to quantify, especially where pollution does not generate severe health damages. Our analysis shows that local water quality protection has global economic implications, and that more effort devoted to understanding the consequences of changes in water quality and valuing the benefits of sustaining or improving water quality is warranted. More

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Quantitative variablesThe intervention described here relies on the IT platform “SmartH2O” for the collection and visualization of smart meter data, the provision of consumption feedback to the user, the delivery of water-saving recommendations, and the engagement of the consumer through a gamification program20,21,34,35. We embedded a gamification mechanism in the digital platform to maximize user retention and stimulate the exploration and sharing of content and the setting and achievement of personal saving goals. Via the gamification mechanisms, users could collect reward points for different actions performed in the digital platform or the achievement of water-saving targets. Reward points consisted of virtual points that the users could redeem for physical rewards. The design of the SmartH2O digital platform and the behavioral change stimuli that have been introduced in the Valencia case-control study (e.g., web and mobile app, different reward schemes), along with their individual elements and the corresponding illustrative screenshots of the platform are provided in the Supplementary Information, consistently with the information published in a previous study21. Other platforms similar to SmartH2O or approaches for water conservation based on digital technologies are reported in the literature, including, e.g., real-time water consumption feedback on in-home displays, interactive dashboards, and games36,37. Yet, to the author’s knowledge, SmartH2O is the first platform of its kind whose effect is rigorously assessed in the medium term and long term.Household-scale water consumption data and smart meter sampling frequencyWater consumption readings measured at the household scale constitute the main quantitative variable of interest used in this observational study to identify behavior changes. The SmartH2O digital platform relies on water consumption information stored in a central database and enables data communication from the water utility to the water consumers (see Supplementary Fig. 1 for its software architecture). Water consumption data are collected by smart meters installed at the household premises, according to a schedule that considers the maximum available frequency of data sampling at each installation (hourly or daily). The consumption data are anonymized by the utility company, filtered, and transferred to the central database of the SmartH2O platform. The content of the central database is published to the user via a web portal and a mobile application, which are the entry points of all users’ interactions with the platform.Besides the time series of water consumption, we also stored the sampling frequency allowed by each household-scale smart meter. Two types of sampling frequencies were available in the considered population, depending on the installed smart meter hardware: hourly or daily.Digital user engagement variablesThe central database of the SmartH2O platform comprises content for improving user awareness, such as water-saving recommendations, and for implementing the gamification program, such as the description of virtual and physical rewards. The interaction of the users with the platform and the overall user experience features several functionalities, including user login, water consumption and smart meter-based feedback visualization, conservation goal settings, and different gamified water conservation awareness actions (see also Supplementary Notes1). We monitored the activity of each user in the SmartH2O platform for the entire duration of the treatment period and gathered quantitative data on these four digital user engagement variables:

(i)

Login count, defined as the total number of logins executed by each user.

(ii)

Non-rewarded action count, defined as the total number of actions performed by each user, with no reward points associated.

(iii)

Rewarded action count, defined as the total number of actions performed by each user, with associated reward points upon their completion.

(iv)

Cumulative reward importance, defined as the total amount of points achieved by each user by completing the rewarded actions. It accounts for the total amount of points, badges, and rewards achieved by an individual user in the SmartH2O platform.

