Moving from total risk to community-based risk trajectories increases transparency and equity in flood risk mitigation planning along urban rivers

After several years of drought, 2023 and early 2024 are reminders of the powers of California’s atmospheric rivers and the devastating flooding they can entail. Aged flood-mitigation infrastructure and climate change exacerbate flood risk for some communities more than for others, highlighting the challenge of equitably mitigating flood risk. Identifying inequities associated with infrastructure projects is now legally required by regional water boards in California, but tools are lacking for making this assessment systematically. We propose that risk trajectories, computed by adding a probabilistic wrapper of flood drivers to models already used in flood-risk-mitigation planning, allows planners to quantify the spatial and temporal variability of risk for communities along river and thereby increase procedural equity by making distributional equity more transparent. While our proposed approach is applicable generally, we demonstrate its impact in the case of San Francisquito Creek, California, where risk trajectories combined with a multi-tier engagement model, helped identify and prevent an inequitable risk transfer.


Introduction
Riverine flood risk is inherently inequitable.Many factors contribute to this inequity starting from the natural, spatial variability of flood exposure along most rivers.This natural variability has been modulated and sometimes amplified by a legacy of policy interventions that have benefited communities unevenly [1][2][3][4][5][6].Compounding the problem, climate change [7] and population growth continue to unevenly intensify flood exposure [8][9][10].Decades of research have shown that this inequity in exposure is greatly magnified by the inequities in the ability of communities to recover from flooding [11][12][13][14][15].However, progress in ensuring flood risk research actually helps vulnerable communities has been slow, potentially due to the lack of incentives for researchers to partake in site specific research and to build strong, time-consuming relationships with practitioners and local partners [16].Thus, while equitable climate adaptation is increasingly becoming a political priority, many recent climate-adaptation measures still tend to use techniques that favor affluent communities [17][18][19], or focus on measures with benefits that gentrify communities, disproportionately affecting or displacing vulnerable populations [20,21].This raises the pressing question of how to prioritize equity concerns in ongoing planning efforts.
The goal of this paper is to demonstrate how progress towards more equitable infrastructure planning can be achieved by combining a multi-tier engagement model with a lightweight flood modeling framework that enables planners to compute individual risk trajectories for communities along-river.Our proposed model is lightweight in the sense that it provides a probabilistic wrapper of flood drivers that can be added to the type of hydraulic models already used in infrastructure planning without requiring a new software or significant computational expense.To ensure actionability, outputs from our flood model are designed through the normative view of scientific coproduction that leverages our partners' experience in maneuvering the complex approval process of large infrastructure projects with the academics' scientific expertise [22].We argue that our model not only improves our ability to reveal and reduce any potentially inequitable transfers of flood risk along urban rivers in a changing climate, but combined with a partnership with decision-making agencies, also provides an immediately actionable way forward because it can be readily integrated into existing planning efforts.While our approach has been implemented in the specific context of San Francisquito Creek, California, both our modeling framework and partnership-based approach to informing decisions apply more generally.
