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Sociodemographic of respondentsA total of 140 households completed surveys with a response rate of 45.0%. The respondents were comprised of 48.6% males (n = 68) and 51.4% females (n = 72) in the general population aged 18 to 64 years, which were differentiated into five age groups: ≤19 (1.4%); 20–29 (22.1%); 30–50 (67.1%); 51–59 (5.0%); ≥60 (4.3%). There was a variation in terms of education levels and employment status; the majority of respondents were Bachelor-degree holders (at least 45%) and working as government servants (60.0%), as tabulated in Table 1. The accounted median monthly household income of Putrajaya is RM 7512 (~USD 1803, mean monthly household income of RM 10401, ~USD 2496), exceeding the national level (RM 4585, ~USD 1100)26. The survey covered household groups: bottom 40% (B40), middle 40% (M40), and top 20% (T20), classified into income groups ≤RM 2999, RM 3000–4999, RM 5000–6999, RM 7000–8999, RM 9000–10999, RM 11000–12999, and ≥RM 13000, where RM 1 approximately equivalent to USD 0.24 in average. On an average, respondents had lived in Putrajaya for seven years.Table 1 Descriptive statistics about risk perception of drinking water supply security with potential EDC contamination.Full size tableHuman morphology and drinking water consumption patternsThe present study involved 140 households with 257 total respondents (n = 257), consisting of infants (n = 4, aged less than 1 year; birth–5; 6–11 months), children (n = 77, aged 1 to 9 years; 1–3; 4–6; 7–9 years), adolescents (n = 37, aged 10 to 19 years; 10–14; 15–19 years), adults (n = 133, aged 20 to 59 years; 20–29; 30–50; 51–59 years) and elderly (n = 6, aged more than 60 years) (Table 2). Age groups were categorized based on previous studies27,28,29,30.Table 2 Age groups and respective mean body weight, body height, body mass index, daily water intake, and daily water intake per body weight.Full size tableThere were no significant differences between males (n = 125) and females (n = 132) in terms of body weight (t(235) = 1.671, p = 0.096), body height (t(225) = 0.804, p = 0.422), body mass index (t(246) = 1.116, p = 0.266), and daily water intake (t(255) = 0.483, p = 0.629). Surprisingly, males consumed more water than females in the United States and Australia19,31. Body weight showed a significant positive correlation to height based on Pearson product-moment correlation test (r = 0.861, p  More

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Adjusting GEFS forecasts to local climatologyWhat amount of correction is required for GEFS forecasts to align with CHIRPS local climatology? The amount of correction varies widely across the globe and throughout the year. Figure 1a shows annual mean bias for GEFS reforecast 15-day totals. In this figure, wetter-than-CHIRPS climatology and systematic over-prediction of 15-day totals by GEFS is indicated by positive mean bias values, while the opposite is indicated by negative values. GEFS forecast mean bias was calculated for each month and then averaged across rainy season months, to focus aggregate results on the rainfall seasons, when precipitation forecasts are relevant. Monthly dry masks excluded locations with a monthly average of less than 10 mm, according to CHIRPS climatology. In general, one consistent result from Fig. 1a is a tendency to increase precipitation in many mountainous tropical and subtropical regions. By design, orographic precipitation enhancements in such regions are represented fairly well in CHIRPS, and these are carried through to CHIRPS-GEFS precipitation forecasts. The CHIRPS-GEFS bias-correction process reduces systematic errors (Fig. 1b), with the overall mean absolute bias error going from 24.1 mm for GEFS to 19.7 mm for CHIRPS-GEFS, an ~18% reduction.Fig. 1Annual mean bias and global error characteristics for GEFS reforecast data compared to CHIRPS, based on 15-day precipitation totals from Day 1, 6, 11, and 16 of each month during 2000–2019. Annual mean bias (a) shows the annual average of differences in GEFS reforecast and CHIRPS monthly means. Annual average error (b) shows the distribution of GEFS reforecast and CHIRPS-GEFS errors (product – CHIRPS). Both panels are based on in-season pixels, which are defined by monthly average CHIRPS  > 10 mm.Full size imageFigure 1a through Fig. 5 are based on GEFS reforecast, CHIRPS, and CHIRPS-GEFS data for the 5-day or 15-day periods beginning on the 1st, 6th, 11th, and 16th day of the month. All these exclude dry season months. Figure 1b shows the corresponding global distribution of annual average error for the GEFS reforecast and CHIRPS-GEFS, and is discussed later.GEFS has a large annual average positive bias of higher-than 40 mm in some areas of the globe, including in central Mexico, Central America, northern South America, the Andes and Himalayan Mountain ranges, and in southern China, Papua New Guinea, and localized areas of central Africa, the Ethiopian Highlands, and the western montane United States (Fig. 1a). GEFS has positive bias, by more than 5 mm for the annual average 15-day period, across the northern United States including in the Midwest, from Mexico’s northern mountains through most of Central America, in northern South America, the Andes range, eastern Brazil, in parts of central Europe, central and northern Asia, in the area from southern China to Myanmar and Thailand, and in northeastern and western India. GEFS has positive bias in portions of East Africa (Rwanda, Burundi, Tanzania, western Ethiopia), West Africa (Cameroon, Gabon), and Southern Africa (Zambia, central Angola, northern Zimbabwe, eastern South Africa). GEFS has negative bias, by more than 5 mm on average, in parts of central and northern Africa, Senegal, northern Australia, central South America, western India, the Yucatan peninsula, and the United States Gulf Coast.GEFS’ systematic bias changes throughout the year, as shown by the monthly mean bias in January, April, July, and October (Fig. 2). This is unsurprising, given that drivers of weather change too, but higher bias in particular months can be problematic for forecast users. In Ethiopia, for example, GEFS overestimates by large amounts during the Kirempt season (e.g., in July) and in October in the southwest. In central Brazil, the bias changes markedly by season, from a high negative bias in October to an expansive wet bias in April. In the Midwestern and northern United States, GEFS also shows a