A green-gray path to global water security and sustainable infrastructure

water management to a heavy reliance on engineering-based approaches. Elsewhere, retaining existing stocks of natural capital creates opportunities to employ blended green-gray water infrastructure. By 2050, annual engineering expenditures are projected to triple to $2.3 trillion, invested mainly in developing economies. In contrast, preserving natural capital for threat suppression represents a potential $3.0 trillion in avoided replacement costs by mid-century. Society pays a premium whenever these nature-based assets are lost, as the engineering costs necessary to achieve an equivalent level of threat management are, on average, twice as expensive. Countries projected to rapidly expand their engineering investments while losing natural capital will be most constrained in realizing green-gray water management. The situation is expected to be most restrictive across the developing world, where the economic, technical, and governance capacities to overcome such challenges remain limited. Our results demonstrate that policies that support blended green-gray approaches offer a pathway to future global water security but will require a strategic commitment to preserving natural capital. Absent such stewardship, the costs of water resource infrastructure and services will likely rise substantially and frustrate efforts to attain universal and sustainable water security.


Introduction
Recent studies on human water security reveal globally significant threats from population and economic growth, mismanaged water use, climate extremes and a general failure to effectively protect landscapes and inland waterways (Vörösmarty et al., 2010;Chaplin-Kramer et al., 2019;Harrison et al., 2016;Gleick, 2018;Tickner et al., 2020;Díaz et al., 2019).The prevailing response to these challenges has been the deployment of traditional engineering, featuring centralized water treatment and distribution systems, and prolific, often massive river impoundments and flood protection infrastructure (McKinsey & Company, 2009;Zarfl et al., 2015;Rodriguez et al., 2012).Roughly 85% of humankind relies on freshwater source areas that are moderately to severely threatened as a byproduct of development, and engineered solutions are routinely applied to substantially reduce the attendant risks (Vörösmarty et al., 2010;Green et al., 2015).Such "gray" engineering is therefore essential in delivering and improving upon the quality of water used by society (HLPW, 2018;OECD, 2012), and underpins an economic sector with annual gross revenues approaching $0.8 trillion (Ashley and Cashman, 2006;McKinsey & Company, 2009).At the same time, this infrastructure is costly to install and maintain (ASCE, 2011;Foster and Briceño-Garmendia, 2010) and outstrips the technical and institutional capacity of many developing nations (HLPW, 2018;Foster and Briceño-Garmendia, 2010;Wehn de Motalvo and Alaerts, 2013).Persistent shortfalls in funding for traditionallyengineered systems (Rodriguez et al., 2012;ASCE, 2011) and the negative and long-lived impacts they often present to the environment (Vörösmarty et al., 2010;Zarfl et al., 2015;Palmer et al., 2015) illustrate the need for alternatives, like those associated with natural capital (Chaplin-Kramer et al., 2019;Harrison et al., 2016;Palmer et al., 2015;Costanza et al., 2017).
Protected watersheds and aquatic ecosystems are recognized as costeffective means to improve water security by combining or "blending" nature-based infrastructure with engineered systems to provide services like safe drinking water, waste processing and dilution, erosion control, and flood risk reduction (Palmer et al., 2015;Costanza et al., 2017;McDonald et al., 2016;Huang et al., 2020).Nevertheless, such naturebased solutions have yet to take root more broadly due in part to the absence of comparative economic evaluations (HLPW, 2018;Palmer et al., 2015;Costanza et al., 2017;McDonald et al., 2016;World Bank, 2015), questions regarding their reliability (Muller et al., 2015), and a shortage of technical know-how (HLPW, 2018;Foster and Briceño-Garmendia, 2010;Wehn de Motalvo and Alaerts, 2013;World Bank, 2015).Additionally, the persistent downward trends in global environmental assets, along with underfunded commitments to their protection and rehabilitation, limit the potential contributions of ecosystem services to human water supply (McDonald et al., 2016;McCarthy et al., 2012;Venter et al., 2016;Watson et al., 2014).Given the globally significant public goods and services offered by environmental systems (Costanza et al., 2014;2016), their diminishment is likely to constrain future economic growth.
Beyond the protection of natural capital, several important calls-toaction on expanding the use of natural systems in water management have materialized across the highest levels of government, business, the multi-lateral banks, and civil society (Browder et al., 2019;HLPW, 2018;WWAP, 2018;OECD, 2019).Designing blended ecosystem and engineered-based management systems could be particularly valuable in regions that retain significant endowments of natural capital that could provide water to sizable numbers of people, but this will require strategic, large-scale stewardship of ecosystem services in terms of both their protection and in many cases rehabilitation (Green et al., 2015;Harrison et al., 2016).Achieving universal water security under the Sustainable Development Goals (SDGs) is motivating serious consideration of such strategies (HLPW, 2018) but requires a coupled framework to assess the global potential for combining green-gray infrastructures.
Here we develop a combined biogeophysical, engineering, and economic framework to assess the global potential for using natural capital (NC) and traditional engineering (TE) to mitigate contemporary and future threats to human water security.After describing the modeling framework, we explore the mechanisms by which TE and NC contain contemporary water security threats.We then present global and continental-scale geographies of projected threats to human water security under future scenarios of population growth, economic development, resource use, and climate change.Next, we project and map society's expected response to these growing threats in terms of deploying TE and retaining NC assets.We then evaluate the contributions of TE and NC to threat management should present-day approaches to water management persist over the remainder of the century.These contributions are interpreted in terms of opportunities for combining TE and NC as policy levers in future threat management.We go on to provide the first global estimate of the economic value of TE and NC in jointly reducing threats to human water security.This portion of the analysis provides an evaluation of replacement costs for services provided by NC, enabling us to explore future policy options, identify places where nature-based solutions are most promising, and rank the readiness of individual regions to confront their water security challenges.We also evaluate the relative penalty paid for replacing any lost natural capital with engineering.Throughout, we consider a multi-decade timespan to assess the durability of benefits associated with engineered and nature-based strategies for sustainable water resource development.