The natural floodplain of San Francisquito Creek, located in the south San Francisco Bay, is now a densely populated urban area, creating issues of flooding, water supply, habitat restoration, and sediment accumulation at an upstream dam [23], in addition to aging infrastructure.Many of these issues could be amplified by increases in the variability and frequency of extreme precipitation events over the past several decades [24,25] that are projected to continue into the future [26], highlighting the need to consider updates to aging infrastructure within the context of climate change.
While current flood-risk-mitigation projects in California have to incorporate sea level rise into their planning [27], it is not yet standard to account for an increase in precipitation extremes.For example, previous planning efforts at San Francisquito Creek accounted for approximately 1 m of sea level rise [28] but did not consider the effect of changes to rainfall.One reason why variability in precipitation is often neglected is that updates to flood-mitigation infrastructure are traditionally assessed only for a single, specific event, commonly referred to as the design event.The 100 year flood, based on exceedance probabilities of past, stationary forcing conditions, is the current standard for floodplain management within state and federal agencies in the United States.However, identifying a single event that constitutes a 100 year flood is not straightforward [29][30][31], particularly in the Californian context where some of the most destructive floods, including the 1861-62 flood [32] and the flooding that occurred in early 2023, were not created by a single rainfall event but by a sequence of atmospheric rivers occurring in close succession.
One of the most extreme flooding events along San Francisquito Creek, shown in figure 1(a), occurred in February 1998.Approximately 1700 properties were impacted during this flood, causing millions of dollars in damage [23].The dashed red box in figure 1(b) highlights the location of the Pope-Chaucer Bridge, where most of the river outflow occurred.After the event, a deliberate attempt was made to move towards joint and collaborative decision-making and the San Francisquito Creek Joint Powers Authority (SFCJPA) was formed by the cities of East Palo Alto, Palo Alto, and Menlo Park, the San Mateo County Flooding and Sea Level Resiliency District and the Santa Clara Valley Water District to lead projects that mitigate the risk of along-river and bay flooding.One recent planned project, the Reach 2 'Urban' project, is an infrastructure modification that increases the capacity of the Pope-Chaucer Bridge, the location of lowest flow capacity along-river [28], allowing for the creek to accommodate flows up to the 1998 event, but also entailing higher flows to pass downstream.In anticipation of the flood-risk transfer implied by these higher flows downstream, a major flood protection project, termed Reach 1 'Downstream' Project, was implemented in 2019 to reduce flooding in East Palo Alto by widening the channel downstream of Highway 101, building engineered levees, and where there was insufficient room, installing flood walls [28] (figure 1(b)).The Reach 1 Project was intentionally implemented prior to addressing flood hotspots higher up the river, which are being assessed through the Reach 2 Project.
Our study shows how the traditional approach to assessing the risk-mitigation benefits of infrastructure projects, such as considering a single design event only, can create blindspots by failing to identify the communities along river for whom flood risk increases due to planned infrastructure updates coupled with climate change.In the case of San Francisquito Creek, these blindspots could have exacerbated longstanding socioeconomic inequities because the creek aligns with a strong gradient in household income and racial diversity (figure 1), despite the incorporation of sea level rise and the input of local communities into planning efforts.Since recognizing this blindspot, the creek's governing agency updated its project plans to eliminate the risk transfer in the affected communities.The development of both a modeling framework using techniques readily accepted in the planning process and a partnership-based approach provides the opportunity for immediate action and has the potential to advance equity in the evaluation of infrastructure projects intended to manage flood risk.