more expansive wet bias in April than in January, July, or October. In some areas, like in southern China and the Andes mountains, GEFS means are higher than CHIRPS means throughout the year.Fig. 2Monthly mean bias for GEFS reforecast data compared to CHIRPS, based on 15-day precipitation totals from Day 1, 6, 11, and 16 of each month during 2000–2019. Mean bias for January (a), April (b), July (c), and October (d) shows the difference in GEFS reforecast and CHIRPS monthly means. Shown for in-season pixels, which are defined by monthly average CHIRPS  > 10 mm.Full size imageThe CHIRPS-GEFS downscaling procedure corrects for systematic errors in GEFS forecasts that vary spatially and temporally. To assess the efficacy of the CHIRPS-GEFS approach, we began by calculating the per-pixel difference between GEFS and CHIRPS, and CHIRPS-GEFS and CHIRPS for 15-day periods. These were calculated for each month, for in-season pixels, and then averaged across the year. We then looked at the histogram of the resulting differences (Fig. 1b), to identify the distribution of annual average errors in these two products. CHIRPS-GEFS errors are shown as gray bars and GEFS errors are overlaid as hollow red bars. A desirable pattern is more small errors (higher bars close to 0 mm) and fewer large magnitude errors (lower bars at larger precipitation values). As shown in Fig. 1b, the bias-correction procedure has this effect, and results in CHIRPS-GEFS having overall lower errors for global rainy seasons compared to GEFS. GEFS 15-day errors more commonly involve over prediction of observed amounts than under prediction, as shown by the higher proportion of positive versus negative moderate to large positive errors. Part of this is due to the lower limit of under prediction being zero precipitation, while over prediction can range from marginal precipitation amounts to very high amounts. As shown in Fig. 1b, the CHIRPS-GEFS bias correction particularly reduces GEFS forecast errors for moderate-to-high rainfall amounts, and it results in a global 15-day error distribution that has a higher proportion of small errors, e.g., errors within −10 mm to 10 mm of CHIRPS values (51% for CHIRPS-GEFS and 43% for GEFS). Errors in categories ranging from 10 mm to 40 mm occur less often in CHIRPS-GEFS, globally, with probabilities in those categories reduced by around 15 and 25 percent at 10 mm to 20 mm and 20 mm to 30 mm, respectively, and by around 30 percent to 40 percent for errors that are higher than 40 mm.Next, we show performance of the 5-day and 15-day CHIRPS-GEFS precipitation forecasts by correlations and mean absolute errors for the historical record, compared to CHIRPS data for these periods. As described in Data Records, multiple outlets use forecast amounts for these periods. In the Usage Notes section, probability of detection scores for 15-day CHIRPS-GEFS in Africa are presented while describing an operational application of the CHIRPS-GEFS for seasonal monitoring. In that discussion we also examine the performance of 5-day forecasts during the 2020–2021 season in key regions of Kenya, Angola, Zambia, Zimbabwe, and Madagascar.Pearson correlation coefficients for 5-day and 15-day CHIRPS-GEFS, compared to CHIRPS (Fig. 3), indicate the ability of forecasts to predict deviations from average. It should be noted that correlations are nearly entirely driven by the information coming from the GEFS forecasts. The conversion to CHIRPS-GEFS adjusts the GEFS values to make them more “CHIRPS-like,” while also approximating the historical context of the GEFS forecast. Wet extremes forecasted by GEFS translate into wet extremes in CHIRPS-GEFS. Areas with very low correlations (R  0.7) are the United States, Western Europe, and Eastern Europe, southeastern South America, southern Central Asia, eastern China, parts of East and Southern Africa, and Australia. Globally, correlations are higher in January, April, and October than in July, which indicates generally higher forecast accuracy in those months. Exceptions are in eastern China, southern Brazil, eastern Mexico, northeastern Ethiopia, and central and southern Australia, where July correlations are not substantially lower. 15-day forecasts also have high correlations in some areas, including in the Western and Midwestern United States in January, in central and northern Australia in April, and in eastern Brazil in January and October.Fig. 3CHIRPS-GEFS 5-day and 15-day Pearson correlation coefficients, as compared to CHIRPS, for January, April, July, and October. (Validation data: CHIRPS 5-day and 15-day totals from the 1st, 6th, 11th, and 16th of the month, for 2000 to 2019. Shown for in-season pixels, which are defined by monthly average CHIRPS  > 10 mm.Full size imageIn Africa, a region where CHIRPS data is actively used by the Famine Early Warning System Network (FEWS NET) and other organizations for seasonal monitoring and drought early warning, forecast correlations indicate moderate to good 5-day and 15-day forecast performance in areas of East Africa, Southern Africa, and western North Africa during rainy season months. Some of the highest 15-day correlations in Africa are during important rainy season months, for example, in northeastern Ethiopia in July and April, in Kenya in April, in Zimbabwe and southern Mozambique in January, and in the Sudanian zone of West Africa in October. Very low correlations indicate low forecast skill in the Sahel, coastal West Africa, and in Central Africa in the DRC, Republic of the Congo, and Gabon.Mean absolute error of the bias-corrected GEFS forecasts highlight the areas where forecast amounts have historically been less reliable (Fig. 4). These indicate non-systematic errors associated with rains not materializing in the forecast location in the forecast period, which can be from GEFS model deficiencies and the inherent challenges of weather forecasting. Extreme precipitation events and warm season, deep moist convection-driven precipitation are notorious challenges for numerical weather prediction systems48,49, and CHIRPS-GEFS data are not immune to this problem. Remotely sensed data, including CHIRPS, also struggle with estimating extreme high rainfall amounts13,50, though since we are comparing CHIRPS-GEFS to CHIRPS, the main source of the large errors shown here would be the GEFS reforecast.Fig. 4CHIRPS-GEFS 5-day and 15-day mean absolute errors, as compared to CHIRPS, for January, April, July, and October. Validation data: CHIRPS 