Design principles for engineering wetlands to improve resilience of coupled built and natural water infrastructure

Intensifying climate extremes and the ageing of built infrastructure have prompted the idea of replacing the ageing built infrastructure with natural infrastructure. In this paper, we discuss how a distributed portfolio of smaller wetlands performs compared to a flood control reservoir in terms of flood mitigation. Using a framework of a loosely coupled land surface model with a hydrodynamic model, in the Brazos basin (Texas), we find that (i) two smaller wetlands have more impact on flood mitigation than one double sized wetland, and (ii) creating multiple wetlands (prioritized based on storage) increases flood mitigation. Further, we find that a portfolio of wetlands equivalent to the size of the submergence area of the biggest flood control reservoir (Whitney) in the basin, can create additional flood control storage, equivalent to ∼10% of the total storage of Lake Whitney. Creating a portfolio of wetlands can increase the overall resiliency of the basin.


Introduction
Extreme weather events (floods, storms and cyclones) between 1980 and 2021 caused losses of $1.8 trillion in the US, and the hardest hit state was Texas, with a loss of $349 billion (NOAA 2022).Characteristics of precipitation and related damages are expected to further intensify, due to the increase in global temperature (Trenberth et al 2003).Built infrastructure for water storage and flood protection (dams, etc) is ageing, both in durability and design concept, especially in developed countries (Lall and Larrauri 2020, Sabo 2020) and hence fails to meet the present day challenge in the face of rising demand and climate uncertainty (Pahl-Wostl 2007, Ho et al 2017, Okkan and Kirdemir 2018, Fletcher et al 2019).The American Society of Civil Engineering (ASCE 2021) reported that the average age of US dams is 57 years and receives a D grade.Hence, there is an investment gap in water infrastructure that has limited maintenance or replacement (Feinstein 2021).For example, the funding gap for improving the resilience of all dams and levees in the US is $151 billion (ASCE 2021).In addition, there are limited sites available for installing larger and centralized built infrastructure.
Natural infrastructure (e.g.wetlands) provides a cost effective solution to improve the functioning of ageing built infrastructure (Palmer et al 2015, Narayan et al 2017, Zhu et al 2020, Vörösmarty et al 2021).Natural wetlands provide 'stackable' ecosystem services with 'layered financial value' such as flood control, water storage, water quality, low flow attenuation and infiltration (to underlying aquifers), etc (Daneshvar et al 2017, Debanshi and Pal 2022, Wang et al 2022).However, wetlands are now disappearing due to climate change, land-use changes, and changes in river flow (Schneider et al 2017, Fluet-Chouinard et al 2023).Recent studies show that 64% of wetlands have disappeared since 1900 AD globally (Davidson 2014;www.ramsar.org).The conterminous US, lost 62 300 acres of wetlands between 2004 and 2009 (Dahl 2011), which is equivalent to the area of Baltimore, US.
Natural wetlands are not a substitute for dams as there is not a 1:1 exchange of functionality (Muller et al 2015, Manuel-Navarrete et al 2019).
First, wetlands are shallower than reservoirs.Second, dam operations are controlled, unlike unmanaged wetlands.Natural infrastructure is not engineered and hence results in higher uncertainty in behavior as compared to more controlled, built infrastructure.Hence, the performance of natural wetlands has been called into doubt with increasing climate uncertainty (Muller et al 2015, Onuma andTsuge 2018).Nevertheless, the construction of multiple smaller wetlands and off channel (floodplain) storage may offer a new out-of-the-box approach that is cost effective, smaller-scale, distributed, and placed in watersheds to strategically relieve stress, improving the resilience of the existing built infrastructure portfolio.
Here, we argue for a paradigm shift that intentionally couples existing built infrastructure with strategically placed and sized-but constructed-natural infrastructure.Constructed wetlands can also be conceived of as distributed, but short-term, storage to provide ecosystem services (Costanza et al 1997, Mitsch andGosselink 2000), including protection against floods and water insecurity (Hey and Philippi 1995, Acreman and Holden 2013, Martinez-Martinez et al 2014, Narayan et al 2017, Fargione et al 2018, Gulbin et al 2019, O'Sullivan et al 2020, Zhu et al 2020, Sheng et al 2021).These nature-based solutions could be human-engineered within the floodplain to recreate natural processes in the procured land, as compared to natural wetlands which are formed by local geology, hydrology, and hydrodynamics.These wetlands can be strategically installed at small scale by local municipalities or river authorities, through private sector water stewardship, and by nongovernmental organizations; however, their siting, design and implementation must be guided by science and strategy (Debaere and Kapral 2021).
In this paper, we leverage well-known quantitative approaches in hydrology to develop a sciencebased strategy which could advance application readiness of wetlands as a tool for bolstering the function of ageing existing built infrastructure (Browder et al 2019, Jean et al 2021, Vörösmarty et al 2021).Specifically, we focus on addressing how to strategically site wetlands to improve the basin-wide flood pool (Zhang and Song 2014).An increase in flood pool (in wetlands) could free up conservation storage (for water supplies) if built infrastructure includes a portfolio of wetlands to relieve pressure on them.In doing this, we pursue the hypothesized, but generally poorly-tested, notion that the decentralized buildout of wetlands ameliorates some of the negative effects of centralized, built infrastructure (Keeler et al 2019, Gourevitch et al 2020, Bremer et al 2021).Specifically, we ask: (1) do bigger constructed wetlands confer more benefit in flood control than smaller wetlands?(2) Are all wetlands equal in terms of benefit, and if not, what characteristics confer maximum benefit?And (3) how does a distributed portfolio of wetlands compare to a flood control reservoir in terms of benefit?