Methods
To characterize the present and future potential for flooding hazards from compounding inland and coastal processes, we implement a hybrid modeling approach [30] which merges statistical and numerical modeling to generate a synthetic ensemble of joint river discharges and coastal water levels and the resulting along-river water level (figure 2).Using outputs from the model, we evaluate the probability of flood initiation for present-day and future climates and determine the uncertainty surrounding the estimates.We repeat these methods for two different river configurations, one representing the current (Baseline) river configuration and one representing the river configuration with the initially proposed infrastructure modifications (Infrastructure).A brief description of the methods is highlighted below, while a complete description of the model formulations and validation are described in the supplementary data.

Statistical model
We obtain instantaneous, 15 min observations of river discharge from 1987-2020 from the US Geological Survey (USGS) 11164500 San Francisquito Creek station and hourly observations from 1997-2020 of measured coastal water level from the National Oceanic and Atmospheric Administration's (NOAA) 9414523 Redwood City station, located approximately 12 km north of the mouth of San Francisquito Creek.We decompose the coastal water level into mean sea level, tide, storm surge, seasonal cycles, and interannual variability related to large-scale climate variability such as the El Niño Southern Oscillation following methods described in [33].
To model the time-varying nature of extreme storm surge and river discharge, and their respective dependencies, we utilize a bivariate point process approach [34,35] with time-dependent distribution parameters [36].We fit de-clustered peak over threshold excesses from storm surge and river discharge to time-dependent generalized extreme value distributions which include seasonal and interannual variability.To investigate the significance and goodness of fit of models involving different arrangements of multiple parameters, we utilize a combination of diagnostic plots, information criteria, and likelihood ratio tests (see supplementary data for details and table S4 for final time-dependent parameterizations).Below extreme thresholds, observations of river discharge are separated by month and fit to lognormal (wet months) and gamma (dry months) distributions and storm surges are fit to monthly logistic distributions.
To synthetically simulate thousands of physically plausible events, we use the bivariate logistic model [35] to sample from the time-dependent extreme value distributions when over the extreme threshold (i.e.11.9 m 3 s −1 for discharge and 0.19 m for storm surge), and from the non-extreme distributions when under the extreme threshold.Using Monte Carlo simulation techniques, we generate 50 synthetic daily records of river discharge, storm surge, tide, monthly mean sea level anomalies, and seasonality, each 1000 years long.

Numerical model and surrogate modeling approach
Our approach combines the millions of synthetic simulations of upstream river discharge and downstream coastal water level with surrogate models [37] developed using output from the Hydrologic Engineering Center's-River Analysis System (HEC-RAS) flow model to produce a large sample of alongriver water levels for robustly evaluating flood risk.We use a HEC-RAS model (v5.03) that was provided to us in October 2019 by Balance Hydrologics Inc for 1D, steady flow conditions.Importantly, all existing planning efforts are based on this model.Our model extends from the USGS 11164500 station to the Bay, covering 12.5 km of San Francisquito Creek, and comprises a transect approximately every 20 m.This Baseline HEC-RAS model represents the river configuration as of 2023 and includes 15 bridges, bank-tops, and a recent modification to the reach downstream of the Highway 101/East Bayshore Road Bridge, called the Reach 1 'Downstream' Project, that widened the channel and installed floodwalls for up to 3 m of protection against high river flows and rising sea levels.
We develop three suites of surrogate models based on HEC-RAS models for the river over a collection of transects: (1) upstream of the Middlefield Road Bridge, (2) between the Middlefield Road Bridge and the Pope-Chaucer Bridge, and (3) downstream of the Pope-Chaucer Bridge.In order to stabilize convergence issues, each of the individual HEC-RAS models allows for outflow over bank-tops using lateral structures [38] at only one of the three collections of transects before results are passed to the next.In the supplementary data, we validate this approach against a full HEC-RAS run with all lateral structures turned on.
We use a subset of approximately 900 river discharge and coastal water level event combinations, which range from 0.2 to 300 m 3 s −1 and −0.3-4.6 m (NAVD88), respectively, as the boundary forcing conditions for surrogate model development.We then derive the surrogate models for each of the defined reaches using a 2D scattered interpolation which allows us to extract the water level for all the synthetic combinations of discharge and coastal water level, even those not modeled directly in HEC-RAS, on a transect-by-transect basis.Water levels extracted from the surrogate models agree well with the water level from direct HEC-RAS model simulations over a set of 100 validation scenarios (figures S2 and S3).

Calculation of the likelihood of flooding
We estimate the likelihood of flooding using the probability of flood initiation for any given along river transect and use this as a proxy for flooding.At each transect, we select the annual maximum water level for each of the 1000 simulated years.Then, using the empirical distribution of annual maximum conditions over the 1000 year long simulation, we compute the annual exceedance probability, or the probability that a water level will meet or exceed the bank elevation during a one-year interval using the Weibull plotting position.We repeat this for all 50 simulations and compute the average and range.