5-day and 15-day totals from the 1st, 6th, 11th, and 16th of the month, for 2000 to 2019. Shown for in-season pixels, which are defined by monthly average CHIRPS  > 10 mm.Full size imageAs shown in Fig. 4, the magnitude of errors follows climatology, with 5-day errors typically under 10 mm for drier rainy season months. In wetter months and locations errors are typically between 10 mm and 20 mm. With higher rainfall magnitude there is greater potential for larger errors. The 15-day forecast errors exhibit a similar spatial pattern to the 5-day errors, and error magnitudes correspond to the three-times larger accumulation interval as well as expected lower skill at longer lead time. Figure 4 shows especially large 15-day mean absolute errors in January near northern Mozambique and Madagascar, in July and October in parts of Central America, in April in central Kenya and southwestern Tanzania, in July in India’s Western Ghats Mountains and in the Himalayas, and in the Maritime Continent. In southeast China, while the 15-day correlations indicated decent skill at forecasting the sign of precipitation anomalies, large 15-day errors indicate the influence of poorly forecast large storms, which unbiasing cannot correct for. In the Amazon rainforest, many areas with low correlations also have high forecast errors, underscoring poor forecast performance there. More

Availability per capitaThe APC water stress indicator represents the state of physical water scarcity. The total population under a certain level of water scarcity is called the stressed population. We calculated the water-stressed population and compared it to earlier estimates for validation. We found that the total population percentage (calculated using the ensemble mean discharge) facing acute physical water stress calculated using the APC of 500 m3/capita/year will vary as to ({54.9}_{-1.7}^{+1.1} %;({47.6}_{-2.5}^{+2.1} % )), ({66.6}_{-3.3}^{+2.8} %;({59.8}_{-6.1}^{+5.6} % )), and ({55.6}_{-1.8}^{+4.2} % ;({47.0}_{-2.6}^{+5.7} %)) (+/− values show the maximum variation considering discharge using single GCM to the ensemble mean discharge) at the end of the century (i.e., the year 2099) under the SSP1–RCP2.6, SSP3–RCP7.0, and SSP5–RCP8.5 scenarios, respectively, representing different socioeconomic and climate conditions considering the MY19 (JO16) future population dataset (methods for scenarios and datasets details). By contrast, 44.5% (45.1%) of the global population faced acute physical water stress at the beginning of the century (i.e., the year 2000). The above percentages correspond to 3.5 (3.3), 7.9 (7.5), and 3.9 (3.4) billion populations for the SSP1–RCP2.6, SSP3–RCP7.0, and SSP5–RCP8.5 scenarios and 2.68 (2.75) billion for the historical scenario (i.e., beginning of the century). The historical value is consistent with the value of 2.7 billion previously reported by Hoekstra et al.13 and 2.4 billion mentioned by Oki and Kanae1.APC enhanced with GDP per capita—country-scale assessmentNext, we analysed the relationship between APC and GDP per capita. First, to revisit the findings of Oki et al.19, we conducted country-level analyses for the beginning (i.e., the year 2000) and end (i.e., the year 2099) of the century. To compare the absolute change for a longer period with the constant exchange rate, we used GDP-PPP per capita (USD 2005) due to its availability and defined water stress (physical and economic water scarcity) for both past and future scenarios using the same threshold line (see “Methods” section). The consistency in the results in terms of distribution of countries (Fig. 1 and Supplementary Fig. 1) for both historical (GPWv4 and HYDE3.2) and future (MY19 and JO16) population datasets confirm the similarity in aggregated country-level population data. We did not find any countries below the threshold line at the end of the century, whereas we found Somalia, Western Sahara, Yemen, and Niger below the threshold line at the beginning of the century (Fig. 1, Supplementary Table 1 for base scenario experimental settings, results for other combinations of climate and population dataset are provided as Supplementary Fig. 1). The comparison of per capita water availability (APC) for countries below the threshold line for this study and additional analysis considering various climate forcing data with the same socioeconomic data showed substantial differences. These arid region countries have less runoff and considerable sensitivity towards the metrological data, causing the large difference in availability per capita (APC) of freshwater (Supplementary Table 2 for comparison of values considering different climate forcing data). Additionally, the quality of socioeconomic data contains uncertainty due to political instability23,24,25,26, defying the hypothesis for these countries. We confirmed that although a few countries can contradict, the hypothesis of Oki et al.19 remains valid for various scenarios considered.Fig. 1: Country-level scatter plot for APC vs GDP-PPP per capita and density plot considering the number of countries for various socioeconomic and climate scenarios.Each circle corresponds to a country, and the circle’s size corresponds to the country’s population. CHN, ESH, IND, NER, SOM, USA, and YEM represent China, Western Sahara, India, Niger, Somalia, United States of America and Yemen, respectively. Yellow, green, red, and blue colours represent the historical, SSP1–RCP2.6, SSP3–RCP7.0, and SSP5–RCP8.5 scenarios, respectively, and the dashed line represents the threshold value for physical and economic water scarcity. The analysis was performed considering the GPWv4 dataset for the historical, i.e., the year 2000 population and MY19 for the future, i.e., the year 2099 population.Full size imageAPC enhanced with GDP per capita—grid-scale assessmentNext, we proceeded with grid-level analyses. We confirmed the existence of locations in the world facing the challenges of economic and physical water scarcity identified at 0.5° resolution (Fig. 2, results of SSP1–RCP2.6 and SSP5–RCP8.5 are shown in Supplementary Fig. 2 and Supplementary Fig. 3). The total population and spatial distribution facing challenges (i.e., grids below the threshold line defined by Eq. 1) differed in the different scenarios.Fig. 2: Grid-level scatter plots for APC vs GDP-PPP per capita and density plot considering the number of grids.