Methods
In the context of human water security (HWS), we define natural capital as a type of infrastructure that constitutes a broad category of physical entities (e.g., upland watersheds, floodplains, lakes, rivers), collectively representing terrestrial and aquatic ecosystems that are intimately connected to the hydrologic cycle.This nature-based infrastructure is functionally analogous to traditionally engineered/built capital infrastructure (e.g., water and wastewater treatment plants, hydraulic conveyances, etc.).Both types of infrastructure can be harnessed to realize improvements in HWS through the services they provide to society.NC has an affiliated portfolio of ecosystem services that can provide clean, reliable drinking water from well-managed upland ecosystems, instream water pollution control, flood protection by wetlands, and a vital source of protein through inland fisheries (Browder et al., 2019;McIntyre et al., 2016;USACE EWN, 2020;Vörösmarty et al., 2018;Stewart-Koster and Bunn, 2016).TE services include public and private water delivery and treatment systems, water storage, and management services.NC can be combined with TE to produce "blended systems" across this broad spectrum of service benefits.Here, we consider NC operating in tandem with TE, evaluating their regional-tocontinental scale geographies and importance, going well beyond both the notion and domain of green infrastructure as currently embraced by urban planners (e.g., green roofs, rain gardens) (Brown, 2013).Natural capital and its affiliated services have also collectively been termed nature-based solutions (Cohen-Shacham et al., 2016;WWAP, 2018).As we explain below, and throughout this study, we inventory and map NC and TE as physical infrastructures.We also derive measures of their affiliated services to society, which we sometimes refer to as their function, but concentrate specifically on their capacity to control threats to HWS.Both NC and TE can gain functionality by investments in maintenance and protection but can lose it by allowing these assets to depreciate over time, through impairment or poor management.
We modified and extended an existing approach that focused on estimating contemporary ambient environmental conditions, how they impose incident threat (T) on HWS, and how such threat is remediated through engineering systems alone (Vörösmarty et al., 2010).The new formulation allows us to: (a) present the global spatial distribution of T and maximum incident threat (T max ) should NC be lost; (b) evaluate the contributions that NC and TE make in preventing and reducing these threats (TR nat and TR eng , respectively); (c) project future T, TR nat , and TR eng ; and (d) estimate the future investment expenditures required for threat-reducing TE and the avoided replacement costs associated with threat prevented by existing NC and its affiliated ecosystem services.This new framework enables us to evaluate, on a common scale, the individual as well as joint roles of TE and NC in mitigating or offsetting projected threat to HWS.We make calculations on 46,517 grid cells (30 ′ lat/long), comprising the continental land mass across which rivers actively flow.Future projections are run for a 30-year duration, +/-15 years of 2005, 2030, 2050 and 2080.Within our computational framework (see Supplementary Material, Fig. S1), HWS ultimately rests on the combination of economic development; water availability, condition, and use; and, the capacity of NC and TE to reduce HWS threat.Our estimated levels of threat to C.J. Vörösmarty et al. renewable freshwater resources are embedded within the runoff and river corridor flows that serve the vast majority of human population (Harrison et al., 2016;Green et al., 2015), and are therefore intimately connected to the ecosystem services provided by natural capital, specifically upstream contributing areas that serve downstream human beneficiaries and water-dependent ecosystems.As shown in our conceptual framework (Figs. 1 and 2), levels of incident threat in a given grid cell (i) will rise in response to poor environmental management but will simultaneously reflect the countervailing impacts of natural capital and ecosystem services, which reduce otherwise higher levels of incident threat in that grid cell (T i ).This threat reduction by natural capital, TR nat,i , essentially goes unobserved, but can be computed, mapped, and compared to TR eng,i using the common biogeophysical and economic units provided by our framework.Should all NC be eliminated at a given location, we can estimate what would be its potential maximum incident threat (T max,i ).T i is therefore a net quantity, representing the balance between human pressures that tend to increase incident threat and its concurrent suppression by existing NC.T i at any location is further reduced to a residual (remaining threat, T rem,i ) through engineered management (TR eng,i ).
In order to project future threats to HWS, we apply advanced geostatistical models, configured over digital river networks, that relate T i to a set of drivers associated with economic development and with wellestablished negative impacts on water systems (e.g., population, GDP, water use, agricultural activities) (OECD, 2012;Venter et al., 2016;Orubu and Omotor, 2011, Tables S1-S3).As we show in the Supplementary Material, these models reproduce well the contemporary spatial patterns of T i from a previous study (Vörösmarty et al., 2010) that used a much larger set of drivers but that have no future analogues.With these new drivers, we use the geostatistical models to project contemporary and future T i , and then estimate TR nat,i and TR eng,i using statistical models based on these projections of T i (see S1 and S3 for detailed calculations).
We estimate and project contemporary and future expenditures on threat-reducing TE using observed patterns of spending on engineering relative to GDP per capita across different countries.By assuming that financial resources are allocated efficiently within countries, we estimate total expenditures on TE for each pixel ($TR eng,i ) (S1.3.1).We then use similar projections to estimate $TR nat,i as the expenditures on TE that would be needed to replace the existing NC if it were to be lost.We allow these avoided replacement costs of preserving current NC to vary depending on our assumptions about the substitutability between TE and NC (corresponding to the concepts of strong and weak sustainability and serving to illustrate an uncertainty envelope) (S1.3.2).We quantify the benefits of preserving NC at the country level with an "avoided penalty" index, which shows the extra efficiency loss if countries were to replace the current NC ecosystem services entirely with threat reduction from TE (S1.3.2).Lastly, we calculate the lower-bound cost of reducing the HWS threat that remains after threat reduction from both existing NC and TE ($T rem,i ) by assuming that all of the remaining threat can be reduced with TE (S1.3.2).
A complete description of the modelling protocol, including variable nomenclature, equations, key assumptions, each input data set, and measures of model performance is given in the Supplementary Material (S1, Figs.S1-S4).Table S1 lists the seven surrogates and their relation to the larger set of drivers from the original threat mapping (Vörösmarty et al., 2010).Table S2 defines all variables used in this study, with units and a corresponding calculation or reference to an equation described in the Supplementary Material.A worked numerical example is given in Table S3.