Each user profile in the SmartH2O platform was associated with a unique smart meter ID, which allowed linking the user activity in the platform with the household water consumption data. User confidentiality was maintained throughout the full study as data were anonymized by the water utility managing the water meters and the central database.Population and study sizeOur observational study was conducted in the city of Valencia, Spain. With a population of 794,288 inhabitants, as reported in 2019 by the Spanish National Institute of Statistics (Institudo Nacional de Estadística)38, Valencia is the third-largest city in Spain. The water utility of Valencia (Global Omnium–EMIVASA) has installed more than 425,000 smart water meters since the early developments in 2006 to monitor the water consumption of nearly all the population39 (the last official census data, recorded in 2011, report 419,994 households in total in Valencia40). The total population considered in this study after application of the exclusion criteria described in the next section included 334 individual households, each equipped with a water meter.The architecture of the smart metering infrastructure deployed in Valencia has been designed in order to be vendor-independent, so it allows for different smart metering solutions to be integrated39. While this is clearly an advantage for procurement, the diversity of hardware has an impact on data sampling and only one of the available technologies supports hourly data collection, which is a preferred requirement for water consumption data quality assessment and provision of sub-daily water consumption information to households in our case-control study. The number of hourly reading meters in Valencia amounts to 168,172 as of July 12th, 2020. EMIVASA also offered its customers access to a web platform where bills and invoices could be managed and also information about the current (daily and monthly) water consumption data was made available.During our observational study, we integrated the digital SmartH2O platform20,21 in the EMIVASA portal. We invited users who already had an account in the platform and a compatible meter reading frequency to voluntarily join our observational study and sign up to the SmartH2O platform. The recruitment campaign was performed using different media channels, namely, newspaper articles on consumer magazines, radio programs, banners on the digital and printed invoices sent to EMIVASA customers, and also a Facebook campaign targeting the Valencia area. At the end of the recruitment campaign, we received 525 applications out of which we obtained a treatment group composed of 223 households after application of the inclusion/exclusion criteria. Out of the households who did not apply to join the case-control study during the recruitment phase, 111 households agreed to be monitored as part of the self-selected control group to be considered as a benchmark group not subject to treatment, after active recruitment via phone by the EMIVASA call center (client service management). Households in the control group had only access to their water consumption data through the already existing platform, which did not offer any type of smart meter-based consumption feedback, behavioral stimuli, and/or gamification elements.Informed consent was obtained from the households monitored in this study. Moreover, the water utility (Global Omnium–EMIVASA) supervised and approved the collection, usage, and processing of the anonymized quantitative variables above described in compliance with the EU General Data Protection Regulation 2016/679 and the pre-existing Spanish law 15/1999 LOPD of 1999 (the SmartH2O study started before the adoption of the GDPR in 2016).Baseline and observation periodsThe treatment period of the case-control study lasted 8.5 months, from June 2016 to February 2017. We also continuously collected anonymized water consumption data for the study population from June 2016 to February 2019 both to conduct the longitudinal study presented in this paper and evaluate water consumption changes over time in comparison with a pre-treatment baseline (June 1st, 2015– April 30th, 2016), as well as to compare water consumption changes in the treatment and control groups. Consistently with the months included in the treatment period (short-term behavior change), we identify the observation period June 1st, 2017–February 2nd, 2018 for medium-term behavior change assessment, and the observation period June 1st, 2018–February 2nd, 2019 for long-term behavior change.Exclusion criteriaThe population considered for analysis of water consumption changes in this observational study was obtained by sequential application of the following exclusion criteria.

1.

Exclusion of empty households. First, we excluded the households with no data in the baseline and treatment period. We classified in this category also the households with a cumulative water consumption lower than 1.5 m3 over the whole baseline and treatment period (which together last nearly 20 months). This threshold value was identified as a conservative choice after consultation with the local water utility and comparison with the average values of water consumption in the entire population (slightly above 0.21 m3/day) and the European average water consumption, which amounts to 128 liters per inhabitant per day (0.128 m3/day)41. A household in the considered population would use ~1.5 m3 in one week (0.21 m3/day × 7 days). While lower values than the average consumption are observed in those days in which the inhabitants spend little time at home, a cumulative consumption of 1.5 m3 over the course of more than 1 year can indicate that the house is generally empty (and possibly the observed water consumption is due to leaks).

2.

Exclusion of households with insufficient data length. We removed the households with water consumption readings for less than 1000 h (approximately 6 weeks). This step guarantees a minimum representation of weekend/weekday water demand variation for more than 1 month (please note that the total duration of the treatment period is 8.5 months).

3.

Exclusion of partially empty households. We excluded the households with more than 90% water consumption readings equal to zero in the baseline or observation period or completely lacking data for one of these two periods. We considered these households to be empty or equipped with faulty meters at least during one of the two short-term periods of interest. The above value threshold of 90% was identified with a trial-and-error procedure and expert-based data analysis that balance the rate of exclusion with the size of the remaining dataset.

4.

Exclusion of households lacking day-of-week representation. We excluded the households with available observations for less than 7 unique day types, to guarantee a minimum representation of water consumption routines that depend on the day of the week. For those households with smart meters recording water consumption with hourly sampling frequency, we removed days with more than 4 h of gaps from the smart meter time series (anomalous meter data logging).

5.

Exclusion of households with anomalous high water consumption. We considered hourly water consumption readings larger than 1 m3 as outliers (we thus removed these hourly readings) and we removed the households with a daily average water consumption larger than 1 m3 in at least one phase of the longitudinal study. High values of water consumption can be observed for specific days (e.g., when customers use water for outdoor irrigation or filling up a pool), yet average daily water consumption values over the selected threshold are more than three times higher than the European average (equivalent to approximately 0.3 m3/day per household). We did not apply more restrictive thresholds, in order not to bias our analysis and avoid unjustified exclusion of high water consumers.