(a) Historical-GPW, (b) Historical-HYDE, (c) Future370-MY19, and (d) Future370-JO16 scenarios. Grid values are represented as circles, and the dashed line represents the threshold line proposed by Oki et al.19. The density plot includes dotted coloured lines (lime and red) for the median and dark shading for the interquartile range (first and third quartiles). The white circle represents the grid size of 20 million population. e Boxplot for the total population facing physical and economic water scarcity (grids below the threshold of Eq. 1) for all considered scenarios. Legend symbols represent the analysis using the discharge considering various GCMs and the ensemble mean of discharge considering all GCMs. *analysis for Historical-GPW and Future-MY scenarios, **analysis for Historical-HYDE and Future-JO scenarios (Supplementary Table 1 for scenarios/ experiment settings, and Supplementary Table 5 for water-scarce population and uncertainty values).Full size imageIt can be observed from the density plots in Fig. 1 and Fig. 2 that there is a rightward shift in the peak and a significant increase in the mean and median values of the GDP-PPP per capita for the future scenarios compared to the historical scenario. The density plot for the APC for the future follows a trend similar to the trend of the past (i.e., a similar frequency distribution of APC at the grid scale), with an increase (decrease) in the median values observed for the future scenarios for MY19 (JO16) at the grid level (Supplementary Table 3 and Supplementary Table 4 for results of all statistical analyses considering future and historical datasets).We calculated the population facing hardship due to both physical and economic water scarcity (i.e., grids below the threshold line defined by Eq. 1). As a result, at the end of the 21st century (i.e., the year 2099), ({0.32}_{+0.00}^{+0.68}) (({234}_{-10}^{+24})) million people were estimated to face hardship under the SSP1–RCP2.6 scenario when using an urban-concentrated, i.e., MY19 (dispersed, i.e., JO16) population dataset. The estimated populations facing hardship under the SSP3–RCP7.0 and SSP5–RCP8.5 scenarios were ({327}_{+35}^{+202}) (({665}_{-67}^{+181})) and ({6.9}_{-1.1}^{+1.2},left({176}_{-3}^{+36}right)) million respectively (+/− values show the maximum variation in the global population facing water scarcity, calculated considering discharge using single GCM and the ensemble mean discharge), compared to 327 (358) million at the beginning of this century (i.e., the year 2000) (Fig. 2e, Supplementary Table 5). Analysis considering MY19 and JO16 population datasets yield three orders of difference in the stressed population at maximum. The total number of water-stressed populations would decrease in the future (except for the SSP3-RCP7.0 with JO16 population distribution i.e., Future370-JO16 experiment) due to an increase in income.Analysis considering various scenarios (Supplementary Table 1 for scenarios) shows that the uncertainty associated with the SSP–RCP scenarios (i.e., maximum, and minimum difference in the population facing scarcity considering any two scenarios among SSP1-RCP2.6, SSP3-RCP7.0, and SSP5-RCP8.5 for the ensemble mean discharge) and global climate models (GCMs) (i.e., maximum and minimum difference in the population facing scarcity considering any two GCMs for a particular SSP-RCP scenario) were in the range of 6.58–489 and 0.03–248 million, respectively (Supplementary Table 5).We found that the population distribution uncertainty (i.e., maximum and minimum difference in the population facing scarcity considering MY19 and JO16 gridded population distribution for a particular SSP-RCP scenario) for the end century (i.e., the year 2099) followed a similar trend and was in the range of 169.1–338 million (Supplementary Table 5). At the same time, the uncertainty at the beginning of the century (i.e., the year 2000) was within ~10 %, considering GPWv4 and HYDE3.2 gridded population datasets, confirming the high accuracy in estimation of historical population and their distribution. The maximum range value is brought by SSP3-RCP7.0, which is attributed to the large dispersion of population distribution in the SSP3. The grid-level analyses revealed that the future prediction includes large uncertainty due to the spatial distribution of within-country population along with the SSP–RCP paths of global sustainability (SSP1–RCP2.6), regional rivalry (SSP3–RCP7.0), and economic optimism (SSP5–RCP8.5) taken by the world (Fig. 3). The number of water-scarce grids (i.e., grids below the threshold line) in the future will increase or decrease compared to the past and depend mainly on the spatial distribution of population and GDP compared to freshwater availability.Fig. 3: Physical and economic water-scarce regions.a Historical (2000) considering the GPWv4 dataset, (b) Historical (2000) considering the HYDE3.2 population dataset, (c) Future (2099) considering the MY19 population dataset, and (d) Future (2099) considering the JO16 population dataset scenarios. The future (2099) case shows the possible combinations of scenarios with different colours; the values inside the circular legend show the number of people (in millions) facing scarcity with ranges representing the minimum and maximum values considering scenarios combination.Full size imageFactor decompositionThe spatial distribution of grids below the threshold line of various historical and future scenarios (Fig. 3) showed that there would be an emergence of new water-scarce grids in the future, i.e., new grids facing water scarcity in future scenarios but were not facing water scarcity in the historical scenarios. These grids will face water scarcity either due to the decrease in freshwater availability (climate change) or GDP-PPP (socioeconomic change) or an increase in the population (socioeconomic change) among the considered variables for the analysis. Fig. 4 presents the boxplot distributions of absolute values for freshwater (mm/year), population density (capita/km2), and GDP-PPP (USD/year) for newly identified water-scarce grids (grids facing scarcity in the future but not facing it in the past), comparing the values for the historical and future scenarios. The freshwater availability (mean and median values) does not change significantly over time for the new water-scarce grids, i.e., the difference between the future scenarios (SSP1–RCP2.6, SSP3–RCP7.0, and SSP5–RCP8.5) and the historical scenario is negligible. Compared to freshwater, there is a significant increase in population density for all