Data and methods
To answer the above questions, we combine well-used and high-fidelity macroscale, land-surface, and routing models, the variable infiltration capacity model [VIC (Liang et al 1994)] and the catchment-based macroscale floodplain model [CaMa-Flood, hereafter CMF (Yamazaki et al 2011)], respectively.Using this model coupling, we implement a series of land-cover and topography change experiments in which wetlands are strategically deployed, replacing existing land uses in the floodplain.Our analysis expands on previous studies in several ways.First, we use macroscale models that provide strategic assessment capabilities for a larger scale deployment of wetlands.Second, we take a strong inference approach (Platt 1964) to analyze the relative impacts of different numbers, sizes, and locations of constructed wetlands on flood.For this we employ a paired experiment.Specifically, we use 'pairing' of one large and two small wetlands and 'control' by using the same total area of wetland coverage in each 'pair' (Zimmerman 1997, Sabo and Power 2002a, 2002b).In this context, 'balanced' designs are those in which the sample size of the two experimental treatments (here 12 vs 24 km 2 ) are equal.In our case, because we controlled for total area, this equates to double the number of 12 km 2 sites 'paired' with larger 24 km 2 sites.Third, we develop a framework to compare the impacts of experimental wetlands and existing reservoirs 'headto-head' regarding flood protection.We devised an index to compare the flood control potential of wetlands and reservoirs.

Study area
Our analysis focuses on the Brazos River watershed in Texas, US, a coastal basin that exhibits the increasingly common hydroclimatic pattern of alternation between floods (from tropical storms and hurricanes) and drought (Fraticelli 2006, Ward et al 2020).Both the natural (land surface and hydroclimate) and human (water management) aspects of the basin are well understood (Wurbs et al 1988, Rajsekhar et al 2011, Wurbs and Ayala 2014, Lee et al 2017, Lee and Singh 2020).Whitney, Stillhouse Hollow and Somerville lakes are key flood control reservoirs operated by the US Army Corps of Engineers (USACE) and Possum Kingdom Lake, Granbury, and Limestone are major storage reservoirs operated by the Brazos River Authority in the basin.

Science of modeling framework
We develop state-of-the-art loosely coupled hydrologic-hydrodynamic models, which can simulate the impact of wetlands on flood and low flows at the basin scale.To limit computational expense, initially we empirically identify a few potential sites to run through the models.

Initial selection of wetland sites
We hypothesize that harnessing the storage characteristics of wetlands in a floodplain will maximize flood control (Acreman and Holden 2013).Based on this, we devise an empirical technique to identify initial wetland sites suitable for flood mitigation (table S1 and section S1.1 in supporting information (SI)).Our aim is to limit the computational expense of intensive process-based models.We perform geospatial analysis at 1 × 1 km spatial resolution to identify potential wetland sites within the Brazos River.Weights are assigned based on the suitability of the geospatial criteria for the functionality of the wetland (site) to mitigate flood and improve water supply.Using this analysis, we identify suitable sites for 12, 24, 36, and 48 km 2 size wetlands (section S1.1 in SI).In this paper we use only 12 and 24 km 2 sizes.For experiments, we have also used smaller size wetlands in larger suitable sites, for instance 12 km 2 instead of 24 km 2 or 48 km 2 .