Increasing threat to human water security and corresponding changes in TE and NC
We simulated three scenarios depicting alternate climatic and socioeconomic development pathways, but report mainly on business-asusual (BAU) projections (IPCC RCP6.0/SSP2; van Vuuren, 2014;O'Neill et al., 2014 [see Supplementary Material Table S5]), featuring a rising global middle class (Fig. 3).Our BAU projections provide a convenient means to reveal likely trends in T i and to explore the limits and opportunities of engineered and nature-based threat management.Under these projections, T grows throughout the 21st century, fueled by rising population density, industrialization, and food production (Fig. 4).This result is consistent with historical trends (Venter et al.,  The rising middle class in China, India, and other non-OECD countries drives these increases, while the OECD remains generally stable (Fig. 3C).
Through mid-century, our projections in Fig. 5 show rich nations reducing much of their incident threat to water resources using TE, while poor countries only partially offset T i in this way, due to their limited investment capacity (Fig. S2A,B).The overall control of contemporary incident threat by TE (T i reduced to T rem,i ) is substantial.Across the OECD countries, this mean reduction (in populationweighted terms) is 58%, while for non-OECD countries it is 49%.NC contributes corresponding levels of 20% and 16% to threat containment that ultimately avoids T max,i and benefits downstream populations, making natural capital an important global-scale asset in HWS management.
By 2050, the projected geographic differences between TE and NC are striking, although engineered approaches are expected to continue to grow strongly under BAU (Fig. 6).Our projections regarding the essential role of TE is corroborated by ongoing construction of massive engineering works with multi-decade planning horizons (Zarfl et al., 2015;Ashley & Cashman, 2006) and the common assumption of their necessity in attaining SDG water targets (HLPW, 2018;OECD, 2019).By 2050, as a result of rapid economic growth and wealth creation, some river basins show significant new deployments of TE (e.g., Niger, Ganges, Changjiang).However, their high levels of threat drivers make it difficult to achieve more than a modest alleviation of T i , even after major engineering investments (Fig. 2).Elsewhere in the developing world, and despite the rapid rise of TE in relative terms, low levels of remaining threat are projected to remain elusive due to limitations in estimated future engineering deployments in absolute terms (e.g., sub-Saharan Africa, Central America, most of Asia and Oceania).Consistent with the general observation that environmental impairment accompanies economic expansion (Vörösmarty et al., 2010;Tickner et al., 2018;Díaz et al., 2019;OECD, 2012;Venter et al., 2016;Orubu and Omotor, 2011), our modeling projects widespread losses of NC under BAU.Losses of ecosystem services are particularly obvious across densely populated or rapidly developing regions (Fig. 6B), precisely those areas requiring the highest levels of threat control (Fig. 4).

