Towards improving the hydrologic design of permeable pavements

The common approach to the hydrologic design of permeable pavements (PPs) uses synthetic rainfall events. This study assessed the validity of the design approach using synthetic rainfall events for undrained PP. Synthetic rainfall events (25-year return period) were used to design undrained pavements for five Norwegian cities. The effectiveness of these pavements was tested using long-term simulation (12–30 years) with high temporal resolution (1 min). The Storm Water Management Model (SWMM) was used to generate time series of surface runoff for PPs and flow duration curves were applied to analyse the hydrological performances. Designing PP using synthetic rainfall events was found to underestimate the storage layer depth of the permeable pavements leading to the frequent occurrence of surface runoff, which is considered a failure of the hydrologic design of undrained pavements. Long-term simulation of surface runoff was found to provide valuable information for the hydrologic design of PP and can be used as a basis for the PP hydrologic design. In the future, it is recommended to use long-term precipitation data generated from climate change models to incorporate the effect of climate change in the design of PP.publishedVersio

Overvannshåndtering med fordrøyende tak

Fordrøyende tak har vært et sentralt forskningstema i Klima 2050 der testfeltet Høvringen utenfor Trondheim har spilt en særlig viktig og samlende rolle. Hensikten med denne rapporten er å gi en kort oversikt over de ulike vitenskapelige artiklene som omhandler fordrøyende tak og hvordan resultatene fra disse artiklene kan brukes. Videre veiledes interesserte lesere til riktig publikasjon avhengig av problemstilling. For hver artikkel gis det et kort sammendrag av den vitenskapelige artikkelen før det gis en kort redegjørelse for hvordan resultatene kan tolkes og brukes. I noen tilfeller gis det også et eksempel på bruk og en kort oppsummering. Helt kort kan resultatene fra Høvringen oppsummeres slik: • Det er utviklet et støtteverktøy som kan brukes av prosjektorganisasjoner som jobber med det fordrøyende tak. Særskilte sjekklister og referanser til andre verktøy o.l. finnes for alle prosjektets faser og gir prosjektleder/ansvarlig prosjekterende/bygg-herre en enkel oversikt over kritiske punkter. • Det kan i mange tilfeller være utfordrende å bruke kun en hendelsesbasert tilnærming til å vurdere ytelsen til fordrøyende tak (gjelder generelt alle naturbaserte løsninger). Bruk av varighetskurver kan være et supplement til å vurdere hvordan en løsning håndterer overvannet gjennom årets normalsituasjoner, og vil dermed kunne gi en god pekepinn på hvor mye kapasitet man kan frigjøre i ledningsnettet (hvis det benyttes ledningsnett). Varighetskurver vil ikke være særlig nyttige for å si noe om effekten av en løsning for å redusere flomtopper i ekstreme nedbørsituasjoner. Kurvene vil uansett vise hvor mye reduksjon av totalt vannvolum man kan forvente nedstrøms en implementert løsning. • En sammenligning av avrenningskoeffisienter målt på lignende takoppbygninger både i laboratorium og i felt viste store variasjoner. Den store variasjonen i målte avrenningskoeffisienter mellom lab og felt illustrerer utfordringene med å beregne effekten av fordrøyende tak med en enkel parameter. • Det er utviklet modeller for å anslå retensjonen fra fordrøyende tak med et toppdekke av sedum. Særlig effekten av geografisk beliggenhet og klima er studert og det gis anbefalinger hvordan ta hensyn til dette. • Videre viste en større sammenligning av ulike fordrøyende tak noen generelle trekk ved de ulike løsningene: o Takene med grønt toppdekke viste større variasjon i det målte fuktighets-innholdet enn takene med toppdekke av belegningsstein på grunn av transpirasjonsprosessen. Dette resulterte i økt retensjon av vann (nedbør som ikke blir avrenning) fra takene med toppdekke av vegetasjon. o Takløsningene med ekstra fordrøyning viste større fordrøyning og flom-toppreduksjon enn tak uten ekstra fordrøyningslag. o Løsninger som kombinerte grønt toppdekke med fordrøyningslag under, oppnådde god fordrøyning og evapotranspirasjon. Dette viste seg å være den beste løsningen for både flomtoppreduksjon og retensjon av vann. o Det er utviklet noen enkle ligninger som gir overslag av hvor mye avrenning man kan forvente fra de ulike takløsningene. • Det er undersøkt om modelleringsverktøyet SWMM kan brukes til å modellere fordrøyende tak. SWMM LID-modellen ble kalibrert ved å bruke avrenningsdata fra ulike byer, og det er gjengitt en rekke ulike parameter-sett som kan brukes. Basert på resultatene er det imidlertid vanskelig å overføre modeller mellom ulike geografiske steder. • Effekten av ulike størrelser er undersøkt i detalj på et fordrøyende tak med lettklinker der en har studert sammenhengen mellom de uavhengige variablene varighet, nedbørintensitet, gjennomsnittlig og toppintensitet, forutgående tørr våt periode og initiell metning med responsparameterne varighet avrenning, forsinkelse avrennings-topp, reduksjon avrenningstopp og innledende avrenning. • Fordrøyende tak har betydelig konsentrasjonstid selv under ekstreme forhold, der vanninnhold i det fordrøyende taket ved starten av hendelsen har større påvirkning enn nedbørsprofilet, intensitet og varighet på kort-tids nedbørhendelsen. Det kan også være verdt å merke seg at nedbørsprofil, intensitet og varighet har liten effekt på forsinkelsen av indikatorene massetyngdepunkt og T50. • Det er utviklet en konseptuell nedbør-avrenningsmodell som kan brukes til å estimere den hydrologiske ytelsen til fordrøyende tak. Modellen er kalibrert med data fra tak lokalisert i fire norske byer og resultatene har vist at modellen kan simulere avrenning fra fordrøyende tak på tvers av flere klimatiske soner og forskjellige takkon-figurasjoner. Oppgitte verdier for parameterne kan benyttes for å estimere den hydrologiske ytelsen til tak med lignende takkonstruksjoner i andre byer. • Til slutt er det undersøkt om ulike maskinlæringsmodeller egner seg til å modellere fordrøyende tak. Det anbefales imidlertid bruk av den konseptuelle nedbør-avrenningsmodell framfor maskinlæringsmodellene for å estimere retensjon. Men det anbefales videre studier for å utforske det fulle potensialet til maskinlærings-modellene. • En gjennomgang av alle løsningene som er testet på Høvringen (i alt seks løsninger i tre generasjoner), viser gode fordrøyende egenskaper ved alle løsningene. • Løsninger med vegetasjon har som forventet høyere retensjon enn løsninger uten vegetasjon.publishedVersio