considered scenarios and a less significant increase (decrease) of GDP-PPP of the grids (regions) for the MY19 (JO16) population datasets (Supplementary Table 6 for statistical analysis), suggesting that the primary reason for the water scarcity in these areas will be population growth.Fig. 4: Comparison of new water-scarce grids (i.e., grids facing physical and economic water scarcity in the future but not in the past).Box plots comparing the absolute values of (a), (d) freshwater availability (mm/year); (b), (e) population density (capita/km2); and (c), (f) GDP-PPP. The analysis for (a), (b), and (c) was performed considering the Future-MY and Historical-GPW Experiment settings, and that of (d), (e), and (f) was performed considering the Future-JO and Historical-HYDE experiment settings (Supplementary Table 1). The error bars show the 100% confidence interval (i.e., 0th and 100th percentile), the bottom and top of the box are the 25th and 75th percentiles, and the line inside the box is the median (50th percentile).Full size imageThe global water scarcity analysis considering various future scenarios (SSP1–RCP2.6, SSP3–RCP7.0, and SSP5–RCP8.5) identify various possible water stress regions (grids below the threshold line) of the world affecting the different number of populations. The common water-scarce grids recognised in all these scenarios (grids showing water scarcity for the SSP1–RCP2.6, SSP3–RCP7.0, and SSP5-RCP8.5 scenarios simultaneously) have the highest possibility (certainty) of facing water scarcity in the future. We compared the sensitivity analyses (methods for the approach adopted and Supplementary Table 7 for sensitive analysis experiment settings) results with the base scenario (Supplementary Table 1) values to know the major factor causing water stress among the considered variables for the grids with the highest possibility of water scarcity. The water-scarce population, which can be simultaneously identified in all future scenarios, will be in the range of 0.46–1.82 (156–393) million (range shows the minimum and maximum population affected considering all three future scenarios), considering the historically available freshwater for future scenarios, i.e., Historical-MY (Historical-JO) experiments. Similarly, the population affected considering the historical population for the future scenarios, i.e., Future-GPW (Future-HYDE) experiments, was determined to be 13 (10–16) million; considering the historical GDP-PPP for the future scenarios, i.e., Future-MY-TG, (Future-JO-TG) experiments, the result was 1514–2928 (1466–3132) million (Supplementary Fig. 4 and Supplementary Fig. 5, Supplementary Table 7 for experiment settings). The comparison of all sensitive analysis scenarios values with the base scenario value of 0.0 (110–269) million (Fig. 3c, d) showed that the effects of the different variables were in the order of GDP  > population > climate for the regions with the highest chances of facing water scarcity in future.Even though the overall water availability on the globe per capita are 6525.16 (6434.99) m3/capita/year for historical (i.e., the year 2000) and 6960.63 (6375.98) m3/capita/year, and 3894.64 (3671.39) m3/capita/year, 6821.34 (6459.90) m3/capita/year for future (i.e. the year 2099) considering SSP1-RCP2.6, SSP3-RCP7.0, and SSP5-RCP8.5 scenarios respectively (values in bracket consider HYDE3.2 and JO16 population datasets), more than 70% of world population faces the physical water scarcity defined using a threshold value of 1700 m3/capita/year of APC15 for all the scenarios (Supplementary Table 8, and Supplementary Note 1). Estimation of population facing severe water stress considering physical aspect only (i.e., APC of 500 m3/capita/year) is 2.7 billion for historical scenarios and 3.9–7.9 (3.3–7.5) billion for the future scenario, whereas considering both physical and economic aspects (i.e., threshold line defined by Oki et al.19) is 301 (333) million for the historical scenarios and 0.33–325 (176–665) million for the future scenarios (Supplementary Fig. 6 and Supplementary Fig. 7). These values show a substantial difference in the water-stressed population when considering only physical aspects and accounting for both physical and economic factors. It also indicates that a few rich (i.e., grids with high GDP-PPP per capita) physical water-scarce regions (water-stressed regions identified using APC) can ease water scarcity by water management and technological measures.The overall analysis revealed the possibility of underestimation (or overestimation) of the population facing scarcity in the future due to large differences associated with the population and GDP data distribution within the country for the SSP scenarios. The spatial distribution of the future population and GDP within and outside a country can be affected by many factors, such as water availability27,28, job opportunities, disaster adaptation and mitigation capability of a location, migration of people29, and different policies, which can be directly and indirectly associated with climatic29,30 and socioeconomic factors27,29. 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Receiver operator curve and area under the curveThe receiver operator curve (ROC) is used to visualise how the model performs independently of the decision threshold, providing a useful tool for visualising how well the classifier avoids false classifications32. The ROC plot shows a trade-off between the True Positive Rate (TPR) or sensitivity, the fraction of observations that are correctly classified, calculated in Eq. (1) as$${rm{TPR}} = frac{{{rm{TP}}}}{{{rm{TP}} + {rm{FN}}}}$$
(1)
where TP is True Positive and FN False Negative, and the False Positive Rates (FPR) or specificity, the fraction of observations that are incorrectly classified, calculated in Eq. (2) as$${rm{FPR}} = frac{{{rm{FP}}}}{{{rm{FP}} + {rm{TN}}}}$$
(2)