Modeling future climate conditions and determining future change in flood risk
Projecting changes in precipitation and the associated river discharge in enough detail to inform specific, local infrastructure projects is challenging.Global climate models do not necessarily provide enough resolution to adequately resolve topography and downscaling adds significant uncertainty, especially in river discharge [39].In many cases, there is also a large disagreement among different global climate modelsfor example, the 30 year average change in precipitation across 32 global climate models for RCP4.5 and RCP8.5 up until the mid-century could range anywhere between −10 and +20% of the present day for the northern Californian coast [40].However, one feature that all current model projections have in common, and that is identified robustly in data from the last few decades [24], is an increase in the variance of precipitation [26,41].
Therefore, instead of choosing a specific climate model to represent future climate conditions, we develop three synthetic joint climate conditions which increase precipitation, increase sea level, and increase both precipitation and sea level together, based on a combination of historical data and future projections for California.Because heavy precipitation and high discharge events are often closely linked in small, steep catchments [42], we assume a change in precipitation variability represents an equal change in discharge variability.This assumption is supported by the precipitation hyteographs and discharge hydrographs for San Francisquito Creek showing close succession on an hourly time scale [43].We model an increase in the future variability of precipitation by increasing the variance (parameterized as the scale parameter) of the extreme and non-extreme discharge events, until the variance of the underlying distribution has increased by 50%, similar to the change in precipitation variability observed for the region over the past several decades [24].
Projected mid-century increases in sea level in the San Francisco Bay Area are between 20 cm and 80 cm, with a median of 30 cm [27,44].We incorporate sea level rise by adding a constant 30 cm to current mean sea level.While changes in the frequency and intensity of storms could drive larger storm surge events, patterns of storm surge variability along the Pacific coast have not changed appreciably over the past few decades [45].
We determine how variations in the climate conditions amplify the probability of flood initiation at along river transects, by computing a flood amplification factor, F A , where and RP cc and RP p are the return periods of the probability of flood initiation averaged over all synthetic simulations for the implemented future climate conditions and for the present-day climate conditions, respectively.We present results up to annual exceedance probabilities of 0.003, or a .3%chance of flood initiation in any given year (which approximates the 300 year return period event).

Results and discussion
3.1.Focusing on a single design forcing condition in planning can obscure an inequitable flood-risk transfer Figure 3(a) displays the probability of flood initiation for present-day climate in the urban portion of the creek (1 km-8 km) for the current river configuration (Baseline).In this figure, we do not show the marshland near the Bay (0 km-1 km), where flooding is desirable, depicted in figure 3(c).We find that the current probability of flood initiation upstream of the Pope-Chaucer Bridge is approximately 2.6% (∼40 yr event) when averaged across nearby transects and the ensemble of 50 simulations.The maximum probability of flood initiation at this location is as high as 4% (∼25 year event) in any given year.
Overtopping upstream of the Pope-Chaucer Bridge will occur during the design event, which is based on the 1998 flood event, and depicted by the red stars.Figure 3(b) shows the probability of flood initiation if the Reach 2 Project was implemented as originally planned.The overall probability of flood initiation anywhere in the urban stretch of San Francisquito Creek reduces from 0.51% to 0.29% and the design event would no longer cause overtopping near Pope-Chaucer Bridge.However, the probability of flood initiation surrounding the University Avenue Bridge increases from approximately negligible to 0.4% (a 250 yr event) on average to a maximum of 1.3% (∼77 year event) at some transects.While it is well known that risk reduction measures adopted in one segment of a river alter risk elsewhere [46][47][48], current approaches to flood-risk management usually neglect this flood risk transfer [49].
To better illustrate the spatial redistribution of flood risk relative to vulnerable communities, we map out where overtopping would occur on average and with what probability in figures 3(c) and (d).As a consequence of the bridge widening planned at Pope-Chaucer, we see that the probability of flood initiation disappears upstream of the bridge, but flood initiation with a lower probability emerges between University Avenue Bridge and Newell Road Bridge (figure 3(d)).The flood risk is almost entirely redistributed to relatively vulnerable communities downstream.Importantly, this risk transfer is only apparent when looking at a larger set of events beyond the