Evaluating the stormwater management model for hydrological simulation of infiltration swales in cold climates

The Stormwater Management Model (SWMM) is a widely used tool for assessing the hydrological performance of infiltration swales. However, validating the accuracy of SWMM simulation against observed data has been challenging, primarily because well-functioning infiltration swales rarely produce surface runoff, especially over short monitoring periods. This study addresses this challenge by using measured subsurface water storage levels for calibration and validation. The study evaluated three SWMM modules, namely, the snowpack, aquifer, and low-impact development (LID) modules, to simulate subsurface water storage levels of an infiltration swale located in a cold climate region during snow and snow-free periods. Global sensitivity analysis was used to identify influential parameters within these modules. The findings revealed that only a few parameters significantly influenced model outputs. Moreover, the aquifer module outperformed the LID module in simulating subsurface water storage due to limitations in setting the initial saturation of the LID module. Furthermore, simulation accuracy was better during snow-free periods due to challenges in simulating snow dynamics during snow periods with the snowpack module. The calibrated models offer valuable insights into the long-term hydrological performance of infiltration swales, enabling practitioners to identify events that trigger flooding in these systems.publishedVersio

Practice makes the model: a critical review of stormwater green infrastructure modelling practice

Green infrastructures (GIs) have in recent decades emerged as sustainable technologies for urban stormwater management, and numerous studies have been conducted to develop and improve hydrological models for GIs. This review aims to assess current practice in GI hydrological modelling, encompassing the selection of model structure, equations, model parametrization and testing, uncertainty analysis, sensitivity analysis, the selection of objective functions for model calibration, and the interpretation of modelling results. During a quantitative and qualitative analysis, based on a paper analysis methodology applied across a sample of 270 published studies, we found that the authors of GI modelling studies generally fail to justify their modelling choices and their alignments between modelling objectives and methods. Some practices, such as uncertainty analysis, were also found to be limited, despite their necessity being widely acknowledged by the scientific community and their application in other fields. In order to improve current GI modelling practice, the authors suggest the following: i) a framework, called STAMP, designed to promote the standardisation of the documentation of GI modelling studies, and ii) improvements in modelling tools for facilitating good practices, iii) the sharing of data for better model testing, iv) the evaluation of the suitability of hydrological equations for GI application, v) the publication of clear statements regarding model limitations and negative results.publishedVersio

Global burden and strength of evidence for 88 risk factors in 204 countries and 811 subnational locations, 1990–2021: a systematic analysis for the Global Burden of Disease Study 2021

Background: Understanding the health consequences associated with exposure to risk factors is necessary to inform public health policy and practice. To systematically quantify the contributions of risk factor exposures to specific health outcomes, the Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) 2021 aims to provide comprehensive estimates of exposure levels, relative health risks, and attributable burden of disease for 88 risk factors in 204 countries and territories and 811 subnational locations, from 1990 to 2021. Methods: The GBD 2021 risk factor analysis used data from 54 561 total distinct sources to produce epidemiological estimates for 88 risk factors and their associated health outcomes for a total of 631 risk–outcome pairs. Pairs were included on the basis of data-driven determination of a risk–outcome association. Age-sex-location-year-specific estimates were generated at global, regional, and national levels. Our approach followed the comparative risk assessment framework predicated on a causal web of hierarchically organised, potentially combinative, modifiable risks. Relative risks (RRs) of a given outcome occurring as a function of risk factor exposure were estimated separately for each risk–outcome pair, and summary exposure values (SEVs), representing