Setting up models
We simulate multiple scenarios by siting individual or strategically chosen combinations of wetlands by replacing existing land use, using the framework of models.We coupled the VIC v4.2.c (section S1.2 in SI) and CMF v3.6.2 (section S1.3 in SI) such that the runoff estimated by the VIC was routed through the CMF.We estimated daily gridded runoff (mm day −1 ) from a vertical column of ∼7 × 7 km (1/16 • ) grid, by forcing the VIC with daily precipitation and maximum and minimum temperatures developed by Livneh et al (2013).
We use the CMF for routing gridded runoff.We use the CMF with ∼11 × 11 km (1/10 • ) global river network (section S1.3 in SI).The 1/16 • runoff (mm day −1 ) simulated by the VIC is converted to 1/10 • runoff (in cumecs) in the CMF using the builtin algorithm, which considers area-weighted averaging to achieve mass conservation.The routed flow is used to estimate the streamflow reaching downstream, at the location of interest.

Calibrating model framework and adjusting runoff
For VIC calibration, we employed a technique aimed at matching surface and subsurface runoff between a previously calibrated VIC v4.0.3 used in Maurer et al (2002) and the version used here (4.2.c).Specifically, three VIC soil parameters (the variable infiltration curve parameter, the maximum velocity of the baseflow parameter, and the depth of the bottom soil layer) are optimized via the implementation of 200 Monte Carlo iterations, matching the runoff ratio between the two versions of VIC.
Most of the parameters in the CMF are already prescribed by Yamazaki et al (2011).We calibrate the CMF by matching the daily streamflow observed at the Hempstead gauge station [US Geological Survey (USGS)] by changing Manning's roughness in the whole basin.We selected the Hempstead station because it covers most of the basin (figure 1).Initially, forcing the runoff from the VIC to CMF resulted in a systematic bias, so we scaled the runoff from the VIC before using it to force the CMF, by applying a monthly scaling factor (a separate multiplication factor for each month).This bias may result from meteorologic forcing, land surface models (LSMs) structure and parameterization, or underrepresented processes.Such bias-correction techniques have been applied to runoff in a recent study (Lin et al 2019).By using the adjusted runoff, and calibrated CMF, we capture the daily pattern of streamflow at Hempstead (section S2.0 and figure S1 in SI).

Representation of wetlands and building scenarios
To understand the impact of wetlands only on flood, we represent wetlands only in the routing model (CMF).We assume that wetlands' impact on hydrology (evapotranspiration and infiltration) is negligible during floods, and hence we do not represent wetlands in the LSM (VIC).We hypothesize that wetlands created in the floodplain have greater impacts on flood mitigation.Floodplain wetlands are deeper than surrounding areas, and storing floodwater and vegetation in wetlands reduces the flow of water.To simulate this, we place the following features in our modeling framework: (1) We modify parameters in CMF to represent wetland features.Specifically, we increase Manning's roughness coefficient by 10% and lower the floodplain depth by 1.5 m to represent wetland.
In CMF, this results in storing floodwater and lowering flood peaks.In CMF, the floodplain depth can be changed for 10%, 20%, …, 100% of the grid.the impact of the size and the number of wetlands on flood.We choose 30 'pairs' of scenarios (i.e. total 60 scenarios) by combining two selected 12 km 2 wetlands in one scenario and comparing it with a scenario of selected 24 km 2 wetland 'controlled' for the same area (figure S2 in SI), (ii) how wetland impact varies with respect to the storage created, as described in item #3 above, and (iii) based on this prioritizing selection of multiple wetlands and their impact in combination as described in item #3.(5) We compare the impact of these scenarios with a baseline scenario-with no experimental wetland.