Blended systems and pathways to future threat control
Well-designed combinations of natural capital and built infrastructure can boost the performance and reduce the costs of engineered solutions (Browder et al., 2019;Palmer et al., 2015;Vörösmarty et al., 2018;WWAP, 2018), with many successful "worked examples" like wetlands functioning alongside massive flood control infrastructure (UNEP-DHI, 2014), healthy catchments purifying urban water supplies (McDonald et al., 2016;Dudley and Stolton, 2003), and wetlands providing effluent treatment in urban water systems (World Bank, 2015).Blended systems could therefore play an important role in future HWS, but only in regions that retain significant endowments of natural capital.To safeguard that potential, strategic stewardship of ecosystem services will be needed, encompassing regional if not continental-scale perspectives (Harrison et al., 2016;Green et al., 2015).
We projected the capacity of TE, NC, and their combination to deliver water services using river network topologies that quantify downstream populations dependent on upstream water source areas and their corresponding levels of incident threat (Harrison et al., 2016;Green et al., 2015) (Fig. 7).The relative roles of TE and NC shift dramatically across the decades and reveal strong path dependencies.Through 2050, our projections show upward trajectories in TE-centered threat management, accompanied by declines in the potential for NC-based threat control.Europe and broad areas of South and East Asia have already lost or will imminently lose NC to the point where higher TE becomes the only viable option for threat control.In these regions, the populationweighted mean threat reduction by engineering (TR eng ) rises from 0.55 to 0.62 and 0.33 to 0.53, respectively, between 2005 and 2050.Over the same period, South and East Asia is projected to experience an overall net loss in threat suppression by NC, with population-weighted average TR nat declining from 0.17 to 0.13, due to rapid intensification of threat drivers.In contrast, NC threat suppression is projected to remain stable but low (~0.2) across much of Europe, reflecting its mature economies and agricultural systems.
While we found similar patterns under each RCP/IPCC scenario, a more aggressive transition to NC-based threat control is plausible, insofar as we tabulate nearly 2.5 billion people today living downstream of high NC assets that could augment the more prevalent TE-based approaches.Broad-scale application of blended green-gray systems would reposition some countries toward a high NC-high TE state (upper right quadrant, Fig. 7 inset).Such a transition is most plausible for South America.Africa also maintains high NC-based potential, but projections of its limited capacity to invest in TE through 2050 means that it will likely fall far short of the combined NC-TE endpoint.Similar shortfalls in TE will continue to hinder the transition to blended green-gray systems across much of the developing world.Our projections show that several countries could still be significantly supported by nature-based threat management, with remaining TR nat,i values in 2050 at least equaling, if not exceeding, their accumulated reductions to that year (e.g., Congo [CG & COG], Sudan, Tanzania, Brazil, Bolivia, Peru) (Table S4).