risk-weighted exposure prevalence, and theoretical minimum risk exposure levels (TMRELs) were estimated for each risk factor. These estimates were used to calculate the population attributable fraction (PAF; ie, the proportional change in health risk that would occur if exposure to a risk factor were reduced to the TMREL). The product of PAFs and disease burden associated with a given outcome, measured in disability-adjusted life-years (DALYs), yielded measures of attributable burden (ie, the proportion of total disease burden attributable to a particular risk factor or combination of risk factors). Adjustments for mediation were applied to account for relationships involving risk factors that act indirectly on outcomes via intermediate risks. Attributable burden estimates were stratified by Socio-demographic Index (SDI) quintile and presented as counts, age-standardised rates, and rankings. To complement estimates of RR and attributable burden, newly developed burden of proof risk function (BPRF) methods were applied to yield supplementary, conservative interpretations of risk–outcome associations based on the consistency of underlying evidence, accounting for unexplained heterogeneity between input data from different studies. Estimates reported represent the mean value across 500 draws from the estimate's distribution, with 95% uncertainty intervals (UIs) calculated as the 2·5th and 97·5th percentile values across the draws. Findings: Among the specific risk factors analysed for this study, particulate matter air pollution was the leading contributor to the global disease burden in 2021, contributing 8·0% (95% UI 6·7–9·4) of total DALYs, followed by high systolic blood pressure (SBP; 7·8% [6·4–9·2]), smoking (5·7% [4·7–6·8]), low birthweight and short gestation (5·6% [4·8–6·3]), and high fasting plasma glucose (FPG; 5·4% [4·8–6·0]). For younger demographics (ie, those aged 0–4 years and 5–14 years), risks such as low birthweight and short gestation and unsafe water, sanitation, and handwashing (WaSH) were among the leading risk factors, while for older age groups, metabolic risks such as high SBP, high body-mass index (BMI), high FPG, and high LDL cholesterol had a greater impact. From 2000 to 2021, there was an observable shift in global health challenges, marked by a decline in the number of all-age DALYs broadly attributable to behavioural risks (decrease of 20·7% [13·9–27·7]) and environmental and occupational risks (decrease of 22·0% [15·5–28·8]), coupled with a 49·4% (42·3–56·9) increase in DALYs attributable to metabolic risks, all reflecting ageing populations and changing lifestyles on a global scale. Age-standardised global DALY rates attributable to high BMI and high FPG rose considerably (15·7% [9·9–21·7] for high BMI and 7·9% [3·3–12·9] for high FPG) over this period, with exposure to these risks increasing annually at rates of 1·8% (1·6–1·9) for high BMI and 1·3% (1·1–1·5) for high FPG. By contrast, the global risk-attributable burden and exposure to many other risk factors declined, notably for risks such as child growth failure and unsafe water source, with age-standardised attributable DALYs decreasing by 71·5% (64·4–78·8) for child growth failure and 66·3% (60·2–72·0) for unsafe water source. We separated risk factors into three groups according to trajectory over time: those with a decreasing attributable burden, due largely to declining risk exposure (eg, diet high in trans-fat and household air pollution) but also to proportionally smaller child and youth populations (eg, child and maternal malnutrition); those for which the burden increased moderately in spite of declining risk exposure, due largely to population ageing (eg, smoking); and those for which the burden increased considerably due to both increasing risk exposure and population ageing (eg, ambient particulate matter air pollution, high BMI, high FPG, and high SBP). Interpretation: Substantial progress has been made in reducing the global disease burden attributable to a range of risk factors, particularly those related to maternal and child health, WaSH, and household air pollution. Maintaining efforts to minimise the impact of these risk factors, especially in low SDI locations, is necessary to sustain progress. Successes in moderating the smoking-related burden by reducing risk exposure highlight the need to advance policies that reduce exposure to other leading risk factors such as ambient particulate matter air pollution and high SBP. Troubling increases in high FPG, high BMI, and other risk factors related to obesity and metabolic syndrome indicate an urgent need to identify and implement interventions