The passing of two lines corresponding to a 100% TPR and a 0% FPR = 1 (TPR versus 1−FPR) is considered a perfect discriminatory ability. This is graphically represented by the ROC curve passing the upper left-hand corner of the plot. The passing of the curve through the diagonal y = x represents a model that is no better than a random guess33. The Area Under the Curve (AUC) is an aggregated measure of performance for all classification thresholds and represents the measure of separability by describing the capability of the predictions in distinguishing between the classes. An AUC measure is returned between zero and one, with zero representing a perfectly inaccurate test and one a perfect test. In general, an AUC of 0.7 to 0.8 is considered acceptable, 0.8 to 0.9 is considered excellent, and >0.9 is outstanding34. Figure 1 shows the ROC curve for the test dataset close to the top left-hand corner and an AUC value of 0.89, suggesting the model has an excellent discriminative ability to distinguish between the classes, and the TPR and FPR appear robust enough to predict failures on the unseen test data.Fig. 1: Test data accuracy, Receiver Operator Curve (ROC) curve with Area Under the Curve (AUC) measure of performance for all classification thresholds.The red line is the ROC curve, and the grey line represents the diagonal y = x and a point where the curve is random.Full size imageThe calibration curve provides a means of observing how close the predictions are to those observed. Since the outcome in this model is the probability of failure between 0 and 1, it is appropriate to use a binning method. Binning is advantageous since it averages the probability of failure for each bin which provides a useful graphical representation of how well the model is calibrated. The mean probability is then compared to the frequency of observed failures in each bin. In this case, a fixed-width binning approach is used, where the data is partitioned into ten bins known as decile analysis, and approach used in similar studies35. A reliability curve provides a means of visualising this comparison, whereby perfectly calibrated probabilities would lie on a diagonal line through the middle of the plot. The briers score is a useful measure of accuracy for probabilistic predictions and is equivalent to the mean squared error whereby the cost function minimises to zero for a perfect model and maximises to 1 for a model with no accuracy4. The Brier’s Score (BS) is calculated in Eq. (3) as$${rm{BS}} = frac{1}{N}mathop {sum }limits_{i = 1}^N (P_i – O_i)^2$$
(3)
where N is the total number of observations, Pi is the prediction probability and Oi is equal to the event outcome failure or no failure. Figure 2 shows the calibration plot for the model and suggests the model is well calibrated for the lower and upper deciles since most bins fit the diagonal. The upper middle deciles do not fit the diagonal where the calibration curve is below or above the diagonal, suggesting the predictions have a lower probability than those seen in the data The briers score of 0.007 is low, suggesting accurate predictions overall.Fig. 2: Test data accuracy, calibration curve with Briers score.The red line is the calibration curve; the grey line represents a perfect fit.Full size imageConfusion matrix and accuracyThe confusion matrix describes the frequency of classification outcomes by explicitly defining the number of True Positives (TP, or Precision), True Negatives (TN), False Positives (FP), and False Negatives (FN). The decision to convert a predicted probability into a class label is determined by an optimal probability threshold such that the value of the response (y_i = left{ {begin{array}{*{20}{c}} {{rm{no}},{rm{failure}},{rm{if}},P_i le {rm{threshold}}} \ {{rm{failure}},{rm{if}},P_i > {rm{threshold}}} end{array}} right.). The default probability threshold within the model is 0.536. By this definition, there remains a practical need to optimise the probability threshold specifically to the behaviour of pipe failures within the imbalanced test data. An optimal probability threshold typically strikes a balance between sensitivity and specificity. However, there is a trade-off between TPR and FPR when altering the threshold, where increasing or decreasing the TPR typically results in the same for the FPR and vice versa. Probability threshold optimisation is an important step in the decision-making process and is specific to each problem. In the case of pipe replacement, expert judgement should be used by reasoning that water companies would seek to avoid unnecessarily replacing pipes that may have a longevity of several decades more, resulting in wasted maintenance effort and cost. Furthermore, only 0.5–1% of the network is typically replaced each year due to budget constraints37. It is therefore important to only identify pipes with the highest probability of failure. Considering this, the optimal threshold is set to reduce the FNs (i.e., pipes predicted to fail when they have not). This reduces the number of TPs predicted as discussed above but targets those pipes most likely to fail.A factorial experimental design was used, whereby the threshold was iterated from 0.01 through to 0.99, observing each threshold to reveal the point where the highest accuracy meets the lowest FN value. The Matthews Correlation Coefficient (MCC) was used to measure accuracy and is useful for imbalanced data since it accounts for the difference in class size and only returns a high accuracy score if all four confusion matrix categories are accurately represented. For this reason, Chicco (2017) argues that it is the correct measure for imbalanced data sets. The MCC describes the prediction accuracy as worst value = −1 and best value = +1 and is calculated as shown in Eq. (4) as follows:$${rm{MCC}} = frac{{{rm{TP times TN – FP times FN}}}}{{sqrt {left( {{rm{TP}} + {rm{FP}}} right)({rm{TP}} + {rm{FN}})({rm{TN}} + {rm{FP}})({rm{TN}} + {rm{FN}})} }}$$
(4)
Table 1 shows a small range of the thresholds for brevity. The optimal threshold in this instance has been identified firstly with the highest MCC accuracy and then the lowest FN. The MCC of 0.27 suggests the model is better than a random fit, but a low MCC value also represents a high percentage of false positives (i.e., values incorrectly identified as non-failure). The balanced accuracy is also a good measure of the accuracy for imbalanced classes, where 1 is high and 0 is low. The balanced accuracy for this model is 0.65. In practical terms, the results are helpful for water companies to target areas for further investigation and potential replacement since they focus on those pipes having the highest probability of failure, yet there are still incorrect predictions that could lead to the potential replacement of pipes unnecessarily. The model predicts 20.20% of all failures occurring in the WDN, found in 7.83% of the WDN pipe network. The results show that approximately 32.80% of the observed pipe failures were correctly predicted as failures, whilst approximately 67.20% of the observed pipe failures were falsely predicted as no failure. If desired, water companies could choose an alternative threshold, one that eliminates FN predictions, however, the number of TP predictions will also reduce.Table 1 Table of thresholds from training data.Full size tableRelative variable influenceThe relative variable influence shows the empirical improvement (I_t^2) accounted for by variable interval xj, averaged across all boosted trees as presented in Eq. (5) as follows38:$$hat J_j^2 = mathop {sum }limits_{{rm{splits}},{rm{on}},x_j} I_t^2$$