An economic perspective
The potential benefits of blended green-gray systems can also be evaluated in economic terms.Recognizing that economic valuation of natural resources is fraught with technical and philosophical issues around sustainability, substitutability, and irreversibility (NRC, 1994), our straightforward approach provides first-order estimates of the threat-reducing economic value of TE and NC, and how they can be jointly used in future water management, by way of estimating avoided replacement costs of NC.While a more complete economic assessment of tradeoffs, opportunity costs, and synergistic cost-savings by green-gray systems is left to future study, important policy-relevant results nonetheless emerge from this initial accounting.
Under BAU, growing financial investments in TE aimed at reducing threat accompany increases in per capita income (Fig. S2A) and are projected to reinforce a heavy reliance on engineering over the remainder of the century (Table 1).With economic expansion and population growth, annual global expenditures on TE infrastructure and operations triple from $0.7 to $2.3 trillion (2020 PPP) from 2005 to 2050.Relative increases are expected to be most rapid in the developing world (Fig. 6A) with its expanding middle class.For China, India, and the non-OECD states, collective annual investments rise between 2005 and 2050, comprising 94% of the total $1.6 trillion increase seen worldwide.
We find two important features of NC-based threat control in current and future HWS-related cost projections (Table 1).First is its role in suppressing T i , which otherwise would reach T max,i .The global replacement cost of this NC-based threat prevention ($TR nat,i ) is estimated at $1.4 trillion worldwide in 2005, expanding to $3.0 trillion by 2050.To put this in perspective, existing NC accounts for 67% and 56% of all prevention and reduction of threat to HWS in 2005 and 2050, respectively.While the biogeophysical importance of NC-based threat prevention is on par with TE-activated threat reduction across many regions (Fig. 5), our estimates show that it is, in fact, greater in aggregate economic terms at the global scale.
The second dimension of TR nat,i is associated with the avoided penalties related to the economic inefficiencies incurred should TE expenditures be used to replace lost ecosystem services.A strongly increasing cost burden falls onto TE wherever there is diminished or degraded NC and where the functionality of this NC needs to be replaced (Fig. 8, S4).We see this most dramatically in the projection for India, and to a lesser extent in France, where most pixels have low levels of threat reduction by existing NC.For India and France, the remaining scarce NC is at a premium and for each unit of NC lost on an areal basis these countries would pay penalties of 160% and 115% (a more than doubling), respectively, should that NC be lost and then replaced by TE (P av in Fig. 8).Much flatter replacement cost curves are apparent for Brazil and Tanzania, reflecting the beneficial effect of their higher stocks of existing NC.While P av is more modest for these countries, they would still pay a substantial premium (a 60-70% higher cost) on the use of engineering to replace the same level of threat control represented by any lost NC.Such penalties amount to a "tax" on human water security from poor environmental management, with the population-weighted global average P av growing from 100% to more than 110% after 2030 (Table 1) and corresponding to the general decline in natural capital (Fig. 6B).
Despite these important investments, there is substantial remaining threat, T rem,i , which could be ameliorated by still larger expenditures in TE (Eq.S19).From 2005 to 2050, we estimate these costs to more than double to over $2.0 trillion.They represent "stranded" threats or impacts from damages to NC that fail to be addressed.These represent in 2005 about 150% of TE outlays, diminishing to 90% in 2050, a reflection of the growing reliance on and effectiveness of TE globally.Despite differences in system definition and methodology, other work corroborates the direction and general magnitude of our estimates (Costanza et al., 2017;McDonald et al., 2016).For example, global economic penalties for the loss of all terrestrial, freshwater-related ecosystem services were previously tabulated (Costanza et al., 2014) as growing at ~ 2% per year between 1997 and 2011.If we assume this to be analogous to the sum of our $TR eng,i and $T rem,i , we get a growth rate of 2.7% annually between 2005 and 2030, a comparable finding considering that a portion of our projected growth rate will be dedicated to investments purely in baseline engineering expansion (i.e., exclusive of compensating for NC-associated impairments), which were not isolated within our calculation scheme.Our projections also seem reasonable given the more rapid growth in the future economy (Fig. 3A).At the same time, the projections of avoided penalties are likely to be underestimated, since they fail to consider any associated human health or biodiversity impacts.

Protecting natural capital for water security
To what practical degree could the positive benefits of NC shown in Table 1 be relied upon and integrated with TE? Natural capital is already used widely by cities across the development spectrum, with one-third of the 100 largest urban areas served by protected forests (Dudley and Stolton, 2003).Expanding the role of protected natural areas in principle could be significant, insofar as designated reserves constitute only 13% of the landmass (Watson et al., 2014) yet serve as water provisioning areas for 80% of the world's population (Harrison et al., 2016).However, protected areas are often positioned where incident threat is moderate-to-high, due to stressors originating outside their boundaries and difficult to control (Harrison et al., 2016).Even ostensibly protected source areas for urban water supply have historically shown substantial degradation (McDonald et al., 2016).
The significant potential replacement costs and penalties of using TE to substitute for existing NC ($TR nat,i ), which totals $3 trillion annually by 2050 (Table 1), provides a strong economic incentive for environmental protection.And, while this stewardship would undoubtedly encompass large tracts of land, recent research demonstrates how targeting critical sub-domains (e.g.riparian wetland restoration for nonpoint pollution control) (Sheldon et al., 2012) and areas of greatest human need (Chaplin-Kramer et al., 2019;Harrison et al., 2016;Green et al., 2015) would make NC protection more tractable.
The avoided penalties (P av ) presented in section 3.3, Table 1, and Fig. S4 provide further justification for green-gray blending in future water infrastructure investment.Our avoided economic penalty estimates show that given the current cost-effectiveness of TE, countries can avoid a penalty that on average, would double the cost to maintain the same level of threat reduction simply by preserving existing NC (Table 1).The sources of such penalties are important to recognize.On the one hand, because the marginal cost of replacing threat reduction from NC increases at an increasing rate as the stock of NC declines (Fig. S4), avoided penalties will increase as NC decreases, directly supporting the argument for natural asset protection.On the other hand, for countries with similar levels of NC, those with less cost-effective TE will suffer from higher penalties.Therefore, the avoided penalties highlight the need for a complementarity in approaches to water security that capitalize on best practices in technical innovation, environmental stewardship, and promoting improved cost-effectiveness and economic incentives.These are management levers that could be controlled by decision makers, after fully understanding the tradeoffs, benefits, beneficiaries, and downsides of any specific plans to combine green-gray water infrastructure (e.g., McCartney et al. 2019, Hurford et al. 2020).
In contrast to the immediate advantages inherent in natural capital protection, post hoc restoration often proves expensive, often spectacularly so, and many case studies point to the wisdom of damage prevention over rehabilitation.For example, $80 billion was expended over multiple decades to rehabilitate the 1,000 km 2 Yamatogawa River in Japan (Tsuzuki & Yoneda, 2012).Organic pollution was controlled, but at a cost of $65 billion in the Rhine (Wilken, 2006).In the U.S., the many tens of thousands of rehabilitation projects for riverine ecosystems (Bernhardt et al., 2005) is a testament to the scope of the problem, supporting a sector with annual revenues of $25 billion that employs more than 200,000 (BenDor et al., 2015).While we have not explicitly evaluated the global costs of either protecting or rehabilitating watersheds and waterways, the endpoint of such interventions could save trillions of dollars in engineering costs that otherwise would be necessary to replace lost NC threat reduction services (Table 1).