Towards improving the calibration practice of conceptual hydrological models of extensive green roofs

Conceptual rainfall-runoff models (CRRMs) can be used as a design tool for green roofs due to their simplicity and acceptable accuracy. This study showed how the uncertainty of CRRM parameters could be reduced by changing the calibration practice, which can enhance the interpretation and identifiability of CRRM parameters. A CRRM was developed and tested on a dataset of 14 extensive green roofs located in four Norwegian cities with different climatic conditions. Two calibration schemes were compared: a common scheme using runoff data as a basis for calibration (single-objective), and a scheme combining runoff and soil moisture data for the calibration (multi-objective scheme). The results confirmed the ability of the CRRM to simulate runoff from extensive green roofs across multiple climatic zones and different roof configurations (Kling Gupta Efficiency > 0.75). The multi-objective calibration scheme was found to reduce the uncertainty of the CRRM parameters, especially the storage parameters, enhancing the physical interpretation of parameter values. The study attempted to give guidelines to estimate parameters of the CRRM which can be used by practitioners for new roof configurations under different climatic conditions

Hydrological performance of lined permeable pavements in Norway

Lined permeable pavements (LPPs) are types of sustainable urban stormwater systems (SUDs) that are suitable for locations with low infiltration capacity or shallow groundwater levels. This study evaluated the hydrological performance of an LPP system in Norway using common detention indicators and flow duration curves (FDCs). Two hydrological models, the Storm Water Management Model (SWMM)-LID module and a reservoir model, were applied to simulate continuous outflows from the LPP system to plot the FDCs. The sensitivity of the parameters of the SWMM-LID module was assessed using the generalized likelihood uncertainty estimation methodology. The LPP system was found to detain the flow effectively based on the median values of the detention indicators (peak reduction = 89%, peak delay = 40 min, centroid delay = 45 min, T50-delay = 86 min). However, these indicators are found to be sensitive to the amount of precipitation and initial conditions. The reservoir model developed in this study was found to yield more accurate simulations (higher NSE) than the SWMM-LID module, and it can be considered a suitable design tool for LPP systems. The FDC offers an informative method to demonstrate the hydrological performance of LPP systems for stormwater engineers and decision-makers

Assessing the effects of four SUDS scenarios on combined sewer overflows in Oslo, Norway: evaluating the low-impact development module of the mike urban model