(5)
The variable influence helps understand which variables contribute more when predicting pipe failures. For GBT models, this is the summation of predictor influence accumulated over all the classifiers. Figure 3 shows the results, suggesting similar findings compared to existing literature. The most important variables are the number of previous failures and pipe length, both a proxy for pipe performance and deterioration. It is worth reiterating that both variables represent the grouped pipe and do not consider individual pipe history. Soil Moisture Deficit (SMD) is the most important weather variable being linked with shrinkage of clay soils and subsequent ground movement in AC pipe failures. Conversely, clay soils and soils shrink–swell potential, both representing ground movement, show lower influence.Fig. 3: Relative variable influence.Bar graph, ranking from highest to lowest, the importance of each variable as determined by the model output.Full size imagePipe diameter, and material are less important factors in this network than as reported in comparable studies11,20,21,39. The relative variable influence of days air frost and temperature is not as high as expected, given their correlation with high pipe failure frequency in iron pipes and the large percentage of iron pipes in the WDN. It is likely to be a result of over summarising the data to facilitate the annual prediction interval. A shorter prediction interval (week, or month) for networkwide groups of pipes is necessary to capture inter-annual variation accurately, but short prediction intervals in the authors’ experience can result in low predictive accuracy. The overall relative variable influence of soil (shrink well, soil corrosivity, Hydrology of Soil Type) is low. From literature and an engineering perspective, soil corrosion is strongly related to the deterioration of metal pipes and their ability to withstand internal and external forces3. It is possible that many pipes in this network may have been rehabilitated and protected against corrosion; however, this information was unavailable at the time of this study. Water source is the only operational variable and shows low influence compared to many other variables. The most important water source is surface water, resulting in lower temperatures during the winter due to its exposure to weather. This causes higher failure rates in metal pipes, yet compared to other variables, the influence is low. Other variables are imaginable such as installation details like bedding and backfill material, surrounding environments providing evidence on loading such as traffic loading and construction works, operational data such as pipe pressure and transients, water quality and spatial failure characteristics. These are not investigated here but will likely result in performance gains.Risk mappingFor the mapping to be effective from an asset management standpoint, the results of the weighted risk analysis should be able to separate out low, medium, and high failures. The number of high failures is expected to be small for two reasons, (1) pipes rarely fail more than once and (2) utilities are only able to allocate investments to those at the greatest risk due to budget limitations and are therefore only interested in the top 1–2% of pipes. The outcome of the weighted risk analysis is presented in Fig. 4, representing a small section of the WDN for clarity. Natural Jenks arranges the risk level into three categories, low [0; ≤0.02], medium [ >0.02; ≤0.06] and high [ >0.06; ≤0.92]. In this scenario, the length of pipe in the high-risk category is 13.9 km of the 300.7 km or 4.6% of the pipe network present in Fig. 4, a useful percentage of the network to target for management decisions. The choropleth risk map approach is an important means of visualising individual pipes or clusters of pipes with the highest risk in the WDN, evidenced in Fig. 4. Figure 4 also highlights how many pipes in this section of the network have a low risk, which is to be expected since many pipes have a low probability of failure and have small diameters, potentially causing less damage if they fail.Fig. 4: Choropleth weighted risk map categorised using Natural Jenks.Risk is calculated as a measure of the probability of pipe failure and the consequence of damage to nearest property and water lost based on pipe diameter. The map represents approximately 2% of the entire UK WDN.Full size imagePractical considerationsCreating groups of pipes was an important step given the low frequency of failures in the UK WDN dataset. Grouping pipes in this way assumes that all pipes in the group share similar failure rates, which is not the case, and thus the approach adopted here presents a suitable solution to this limitation. Grouping pipes on a lower spatial scale can capture localised influences on pipe performance, that can often be obfuscated when generalising over the whole network. However, the approach used may not be as useful for rural areas where fewer pipes are present, where smaller scales may be more appropriate (e.g., 1:100,000 is a smaller scale than 1:100). Further investigation into grouping scales is merited. Optimisation the threshold is challenging and inevitably leads to inappropriately classified failures on either side of the threshold. Optimising is even more difficult with imbalanced data sets since conventional classification methods are built to assume that all classes are equal. An alternative approach was applied in this study, which used MCC accuracy and FN to set a threshold, reducing the potential for wasting budgets replacing pipes that will not fail. In the process, the number of TPs was reduced to 32.80% of the observed pipe failures, whilst the number of FPs was 67.20% of the observed pipe failures, which may not present a good argument to professionals. Despite this, the results can be used directly in strategic planning, which sets long-term key