Conclusion
Our unified framework linking natural capital to traditional engineering enables us to determine how the ongoing loss of well- functioning ecosystems and the subsequent replacement of their affiliated environmental services through engineering strengthens or compromises water security over regions and continents.These findings support, for the first time at the global scale and in the domain of water resources, some key tenets as first proposed in the early ecosystem services literature (Odum 1973).Chief among these is the concept that environmental services typically go unrecognized until they are compromised, creating economic hardship when society elects to replace them or abandon them to environmental degradation.While there are inherent uncertainties in our projections, our assessment of threat reduction by natural capital (TR nat ) demonstrates the value of such hidden ecosystem services, which substantially dampen otherwise higher human water security threat.They are functionally of the same order globally as services deployed through engineering, but in economic terms they substantially exceed the value of engineered water management.Should the otherwise free public subsidies conveyed by the environment be lost, we calculate that their replacement cost will be at a substantial penalty-at least twice the cost, on average, for each equivalent unit of water security services provided by engineering.
Mounting losses of natural capital as the global economy continues to expand translates into substantially higher costs and inefficiencies for achieving water security in the future.Cost-containment and sustainable water resource development can be achieved by preserving natural capital and incorporating it wisely into a next generation of water management systems.
These findings bear important policy implications; but, before any strategic shift to green-gray approaches in water security can be realized, several pressing, practical challenges must be confronted.Global investments in protected areas and their maintenance amounts to < 3% of water sector expenditures, with chronic shortfalls totaling tens of billions of dollars annually (McCarthy et al., 2012).Moreover, investments aimed at rehabilitating and/or protecting water-critical ecosystems amounted to only $12.3 billion worldwide in 2013 (Bennett & Carroll, 2014), while monitoring networks to track the status of water systems continue their general decline (Lawford et al., 2013;Fekete et al. 2015).
Fig. 9 shows the shifting worldwide pattern of country-level investments in TE as well as in the burden of NC replacement costs through Fig. 7. Geography of traditional engineering and natural capital in threat management in 2005 (left) and 2050 (right).Mapped color densities represent downstream populations served by water source areas.Business-as-usual trends in the growth of incident threat and societal response (Figs. 3,4) mean that nearly all areas improve their engineered water services and will reside in the High-TE/High-NC (green color) or High TE / Low-NC (red) category by 2050.Red areas suggest strong path dependencies in future threat management, requiring a nearly exclusive reliance on TE; green indicates the potential for blending NC-TE approaches.High-to-Low thresholds determined from population-weighted global mean threat containment in 2005 (TR eng = 0.38; TR nat = 0.20).(For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)mid-century.A commitment to the protection of nature-based assets would yield broad global benefits.For developing countries with an accelerating rise in both TE investments and NC replacement costs, preserving NC would arguably be at a still higher premium.Yet, these are the countries that are least able financially to accommodate the rapid installation of TE and simultaneous losses in NC, exacerbated by a raft of additional institutional, technical, and human capital obstacles (Cornell University et al., 2020;HLPW, 2018;Vörösmarty et al., 2018;Wehn de Motalvo and Alaerts, 2013).Sub-Saharan Africa is emblematic of these challenges (e.g., Nigeria, DR Congo, Ethiopia, Sudan), given its rapidly rising demands for water services, limited TE investment potential, and poor track record in maintaining its current infrastructure (Foster and Briceño-Garmendia, 2010).Yet, much of the continent could benefit from protecting a relatively abundant stock of NC over the next decades (Fig. 7), and successful demonstrations of green-gray water management there are already in place (e.g., World Bank, 2015).
While the expanding global middle class spells success for poverty alleviation under SDG-1, we have shown that BAU approaches to water resource management will embody costly negative impacts on freshwater resources under SDG-6.This is a prime example of incongruities inherent within the SDG framework (International Council for Science ICSU, 2017), and suggests the wisdom of pursuing cross-sectoral synergies.Cost-effective greening of water management represents an important opportunity to liberate financial resources and benefit other aspects of the sustainable development agenda, given water's preeminent role in human enterprise and among global economic risks (World Economic Forum WEF, 2020).A redesign of business-as-usual practices is also timely given insufficient financial commitments to TE-based water resource development (Rodriguez et al., 2012;HLPW, 2018).This important constraint is not confined to the developing world.In the U.S., an annual $55 billion shortfall in capital investment for water engineering means that only 40% of today's needs are satisfied, with underfunding slated to rise to $144 billion in 2040 (ASCE, 2011), unless pending legislation begins to reverse this trend (The White House, 2021).
Given the global economic significance of investments in water resources that is apparent throughout the century, we see wisdom in pursuing a strategic transition to water management systems that are inherently more cost-effective and sustainable (Gleick, 2018, Liu et al. 2013), and capable of reliably serving large numbers of people (Chaplin-Kramer et al., 2019;Harrison et al., 2016;Green et al., 2015).An improved alliance between natural capital and traditionally-engineered