Paved surfaces, increased precipitation intensities in addition to limited capacity in the sewer systems, cause a higher risk of combined sewer overflows (CSOs). Sustainable drainage systems (SUDS) offer an alternative approach to mitigate CSO by managing the stormwater locally. Seven SUDS scenarios, developed based on the concept of effective impervious area reduction, have been implemented in the Grefsen catchment using the Mike Urban model. This study evaluated the hydrological performance of two SUDS controls (i.e. green roof (GR) and rain garden (RG)) modules of the model and the effect of the SUDS scenarios on the CSOs using event-based and continuous simulations. The Nash–Sutcliffe efficiency (NSE) along with flow duration curves (FDCs) has been used for evaluating the model performance. Event-based evaluations revealed the superior performance of the RG in reducing CSOs for larger precipitation events, while GRs were proven to have beneficial outcomes during smaller events. The study illustrated another way of assessing the continuous simulations by employing the FDCs. The FDCs were assessed against a discharge threshold at the outlet (which authorities can set as design criteria) of the catchment in terms of the extent, each scenario reduced occurrence and duration of outflow that invokes flow in the overflow pipe

Global fertility in 204 countries and territories, 1950–2021, with forecasts to 2100: a comprehensive demographic analysis for the Global Burden of Disease Study 2021

BackgroundAccurate assessments of current and future fertility—including overall trends and changing population age structures across countries and regions—are essential to help plan for the profound social, economic, environmental, and geopolitical challenges that these changes will bring. Estimates and projections of fertility are necessary to inform policies involving resource and health-care needs, labour supply, education, gender equality, and family planning and support. The Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) 2021 produced up-to-date and comprehensive demographic assessments of key fertility indicators at global, regional, and national levels from 1950 to 2021 and forecast fertility metrics to 2100 based on a reference scenario and key policy-dependent alternative scenarios. MethodsTo estimate fertility indicators from 1950 to 2021, mixed-effects regression models and spatiotemporal Gaussian process regression were used to synthesise data from 8709 country-years of vital and sample registrations, 1455 surveys and censuses, and 150 other sources, and to generate age-specific fertility rates (ASFRs) for 5-year age groups from age 10 years to 54 years. ASFRs were summed across age groups to produce estimates of total fertility rate (TFR). Livebirths were calculated by multiplying ASFR and age-specific female population, then summing across ages 10–54 years. To forecast future fertility up to 2100, our Institute for Health Metrics and Evaluation (IHME) forecasting model was based on projections of completed cohort fertility at age 50 years (CCF50; the average number of children born over time to females from a specified birth cohort), which yields more stable and accurate measures of fertility than directly modelling TFR. CCF50 was modelled using an ensemble approach in which three sub-models (with two, three, and four covariates variously consisting of female educational attainment, contraceptive met need, population density in habitable areas, and under-5 mortality) were given equal weights, and analyses were conducted utilising the MR-BRT (meta-regression—Bayesian, regularised, trimmed) tool. To capture time-series trends in CCF50 not explained by these covariates, we used a first-order autoregressive model on the residual term. CCF50 as a proportion of each 5-year ASFR was predicted using a linear mixed-effects model with fixed-effects covariates (female educational attainment and contraceptive met need) and random intercepts for geographical regions. Projected TFRs were then computed for each calendar year as the sum of single-year ASFRs across age groups. The reference forecast is our estimate of the most likely fertility future given the model, past fertility, forecasts of covariates, and historical relationships between covariates and fertility. We additionally