Climate change complicates the question of how to set an acceptable risk threshold and for whom
One could argue that the flood risk transfer mapped out in figure 3 falls into the category of acceptable risk, because the level of acceptable risk is typically equated with the design event.Figure 4(a) shows how risk compounds over time under an increase in precipitation variability, implying the risk to flood initiation increases from approximately a 215 year event to a 75 year event at transects near University Avenue Bridge and from a 430 year to a 160 year event at transects near Highway 101/East Bayshore Road Bridge.Thus, our results show that what might be an acceptable flood risk now may no longer be acceptable in a few years or decades due to climate change.
The challenge then becomes identifying who decides what an acceptable level of risk is and for whom.When estimating return periods based on historic data, the communities between University Avenue and Newell Road Bridge face a probability of flood initiation well below the threshold chosen for the design event.In contrast, accounting for a doubling of the variability of precipitation entails return periods above the threshold for acceptable risk (figure 4(b)).Because changes in precipitation were not considered in the initial planning efforts, the emerging risk of more frequent flooding in vulnerable areas had not been realized.Another important consideration is that for the communities between University Avenue Bridge and Highway 101/East Bayshore Road Bridge, our model results show that the current risk of riverine flooding is low.Households in these socially vulnerable communities might not have any insurance or adaptations in place that could lower flood impacts, may experience greater damages proportional to their resources, and may be less likely to receive federal assistance for recovery [50].

The path towards impact: integrating flood model metrics with a multi-tier engagement model
Many existing studies focusing on equity in flood-risk mitigation document flood risk inequities either at the local [4,51,52] or the global scale [7,10,53,54].While a valuable starting point, the common focus on distributional inequities has been criticized as insufficient, calling for more attention to how patterns of inequity are produced and sustained [55][56][57].There is no simple answer to this systemic dimension of inequitable flood-risk management, but one theme that has proven to be productive in guiding planning towards greater equity is a dual focus on distributive and procedural inequities [58].Here, we combine these two vantage points, to identify an actionable and transferable way forward that relies equally on an intentionally designed multi-tier engagement model and a flood model developed specifically to quantify and thereby elevate a community concern that could not be substantiated in the standard flood modeling framework traditionally used in planning.
The concern about a possible flood risk transfer associated with the initial plans of the Reach 2 Project was expressed to us by staff members from the City of East Palo Alto.Similar concerns had previously been raised by the City of East Palo Alto during the review stage of the planned infrastructure modifications [59], but SFCJPA could not substantiate these concerns for the agreed-upon design event.This finding is consistent with our analysis in figure 3(b) where the absence of red stars downstream indicates that the flow associated with the design event would be accommodated without initiating flooding.However, our research also shows that flood risk is still being transferred when riverine fluxes slightly exceed those specified in the design event, highlighting the validity of the City of East Palo Alto's concerns.The disconnect hence emerged because of an overly narrow definition of equity with respect to one specific design event that is represented in the standard model.
The fact that the City of East Palo Alto's concerns remained unresolved demonstrates that the opportunity for cities and/or communities to provide input on infrastructure projects, even when that city is equally represented in the decision-making agency, does not in itself ensure procedural equity.Similarly, it demonstrates the bias imparted into the equity issues by standard models that were not designed to identify equity.We propose that progress towards more equitable decision making in large infrastructure projects hence requires the integration of an engagement model with intentional flood model design aimed specifically at quantifying the spatial and temporal variability of risk.Not all cities have the capacity to assess the technical details of large infrastructure projects and the possible ramifications for their specific community and may lack funding, resources, or data to develop analytical models themselves [60].
Once we had validated the concerns expressed by the City of East Palo Alto, we developed a strategic partnership with the SFCJPA to address this issue.Our model designed as a probabilistic wrapper of flood drivers inputted into the HEC-RAS model already used by SFCJPA and other project partners in planning, was critical for the success of this partnership, since the standard HEC-RAS model still provided a common basis to which our extensions added the dimension of spatial and temporal variability of risk [58,61,62].Figure 5 shows the metric that we have found most useful in communicating our concerns to decision-making agencies like SFCJPA.
The top row of panels (figures 5(a)-(c)) isolates how increasing discharge variability amplifies flood risk, and the bottom row of panels (figures 5(d)-(f)) shows that increasing sea level no longer amplifies along-river flood risk if existing infrastructure remains intact.The future climate condition increasing both discharge and sea level show the same results as increasing discharge variability alone.The figure columns focus on specific locations along river.The large magnitude change in flood risk with increasing river discharge (figures 5(a)-(c)) between river configurations (highlighted by the blue circles) is a consequence of the initially planned infrastructure updates.It shows no change in risk for Middlefield Bridge, where no updates are currently planned, a risk reduction around the Pope-Chaucer Bridge where Green and purple arrows indicate a risk reduction or a risk amplification, respectively.We emphasize that a flood amplification factor of zero does not mean an absence of flood risk but rather the absence of an amplification of risk.For the sake of easier comparison, we plot these flood amplification factors for historic return periods, keeping in mind that these may no longer accurately describe current climatic conditions.the bridge will be widened, and a risk amplification near University Avenue Bridge and Newell Road Bridge.Thus, the redistribution of flood-risk is largely driven by changes in infrastructure.
Comparing the two rows in figure 5 highlights that a continued increase in the precipitation variability, evaluated here as riverine discharge, is the primary factor amplifying flood risk at San Francisquito Creek in a changing climate, rather than sea level rise.In fact, a horizontal trend of F A = 1, such as figures 5(d)-(f) shows, implies that flood risk alongriver is largely unaffected by sea level rise.While modifications implemented in the Reach 1 Project accommodate up to 1 m of sea level rise, it is worth noting that a sea level increase of 1 m over the next few decades would require a dramatic, order-ofmagnitude increase in the rate of sea level rise in the near future, given the current rate of approximately 2 mm yr −1 [63].While not impossible [44,64,65] sea level rising by 1 m is one extreme within a wide probability distribution of possible future sea levels.In contrast, data for California shows that the variance of precipitation distribution has approximately doubled since 1970 [24] and it will likely continue [26].There is hence a notable disconnect between the precautions taken to avoid flood amplification due to sea level rise and the choice not to explicitly consider a continued increase in the variability in precipitation in planning, suggesting that the planning process at San Francisquito Creek was guided primarily by the concern over rising sea levels as also apparent in other adaptation efforts in the San Francisco Bay Area [66,67].