Table 1
Global estimates of rising expenditures in traditional engineering (TE), natural capital (NC) benefits expressed as avoided replacement costs, and the penalties incurred should NC be lost and replaced by TE.Allocations for TE infrastructure accommodate expanding water demands and loss of NC over time.The costs to remediate remaining threat, unrecovered by this TE, are also substantial, exceeding TE expenditures in the early part of the century until TE expenditures accelerate.Intact NC dampens otherwise higher levels of threat and greatly exceeds the value of TE threat mitigation.Relative contributions of NC decline over time due to degraded ecosystem services and expanding reliance on TE.All values in the first three rows are in billions of US $ 2020 PPP a ; for NC these represent TE-based avoided replacement cost equivalents.a Converted from US $ 2005 to 2020 PPP (purchasing power parity) using BLS (2020).b $TR eng,i , total TE-based threat remediation (Spend eng , Eq. S11 for countries); Eq.S12 for individual pixels.Includes the net cost of capital, operations, and maintenance.c $TR nat,i , threat prevention considered as avoided costs.The range in parentheses shows the upper and lower limits from the power function used in Eqs.S14, S15, and S16.d $T rem,i , the cost to remediate remaining incident threat calculated as a residual based on Eq.S19.
e Calculated relative to the sum of the value of threat reduction by TE and threat prevention by NC.
f Population-weighted avoided penalty, P av (Eq.S18).infrastructure researchers and practitioners, starting with the training of our next generation workforce to co-manage issues going well beyond engineering alone (e.g., social and environmental equity) (Kelly, 2008), should go far towards achieving these objectives.In doing so, society will also benefit from the non-economic value of sustainably managed natural capital (Tickner et al., 2018;Díaz et al., 2019), including its biodiversity and essential earth system support services like climate stabilization.Traditional engineering is a necessary part of the solution, but it is neither economically nor environmentally feasible as the sole approach to sustainable water development.

Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Fig. 1 .
Fig.1.Conceptual framework and key water security threat nomenclature.Threat is apportioned in terms of its control by natural capital (NC) and traditional engineering (TE), plus any residual impairment.A parallel set of variables for replacement cost estimates (not shown for brevity) can be found in TableS2.The variables shown are computed on a grid-cell basis and denoted by i elsewhere in the text.Additional nomenclature, intermediate steps and specific equations, input data, and assumptions are described in the Supplementary Material.
C.J.Vörösmarty et al. 2016) and present-day geographical patterns(Vörösmarty et al., 2010) that generally favor threat intensification over its spatial expansion.By 2080, population-weighted global mean T i increases by 10% over 2005 levels, with much of the change focused on rapidly developing countries.

Fig. 2 .
Fig. 2. Features of water security threat and its control.(A) Water supply conveyed to downstream populations in the absence of human impacts.(B) Environmental stressors produce a maximum potential incident threat; T max represents the endpoint of complete removal of natural capital and its associated threat suppression.(C) Natural capital reduces the maximum to incident threat, the level observed and acted upon by engineered remediation.(D) A residual threat remains after engineered interventions.

Fig. 3 .
Fig. 3. Growth and re-distribution of global income and the affiliated rise in incident threat.(A) The impact of anticipated global economic development moves overall population distributions to the right, reflecting the rise of the global middle class.Estimates are derived from the IPCC-AR5, SSP database (SSP, 2016).All values are in GDP-PPP/capita (2000 $).(B) Future distributions of T (for 2050) are similar to those of the present, stabilized across the United States and Europe, but accelerating across Western Africa, South and East Asia.(C) Mean population-weighted trajectories for major economic blocks reflect rapid demographic and economic growth and agricultural intensification followed by slowing and stabilization.Pixels reported at 30 ′ lat/long; non-discharging landmass shown in white.