6.

Exclusion of households with unrealistic short-term consumption change levels. We excluded the households with extreme values of short-term consumption change during the treatment period, which were identified as outliers by Tukey’s fences42. According to Tukey’s fences, a data point xi is considered an outlier if:$$x_i notin [Q_1 – kleft( {Q_3 – Q_1} right),Q_3 + k(Q_3 – Q_1)]$$
(1)

where Q1 is the 25th empirical quartile (i.e., 25% of the data is lower than this point) and Q3 is the 75th empirical quartile (i.e., 75% of the data is lower than this point), and k = 1.5. Tukey’s fences with k = 1.5 approximate the 99.7% confidence interval defined for normal distributions by a distance of three standard deviations from the mean.

7.

Exclusion of households with anomalous conditions in medium-term and long-term. We excluded 51 households that met the above exclusion criteria 1–6 during either the medium-term or long-term observation periods. Water consumption change patterns would be incomplete/anomalous for these households, with at least one missing/anomalous period out of the four periods of interest (i.e., baseline, treatment period, or following observation periods in 2018 and 2019).

With the above exclusion criteria, we obtained the 334 households considered for behavior change analysis in this observational study. More details on the population size after application of each exclusion criteria are reported with a flow diagram in Supplementary Fig. 1043. It is worth noting that only less than 2% of high consumption households have been excluded, while most of the other excluded households had insufficient data or unrealistically low consumption levels. Also, the number of households in the sample considered here differ from those considered in the evaluation of the SmartH2O project44, due to the different temporal length of the two studies and the application of the exclusion criteria on data recorded in different periods (the SmartH2O project only included the baseline and treatment periods).Adopting the same criteria to exclude households from the behavior change analysis only during the summer period (Fig. 1d) resulted in a reduced population of 179 households (101 households in the treatment group and 78 households in the control group), due to limited data availability for the summer period. Similarly, a subset of 198 households in the treatment group was considered for the correlation analysis by logistic regression (Fig. 4), as the excluded 25 households presented incomplete smart meter data or incomplete information on their usage of the digital SmartH2O application.Data analysis and statistical methodsWe performed customer segmentation to analyze heterogeneous long-term behavior change patterns (Fig. 3 and Supplementary Fig. 9). We applied agglomerative hierarchical clustering45 to the patterns of average daily household water consumption during the entire duration of the longitudinal study. Here, a water consumption pattern of a household is a vector that contains four values of average daily water consumption, i.e., one for each period of the observational study, including the baseline (see “Methods” section–Baseline and observation periods). The only variable given as input to the hierarchical clustering algorithm consists of household-scale average water consumption per day for each phase of our observational study, which spans the baseline and the three observation periods in 2017, 2018, and 2019. Complete linkage and correlation distance were considered for hierarchical clustering. Complete linkage calculates the distance between two household clusters as the distance between the farthest pair of household water consumption patterns in the two household clusters, i.e., the maximum distance formulated as follows:46$$dleft( {u,v} right) = {mathrm{max}}left( {{mathrm{dist}}left( {uleft( {x_i} right),vleft( {z_i} right)} right)} right.$$
(2)
where d(u,v) is the distance between clusters u and v, xi are the points belonging to cluster u and zi those belonging to cluster v. Given two vectors of observations xi and xj, which in our study correspond to the water consumption patterns of two households (each with N elements, with N = 4, where each element is the household-scale average water consumption per day for the baseline and three observation periods) and their mean values ((bar x_i) and (bar x_j)) the correlation distance used by hierarchical clustering is calculated as follows:47$${mathrm{dist}}left( {x_i,x_j} right) = 1 – frac{{(x_i – bar x_i) cdot (x_j – bar x_j)}}{{left| {x_i – bar x_i} right|_2left| {x_j – bar x_j} right|_2}}$$
(3)