Implications
The challenges encountered at San Francisquito Creek are symptomatic of other riverine systems in California, where severe flooding from heavy precipitation during atmospheric river events caused losses exceeding US $1 billion in damages in both 2017 and 2021, and estimates for 2023 are US $4.6 billion [68].How can we rise to the challenges that increasing flood risk poses to California, and how do we do so in an equitable way?Minimizing the total flood risk along-river is crucial for justifying the substantial cost of large infrastructure projects [69], but a reduction in total flood risk does not necessarily imply that risk is reduced everywhere along the river, and current planning processes rarely provide transparency about relative changes in risk.
Environmental regulations in the United States through the California Environmental Quality Act and the National Environmental Policy Act more broadly specify that an infrastructure project cannot exacerbate risks as a result of implementation or must propose a means of ameliorating.However, risk increase due to climate change is not typically assessed within the context of this regulation.Since the downstream risk transfer increases with event severity, it is bound to increase with climate change.Not considering this feedback could create blind spots that leave downstream communities unaware of the increasing risk that they are facing.
What is the alternative?Past modeling efforts have focused mostly on an improved statistical description of extreme events/design events in a changing climate [70][71][72] and/or the use of global or regional climate models [73], but both efforts can entail high uncertainty [72,74] that reflects our inevitable lack of knowledge of future conditions.Other suggestions include choosing the design event in planning based on consequences or impact-relevant thresholds [75,76] or analyzing river-flow dynamics from a more holistic, systemic point of view [49] to optimize both total cost and equity in flood risk distribution [62].However, these approaches are complex and timeintensive to implement [62] and not necessarily compatible with current planning practices and mandated guidelines.
Here, we propose a different approach to advance equity in risk-mitigation planning that prioritizes actionable over abstract knowledge creation by integrating flood model design with a multi-tier engagement model.Prior work has clearly demonstrated the potential of scientific coproduction [22], but also pointed to a persistent divide between theorist and activist approaches that needs to be abridged [78].To unite the theoretical, activist, and monetary dimensions inherent to large infrastructure projects, we started from a need expressed to us by one of our long-term community partners, the City of East Palo Alto.We then created a strategic partnership with one of several key decision-making agencies, the SFCJPA, whose explicit vision is to 'equitably and cooperatively manage […]' San Francisquito Creek.Finally, we engaged in a dialogue with other agencies and community groups from local Non-Governmental-Organizations like Climate Resilient Communities, to companies engaged in the planning such as Balance Hydrologics Inc, and the San Francisco Bay Regional Water Quality Control Board.
Each of our partners provided a uniquely valuable perspective-from the City of East Palo Alto identifying an important concern, to the SFCJPA engaging in a continued dialogue on how to substantiate the concern, and the San Francisco Bay Regional Water Quality Control Board reaching out to us to be appraised of the discussion.We found that the metric of community-specific risk trajectories was particularly valuable in these discussions because it provides a community-based lens through which planners can 1.consider water levels from an ensemble of events rather than a single design event, 2. account for increasing variability in precipitation due to climate change, and 3. quantify the spatial and temporal variability of risk to increase procedural equity.We emphasize that the ease of computation of these risk trajectories through a probabilistic wrapper of flood drivers added to an existing, agreed-upon model was critical for identifying a specific and actionable way to improve the status quo.
The actionability of our approach is evidenced by the fact that a previously overlooked risk transfer from communities near the Pope-Chaucer Bridge to communities around the University Avenue and Newell Road Bridges was avoided.Assisted by our analysis, the SFCJPA has updated its project plans to eliminate the risk transfer discussed here by proposing elevated bank treatments in the affected communities around University Avenue and Newell Road Bridges.
There is no doubt that challenges remain, but conversations between project partners are ongoing and significant and exciting progress is being made.While we have designed and implemented our model in the specific context of San Francisquito Creek, it translates to riverine systems in California and beyond.Maybe most importantly, our work shows the value of engaging with multiple different partners participating in a given project on a model that is designed to address specific community concerns while elevating current modeling practices, rather than attempting to replace existing efforts entirely.The context of this project was fortuitous and that might not be the case in other settings, but the progress made at San Francisquito Creek suggests that our partnershipbased approach and continued engagement paired with a flood model and custom-designed metrics has the potential to lead to more equitable outcomes elsewhere.