Estimating flood index (FI) to compare performance of infrastructures
As wetland and built reservoirs are different in terms of how they store water (shallow vs deep storage), the resources available for a head-to-head comparison are lacking.Here, we formulate new empirical metrics, FI (equation ( 1)).To estimate Fl, the reduction in flood magnitude by infrastructure (natural or built) is divided by storage (control for area) achieved by infrastructure (equation ( 1)).To estimate the reduction in flow (inflow minus outflow) for reservoirs, we calculate inflow (outflow) based on the discharge at the gauge station upstream (downstream) of the reservoir.Flow data is obtained from USGS (www.usgs.gov).We obtain storage (pool capacity) of the reservoir from the Texas Water Development Board (www.waterdatafortexas.org).We find that flow data from USGS is available for water years between 1963 and 2010, and hence we limit analysis to that period.Similarly, we estimate the inflow for a grid containing an experimental wetland using outflow from upstream grids.Reduction in flow through wetland is inflow minus outflow from the grid.We use maximum storage reached by the wetland grid ) and consider it as potential storage for the wetland.In the absence of inflow data for each infrastructure (wetlands and reservoirs), we use outflow from the upstream location (grid and gauge, respectively).So, here, we assume outflow from the upstream location reaches the downstream infrastructure the same day without any change, FI = (inflow − outflow) /storage. (1) In the following section, we discuss results from three experiments.First, we compare the performance of 30 closely-located, experimental combinations of wetlands-a pair of two smaller (∼12 km 2 ) and one larger (∼24 km 2 ) sites-to assess the effect of size on flood control.Second, we rank the selection of individual wetlands (all as 12 km 2 ) by comparing their impacts as a function of their storage potential.Third, we compare the performance of the wetlands' portfolio and an important flood control reservoir in the same basin, Lake Whitney (as the impact from a single wetland is small compared to that from a large reservoir) and use FI to compare the performance of wetlands to multiple reservoirs in the basin.

Size vs. number
To test the hypothesis that multiple small wetlands are more effective in flood mitigation than a single large wetland, we compare impacts of 30 pairs of two 12 km 2 (small) and one 24 km 2 (large) wetlands on flood (figure S2 in SI).We estimate the reduction in daily maximum peaks as compared to the baseline scenario over the period of record from 1916 to 2010.We compare the impact of each pair at the grid cell most immediately downstream of all three wetlands.Small, constructed wetlands (two 12 km 2 ) had nearly a six times greater impact on the reduction in flood peak than a single large wetland (24 km 2 ) (figure 2; df = 29, P < 0.05).The greater impact of these two small wetlands was due to an increase in their storage potential (figure S3 in SI).This is attributable to phenomena such as the backwater effect.Generalizing, a decentralized siting of multiple smaller wetlands creates more benefits versus centralized natural infrastructure (figure 2).

Prioritizing wetlands selection
Based on the previous results, we understand the existence of heterogeneity in wetlands impact even if similar in size, and hence the impacts may not be additive in a portfolio of similarly sized wetlands (section S3.2 in SI and figure 2).Given this heterogeneity, we hypothesize instead that rank-ordered impact has limiting returns and that storage potential drives these.In other words, wetlands which tend to hold more water during floods confer more flood control benefit.Stakeholders who know the characteristics of impact should be able to develop a cogent strategy for the phased construction of natural infrastructure throughout a river basin.Above this, it will provide stakeholders with science-based tools to assist in making informed decisions for flexible water infrastructure planning (Fletcher et al 2019) and possible sequencing (Beh et al 2015).
To test this hypothesis, first we run 147 scenarios by running each of 147 wetlands as 12 km 2 (even though sites may be larger than 12 km 2 ).Then, we estimate the impact of a few representative subsets of wetland portfolios from one project to 50 projects (in ranked impact) of 12 km 2 size wetlands using the top 50 (of 147 total) wetlands by storage.We group the top ranked 1, 5, 10, …50 wetlands in scenarios.We then plot the number of wetlands against the cumulative impact (figure 3) and observe a saturating relationship, signifying limiting returns.Portfolio impact increased linearly from sizes of 1 to 30 but yielded limiting returns with higher numbers of wetlands.This suggests that not all wetlands have equal impact, even when controlling for size.Moreover, there is an upper limit to the impact of natural infrastructure (Muller et al 2015): less than 30 of 147 produced maximum impact.Thus, impact is additive, but to a limit.By constructing thirty 12 km 2 wetlands, we found that flood peak is reduced by 9.5% (1048 cumecs, figure 3).