decisions regarding maintenance and potential replacement of pipes. Predicting the probability of failure is an essential response since it enables the identification and prioritisation of risk across the network. This methodology could also be used to provide longer-term predictions to support the development of Asset Management Plan, which cover a five-year period of regulated investment.Categorising the pipes based on a weighted risk analysis and visually presenting them using Natural Jenks offers a useful method for prioritising pipes based on the consequence of their failure and is an easily assessed cartographic presentation. It extends the probability of failure into a more useful measure of risk, providing more information for decision makers. The use of distance to property in this study is a simple approach to determine flooding. To provide a realistic determination of flooding, an understanding of key geographical features for overland flow routing is required40. The list of consequences was limited in this study and could be extended when such data is available. There are potentially numerous consequences of failure inherent to each network, yet common consequences include loss of water, potential disruption, reduction in water quality, reliability, direct costs (damage to property and infrastructure and pipe repair and replacement) and indirect costs (environmental and social)8. In this study, the risk estimates were concluded by expert knowledge, and any contextual mismatch between weightings could potentially skew the outcomes. Therefore, the weightings should be considered carefully by network professionals. At an engineering level, the risk mapping can be further used to determine areas of the network leading to a high probability of failure, which can be used to take constructive pre-emptive actions towards extending the life of future pipe construction41.The economic benefits of this model will manifest when performing proactive maintenance, potentially averting associated risks that may arise from damaging properties and infrastructure. It is anticipated that the modelling approach proposed will enhance decision-making at a local level, facilitated through numerical outputs which report on the serviceability of the WDN and help meet regulatory performance targets avoiding heavy fines. Operationally, the approach will help with highlighting short pipe segments for repair and replacement though graphical outputs, these are practical lengths of pipes for operational teams that typically do not replace kms of pipe at any given time42. This approach shows similar performance to comparable GBT studies11,20, but is beneficial since the method provides reliable predictions on a shorter annual time frame. The method here is also computationally easier to develop than other more complex machine learning methods such as neural networks and Bayesian Neural Networks.The predictions rely on the quality of the data, and several challenges were presented during the cleaning and processing, most notably the location of the pipe failures, many of which were geographically displaced, and some by a considerable distance yet was necessary to retain all the failures in the dataset. These were snapped to the nearest pipe with similar characteristics, yet it is conceivable that some were incorrectly placed despite the protocols established for the snapping process. Further limitations to the study include limited data, where pressure data or other operational data may have proved useful, the advantage of which may consist of increased model accuracy and interpretability. Over-summarised local conditions can also affect the model accuracy, and in this study, the local soil conditions were presented from a soil map at 1:250,000 scale. Likewise, the weather variables were highly summarised to an annual scale from a 40 × 40 km grid source. Inevitably these limitations will affect the model, which can potentially hinder effective decision-making. There are several challenges faced when modelling pipe failures, from uncertainties in data collection and management to specific data processing solutions. There is a need to understand these holistically, and from the view of current practice for a more in-depth perspective of current challenges in practice that may hinder useful data gathering. In addition, future research aimed at understanding how practitioners understand pipe failure models, the limitations, and opportunities is beneficial, since there is often a discord between the capabilities of modelling and user expectations. This further research may help to improve pipe failure models by encouraging enhancements in the pipe failure model process that promotes quality data capture.Concluding remarksThis study considered the prediction of pipe failures using a GBT model and establishing the risk based on weighted risk analysis to prioritise pipes for proactive management. A 1 km spatial scale was included in this model when grouping the pipes, which aimed to capture localised conditions and remove the failure rate disparities shared when grouping pipes across a network. This spatial scale, together with a short prediction interval, the absence of some essential variables, and additional inherent problems with pipe failure data sets, has ultimately resulted in acceptable accuracy. However, in practical terms, when used in conjunction with expert knowledge, the results provide a useful approximation of potential failures and a better understanding of the current WDN to help plan rehabilitation and replacement efforts. Improving model accuracy may be achieved by increasing the prediction interval to five-year asset management plan, potentially accumulating more failures per pipe group from which to predict. Yet this may not be as useful to water companies where management decisions are typically annual. Furthermore, understanding the issues faced with data collection and quality from current practice may help to encourage data quantity and quality, and could potentially provide marked improvements in the final predictions.Further suggested research includes exploring different pipe grouping variations, collecting more data on the consequences of failure to enhance the weighted risk analysis and, expanding on this idea, understanding the data quantity and quality issues from current practice, and exploring feature engineering techniques to derive more valuable data sets that may improve model accuracy. More