produced forecasts for multiple alternative scenarios in each location: the UN Sustainable Development Goal (SDG) for education is achieved by 2030; the contraceptive met need SDG is achieved by 2030; pro-natal policies are enacted to create supportive environments for those who give birth; and the previous three scenarios combined. Uncertainty from past data inputs and model estimation was propagated throughout analyses by taking 1000 draws for past and present fertility estimates and 500 draws for future forecasts from the estimated distribution for each metric, with 95% uncertainty intervals (UIs) given as the 2·5 and 97·5 percentiles of the draws. To evaluate the forecasting performance of our model and others, we computed skill values—a metric assessing gain in forecasting accuracy—by comparing predicted versus observed ASFRs from the past 15 years (2007–21). A positive skill metric indicates that the model being evaluated performs better than the baseline model (here, a simplified model holding 2007 values constant in the future), and a negative metric indicates that the evaluated model performs worse than baseline. FindingsDuring the period from 1950 to 2021, global TFR more than halved, from 4·84 (95% UI 4·63–5·06) to 2·23 (2·09–2·38). Global annual livebirths peaked in 2016 at 142 million (95% UI 137–147), declining to 129 million (121–138) in 2021. Fertility rates declined in all countries and territories since 1950, with TFR remaining above 2·1—canonically considered replacement-level fertility—in 94 (46·1%) countries and territories in 2021. This included 44 of 46 countries in sub-Saharan Africa, which was the super-region with the largest share of livebirths in 2021 (29·2% [28·7–29·6]). 47 countries and territories in which lowest estimated fertility between 1950 and 2021 was below replacement experienced one or more subsequent years with higher fertility; only three of these locations rebounded above replacement levels. Future fertility rates were projected to continue to decline worldwide, reaching a global TFR of 1·83 (1·59–2·08) in 2050 and 1·59 (1·25–1·96) in 2100 under the reference scenario. The number of countries and territories with fertility rates remaining above replacement was forecast to be 49 (24·0%) in 2050 and only six (2·9%) in 2100, with three of these six countries included in the 2021 World Bank-defined low-income group, all located in the GBD super-region of sub-Saharan Africa. The proportion of livebirths occurring in sub-Saharan Africa was forecast to increase to more than half of the world's livebirths in 2100, to 41·3% (39·6–43·1) in 2050 and 54·3% (47·1–59·5) in 2100. The share of livebirths was projected to decline between 2021 and 2100 in most of the six other super-regions—decreasing, for example, in south Asia from 24·8% (23·7–25·8) in 2021 to 16·7% (14·3–19·1) in 2050 and 7·1% (4·4–10·1) in 2100—but was forecast to increase modestly in the north Africa and Middle East and high-income super-regions. Forecast estimates for the alternative combined scenario suggest that meeting SDG targets for education and contraceptive met need, as well as implementing pro-natal policies, would result in global TFRs of 1·65 (1·40–1·92) in 2050 and 1·62 (1·35–1·95) in 2100. The forecasting skill metric values for the IHME model were positive across all age groups, indicating that the model is better than the constant prediction. InterpretationFertility is declining globally, with rates in more than half of all countries and territories in 2021 below replacement level. Trends since 2000 show considerable heterogeneity in the steepness of declines, and only a small number of countries experienced even a slight fertility rebound after their lowest observed rate, with none reaching replacement level. Additionally, the distribution of livebirths across the globe is shifting, with a greater proportion occurring in the lowest-income countries. Future fertility rates will continue to decline worldwide and will remain low even under successful implementation of pro-natal policies. These changes will have far-reaching economic and societal consequences due to ageing populations and declining workforces in higher-income countries, combined with an increasing share of livebirths among the already poorest regions of the world. FundingBill & Melinda Gates Foundation