Fig. 4 .
Fig. 4. Projections of future incident threat T under the business-as-usual (BAU) scenario.The estimates are based on IPCC (RCP 6.0/SSP2 combination [SSP, 2016]) reflecting the spatial distribution of regional development determined by macro-economic trends and population growth.Throughout the simulation timeframe, threat generally intensifies over previously threatened areas, in lieu of a broadening, or extensification, of the spatial domain of T.

Fig. 5 .
Fig. 5. Components of incident threat containment and final threat remaining (T rem,i ) in 2050.(A) Engineering-remediated threat reduction (TR eng,i ) at pointof-service prevails in middle-to-high income countries.(B) TR nat,i limits otherwise higher T and is generally inversely related to proximity to human population and economic activity.(C) T rem,i represents T i after TE interventions and accounts for the effect of NC threat reduction.(D) Mean values of threat components for countries grouped by income; non-linear trajectories exist in both T i and its remediation by TR eng,i with rising income, a pattern consistent with present-day tendencies (1).Total threat attenuated by engineering and natural capital is the sum of panel values in (A) and (B) (purple and green, respectively in panel D), in turn giving the remaining threat (T rem,i ).T i and TR eng,i means are weighted by local population, TR nat,i by downstream river corridor population.TR nat,i maximum is 0.53, representing theoretically pristine water source areas.(For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 6 .
Fig. 6.Threat control by traditional engineering and natural capital in year 2050, relative to 2005.(A) Threat reduction by engineering (TR eng ) and (B) natural capital (TR nat ).The business-as-usual case shows growing emphasis on TE globally.Despite rapid growth in relative terms, many developing world regions (e.g.sub-Saharan Africa) have limited TE systems by mid-century in absolute terms.NC losses are a byproduct of development, limited environmental protection, and some TE interventions themselves (e.g., sewerage works with poor treatment; excessive dam construction).

Fig. 8 .
Fig.8.Annual replacement costs per unit area for existing natural capital ($TR nat,i ) through traditional engineering in 2050 in four different countries.Grey bars represent the proportion of pixels in each country with each level of TR nat,i on the horizontal axis.The blue curves represent the per square km cost to replace the existing natural capital in the pixels in each bin.Country-level specificity arises from differences in the cost effectiveness of engineered management of threat across the globe (Eqs.S13 & S14).Total replacement cost (Σ$TR nat,i ) and avoided penalty (P av ) are at the national level (percent and US $ 2020 PPP, respectively).Fig.S4gives the general response function.(For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) authorship contribution statement Charles J. Vörösmarty: Conceptualization, Supervision, Writingoriginal draft, Writingreview & editing.Ben Stewart-Koster: Conceptualization, Data curation, Formal analysis, Methodology, Validation, Writingoriginal draft, Writingreview & editing.Pamela A. Green: Conceptualization, Data curation, Formal analysis, Methodology, Validation, Writingoriginal draft, Writingreview & editing.Edward L. Boone: Conceptualization, Formal analysis, Methodology, Validation.Martina Flörke: Conceptualization, Formal analysis.Günther Fischer: Conceptualization, Formal analysis.David A. Wiberg: Conceptualization, Writingreview & editing.Stuart E. Bunn: Conceptualization, Writingreview & editing.Anik Bhaduri: Conceptualization, Writingreview & editing.Peter B. McIntyre: Conceptualization, Writingreview & editing.Claudia Sadoff: Conceptualization.Hongxing Liu: Conceptualization, Formal analysis, Methodology, Writingreview & editing.David Stifel: Conceptualization, Formal analysis, Methodology, Writingreview & editing.

Fig. 9 .
Fig. 9. Nations ranked by projected expenditures on TE investments and replacement cost of NC. (left panels) Countries labeled in red experience the most rapid relative increases in required TE expansion ($TR eng ), while also incurring increased cost to replace NC ($TR nat ).These tend to be poor countries.Countries with general declines in both variables (labeled blue) are typically richer.(right panels) Rankings (1 = highest) in 2050 versus 2005, with colors reflecting quartiles of a 2017 index of institutional capacity, technology, and human capital (Cornell University et al., 2020) (highest index score [purple] = 1, typically more wealthy countries); sizes indicate expenditure levels.Countries above 1:1 line move to higher rank in required expenditures/penalties.Relative to rich countries, the developing world faces the dual challenge of financing more rapid deployment of traditional water engineering while simultaneously coping with degraded natural capital, which itself increases the costs of water resource systems.(For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)