Comparing the performance of natural and built infrastructure
One of the heated and unresolved debates about nature-based approaches to water resilience is their limited performance against the impact of centralized, built infrastructure (Muller et al 2015).We argue that this comparison is unfair in part because of the size of built infrastructure.Instead, a headto-head comparison, controlling for infrastructure scale, is warranted.Here, we compare the performance of wetland construction with existing flood control reservoirs operated by the USACE-to reveal the benefits that well-sited wetlands might have on operations and the flood pool of existing reservoirs operated for flood control.
To do this, we compare the performance of a portfolio of wetlands with Lake Whitney, the largest flood control reservoir in the Brazos basin.Lake Whitney encompasses 52 693 acres with a flood storage capacity of 2.5 × 10 9 m 3 (US Army Engineer District Fort Worth 2020).Using maximum potential storage, controlled for area, we estimate that the construction of 18 wetlands of 12 km 2 (i.e.53 819 acres) size would increase the natural flood pool by nearly 2.5 × 10 8 m 3 (top panel of figure 3), i.e. ∼10% of Whitney's total storage capacity.Thus, multiple distributed wetlands can provide complimentary storage to reservoirs.

FI-to compare the performance of infrastructure in flood mitigation standardized by storage
Both natural and grey infrastructure differ in terms of depth, and hence, their impact will vary.To compare this, we devise and employ FI, which gives flood mitigation scaled to maximum storage (equation ( 1)).We found that the FI for most wetlands ranges from 0 to 0.45 (median = 0.41, green bars in figure 4), which exceeds that of three of the flood control reservoirs in the basin (Whitney, Stillhouse hollow and Somerville lakes) on a per-area basis (FI ∼ 0.05-0.2;median = 0.08, hollow colored circles in figure 4).This suggests that the efficacy of wetlands is within the range of reservoirs based on the storage created.There will be uncertainty associated with this analysis due to differences in control of reservoirs and (uncontrolled) wetlands.

Conclusion
In this paper, we design experiments with modeled systems of wetlands to evaluate how the strategic siting of wetlands provides additional storage and flood control in the Brazos basin.Our results provide four lines of evidence that natural infrastructure significantly enhances resilience to flood-drought extremes, thereby complementing existing built water infrastructure.First, size matters.A couple of small wetlands are better than a single large wetland of equal area.Therefore, it may be more economical and manageable to site and restore smaller wetlands in the Brazos basin.Second, the addition of wetland to the water infrastructure portfolio increases storage capacity (figure 3, top panel), but not all small wetlands are equal in terms of impact.Storage volume varies considerably-even among wetlands with impacts in the top 50-and has a significant impact on flood control outcomes.Third, a portfolio of small strategically distributed wetlands, with an eye to maximizing storage volume, can offer substantial gains in flood protection (figure 3 bottom panel).Hence, science-based tools can help stakeholders to identify and sequence out the installation of wetlands with more storage potential for flood reduction than random actof-kindness installation.Fourth, multiple (∼18) wetlands can provide storage equivalent to ∼10% of big flood control reservoirs, and the impact of wetlands per storage is five times the impact of reservoir per storage created (based on comparison of median FIs).
Hence, the impact of potential natural infrastructure in this basin is in proportion to that of existing reservoirs.Hence, we propose that combining the additional storage created by wetlands can reduce the operational load on ageing dams and, hence, we advocate for the design and co-operation of both types of infrastructure.We briefly elaborate on each of these findings and probable next steps in sections S3.0 and S4.0 in SI.
Our findings offer guidance to practitioners charged with increasing the adaptive capacity and resilience of ageing reservoir systems.Since resources for conservation and water stewardship are limited, water resource managers should allocate funds to establish portfolios of smaller wetlands and build larger portfolios over time as capital is raised.

Figure 1 .
Figure 1.Location of experimental wetland sites in the Brazos River basin.

Figure 2 .
Figure 2. Comparison of the reduction in flood peaks achieved by one 24 km 2 and two 12 km 2 wetlands (sample size: 30 pairs).The Y-axis shows a reduction in a 15 d flood just before the maximum flow (1916-2010).

Figure 3 .
Figure 3. Top panel shows increase in the maximum (1916-2010) storage for top fifty 12 km 2 wetlands with increase in number of wetlands.Bottom panel shows the relationship between the impact of number of wetland/s on flow at the Brazos mouth.Boxplot shows uncertainty in impact for top-ten simulated annual floods for the period of 1916-2010.Y-axis shows reduction in 15 days flood just before the maximum peak during the top ten events.

Figure 4 .
Figure 4. Histogram of FI estimated for all wetlands (scenarios with individual wetlands; shown by green bars).Red, green, and brown hollow circles show FI estimated for Whitney, Stillhouse Hollow, and Somerville Lake, respectively [no relation between FI of reservoir and y-axis (frequency)].Gray box encloses range of FI shown in reservoirs.
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