Global fertility in 204 countries and territories, 1950–2021, with forecasts to 2100: a comprehensive demographic analysis for the Global Burden of Disease Study 2021

BackgroundAccurate assessments of current and future fertility—including overall trends and changing population age structures across countries and regions—are essential to help plan for the profound social, economic, environmental, and geopolitical challenges that these changes will bring. Estimates and projections of fertility are necessary to inform policies involving resource and health-care needs, labour supply, education, gender equality, and family planning and support. The Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) 2021 produced up-to-date and comprehensive demographic assessments of key fertility indicators at global, regional, and national levels from 1950 to 2021 and forecast fertility metrics to 2100 based on a reference scenario and key policy-dependent alternative scenarios.MethodsTo estimate fertility indicators from 1950 to 2021, mixed-effects regression models and spatiotemporal Gaussian process regression were used to synthesise data from 8709 country-years of vital and sample registrations, 1455 surveys and censuses, and 150 other sources, and to generate age-specific fertility rates (ASFRs) for 5-year age groups from age 10 years to 54 years. ASFRs were summed across age groups to produce estimates of total fertility rate (TFR). Livebirths were calculated by multiplying ASFR and age-specific female population, then summing across ages 10–54 years. To forecast future fertility up to 2100, our Institute for Health Metrics and Evaluation (IHME) forecasting model was based on projections of completed cohort fertility at age 50 years (CCF50; the average number of children born over time to females from a specified birth cohort), which yields more stable and accurate measures of fertility than directly modelling TFR. CCF50 was modelled using an ensemble approach in which three sub-models (with two, three, and four covariates variously consisting of female educational attainment, contraceptive met need, population density in habitable areas, and under-5 mortality) were given equal weights, and analyses were conducted utilising the MR-BRT (meta-regression—Bayesian, regularised, trimmed) tool. To capture time-series trends in CCF50 not explained by these covariates, we used a first-order autoregressive model on the residual term. CCF50 as a proportion of each 5-year ASFR was predicted using a linear mixed-effects model with fixed-effects covariates (female educational attainment and contraceptive met need) and random intercepts for geographical regions. Projected TFRs were then computed for each calendar year as the sum of single-year ASFRs across age groups. The reference forecast is our estimate of the most likely fertility future given the model, past fertility, forecasts of covariates, and historical relationships between covariates and fertility. We additionally produced forecasts for multiple alternative scenarios in each location: the UN Sustainable Development Goal (SDG) for education is achieved by 2030; the contraceptive met need SDG is achieved by 2030; pro-natal policies are enacted to create supportive environments for those who give birth; and the previous three scenarios combined. Uncertainty from past data inputs and model estimation was propagated throughout analyses by taking 1000 draws for past and present fertility estimates and 500 draws for future forecasts from the estimated distribution for each metric, with 95% uncertainty intervals (UIs) given as the 2·5 and 97·5 percentiles of the draws. To evaluate the forecasting performance of our model and others, we computed skill values—a metric assessing gain in forecasting accuracy—by comparing predicted versus observed ASFRs from the past 15 years (2007–21). A positive skill metric indicates that the model being evaluated performs better than the baseline model (here, a simplified model holding 2007 values constant in the future), and a negative metric indicates that the evaluated model performs worse than baseline.FindingsDuring the period from 1950 to 2021, global TFR more than halved, from 4·84 (95% UI 4·63–5·06) to 2·23 (2·09–2·38). Global annual livebirths peaked in 2016 at 142 million (95% UI 137–147), declining to 129 million (121–138) in 2021. Fertility rates declined in all countries and territories since 1950, with TFR remaining above 2·1—canonically considered replacement-level fertility—in 94 (46·1%) countries and territories in 2021. This included 44 of 46 countries in sub-Saharan Africa, which was the super-region with the largest share of livebirths in 2021 (29·2% [28·7–29·6]). 47 countries and territories in which lowest estimated fertility between 1950 and 2021 was below replacement experienced one or more subsequent years with higher fertility; only three of these locations rebounded above replacement levels. Future fertility rates were projected to continue to decline worldwide, reaching a global TFR of 1·83 (1·59–2·08) in 2050 and 1·59 (1·25–1·96) in 2100 under the reference scenario. The number of countries and territories with fertility rates remaining above replacement was forecast to be 49 (24·0%) in 2050 and only six (2·9%) in 2100, with three of these six countries included in the 2021 World Bank-defined low-income group, all located in the GBD super-region of sub-Saharan Africa. The proportion of livebirths occurring in sub-Saharan Africa was forecast to increase to more than half of the world's livebirths in 2100, to 41·3% (39·6–43·1) in 2050 and 54·3% (47·1–59·5) in 2100. The share of livebirths was projected to decline between 2021 and 2100 in most of the six other super-regions—decreasing, for example, in south Asia from 24·8% (23·7–25·8) in 2021 to 16·7% (14·3–19·1) in 2050 and 7·1% (4·4–10·1) in 2100—but was forecast to increase modestly in the north Africa and Middle East and high-income super-regions. Forecast estimates for the alternative combined scenario suggest that meeting SDG targets for education and contraceptive met need, as well as implementing pro-natal policies, would result in global TFRs of 1·65 (1·40–1·92) in 2050 and 1·62 (1·35–1·95) in 2100. The forecasting skill metric values for the IHME model were positive across all age groups, indicating that the model is better than the constant prediction.InterpretationFertility is declining globally, with rates in more than half of all countries and territories in 2021 below replacement level. Trends since 2000 show considerable heterogeneity in the steepness of declines, and only a small number of countries experienced even a slight fertility rebound after their lowest observed rate, with none reaching replacement level. Additionally, the distribution of livebirths across the globe is shifting, with a greater proportion occurring in the lowest-income countries. Future fertility rates will continue to decline worldwide and will remain low even under successful implementation of pro-natal policies. These changes will have far-reaching economic and societal consequences due to ageing populations and declining workforces in higher-income countries, combined with an increasing share of livebirths among the already poorest regions of the world.</p