We considered hierarchical clustering as an appropriate choice because the analysis of the different hierarchical levels allowed the discovery of heterogeneous water consumption behaviors that would be potentially hidden if algorithms requiring a predefined number of clusters were used. We adopted complete linkage clustering to avoid that individual, mutually close households would force pairs of clusters representing different behaviors to merge. Also, we adopted correlation distance as we wanted to identify similarities in water consumption patterns over time, rather than in water consumption volumes.After clustering the households in the treatment group with the above hierarchical clustering, similarly to a previous study18, we analyzed the coefficients of a logistic regression classifier cross-validated with binary tests to identify which candidate factors correlate with the main behavior change patterns that characterize the households in the treatment group (Fig. 4 and Supplementary Table 3). In this study, the input candidate factors consist of five independent variables that comprise the availability of smart meter hourly data frequency and the four digital user engagement variables, i.e., login count, non-rewarded action count, rewarded action count, and cumulative reward importance. First, we balanced the distribution of the households in the treatment group across the behavior change segments considered in the binary tests by Synthetic Minority Over-sampling Technique (SMOTE)48. SMOTE oversamples the minority class to balance the sample distribution of a labeled dataset over the different classes. As we consider binary test where only two behavior change segments (or two groups of behavior change segments) are compared, the majority class represents the behavior change segment (or group of behavior change segments) with the highest number of samples and vice versa for the minority class. According to the SMOTE formulation48, starting from a sample ci,initial, which in this study is the vector of input candidate factors for a household i in the minority class, a new sample ci,new is generated on the line between ci,initial, and one of its k nearest-neighbors cj,initial, with the following formula:$$c_{i,{mathrm{new}}} = c_{i,{mathrm{initial}}} + lambda (c_{j,{mathrm{initial}}} – c_{i,{mathrm{initial}}})$$
(4)
where λ is a random number between 0 and 1, and k = 5 nearest neighbors computed based on Euclidean distance are considered by default48. Among the possible options to perform class balancing, here we adopted a “not majority” strategy to over-sample the minority classes, i.e., we resample all classes but the majority class (which, in our binary problem, is equivalent to resampling the minority class).Second, we trained a logistic regression classifier49 with k-fold cross-validation (k = 5) and evaluated its performance via weighted F1 score. In our binary problem, the logistic regression classifier models the class membership probability P(yi,p = 1) for household i, where yi,p = 1 indicates that the household belongs to behavior change pattern p (else yi,p = 0, according to the following logistic function:$$Pleft( {y_{i,p} = 1} right) = frac{1}{{1 + exp^{ – f(c_i)}}}$$
(5)
where f(ci) is a linear function where the input variables ci are weighted by corresponding coefficients α:$$fleft( {c_i} right) = alpha _0 + alpha _1c_{i,1} + alpha _2c_{i,2} + ldots + alpha _Mc_{i,M} + varepsilon _i$$
(6)
In this study, M = 5, ci,1 is a binary variable representing the availability of smart meter with hourly data frequency, ci,{2,3,4,5} are the four digital user engagement variables defined above, α0 is the intercept of the logistic regression, and εi is random noise. We normalized the variables before logistic regression classification by subtracting the mean and dividing by the standard deviation to rescale them to comparable value ranges. The analysis of their corresponding logistic regression coefficients reveals how these variables discriminate among different clusters of water consumers and, thus, how they are potential determinants of defined water consumption behaviors. The F1 score (FS) is first calculated for each behavior change pattern (or group of patterns) p as the harmonic mean of the precision and recall achieved by the logistic regression classifier, formulated as follows:$${mathrm{FS}}_p = 2 times frac{{({mathrm{precision}}_p times {mathrm{recall}}_p)}}{{({mathrm{precision}}_p + {mathrm{recall}}_p)}}$$
(7)
$${mathrm{Precision}}_p = frac{{{mathrm{TP}}_p}}{{{mathrm{TP}}_p + {mathrm{FP}}_p}}$$
(8)
$${mathrm{Recall}}_p = frac{{{mathrm{TP}}_p}}{{{mathrm{TP}}_p + {mathrm{FN}}_p}}$$
(9)
where, given positive and negative classes, TPp, FPp, and FNp are the number of true positive elements (the classifier correctly predicts the positive class for them), false-positive elements (the classifier incorrectly predicts the positive class), and false negative elements (the classifier incorrectly predicts the negative class). A weighted average of the FSp is then computed to account for class imbalance:$${mathrm{FS}}_{{mathrm{average}}} = frac{1}{H}mathop {sum }limits_{p in P} |p| times {mathrm{FS}}_p$$
(10)
where P is the total number of classes p and H is the total number of elements aggregated across all classes.Software implementationWe coded the exclusion criteria in Matlab and used the “prctile” function for the calculation of the quantiles in Tukey’s fences (last Matlab version tested: R2020b)50. We implemented the customer segmentation analysis and logistic regression classifier in Python (version 3.7.1): the customer segmentation analysis relies on the hierarchical clustering included in the SciPy library51; the logistic regression classifier, along with its k-fold cross-validation and performance evaluation, were implemented using the machine learning library Scikit-learn52; SMOTE oversampling was implemented using the Imbalanced-learn toolbox53. A notebook with the Python code used to generate the results reported in this article is available in a public GitHub repository54. More

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