Data availability statement
Measured water level and tidal predictions for the Redwood City Tide Gauge are available through the National Oceanic and Atmospheric Administration (NOAA) National Ocean Service (NOS) website (https://tidesandcurrents.noaa.gov/stationhome.html?id=9414523) and river discharge is available through the US Geological Survey (USGS) National Water Information System (https://waterdata.usgs.gov/nwis).The MATLAB code [77] used in this paper to generate simulations of coastal water level and river discharge, surrogate models, and compute the probability of flood initiation along San Francisquito Creek is available at the URL/DOI below with open access.The usage instructions are provided in the README file of the repository.The codes reproduce all variables from present-day simulation #1 and water levels via surrogate model output for one example transect.Input data for running the codes, including model parameterizations and HEC-RAS water surface elevations are provided, however, due to the large number of river transects and simulations, the rest of the data supporting this study is available on request from corresponding author K.A.S.
The data that support the findings of this study are openly available at the following URL/DOI: https:// zenodo.org/doi/10.5281/zenodo.5949379.

Figure 1 .
Figure 1.Map of past flooding, household income, racial diversity, and proposed infrastructure changes along San Francisquito Creek.(a) Approximate areas of flooding across the urban landscape during the 1998 El Niño event.Flooding is depicted in blue, grey bars indicate bridges along-river, green colors indicate areas with average incomes higher than the median for San Mateo County, while pink colors indicate average incomes lower than the median per census block group.Numbers [1-5] indicate the bridges of interest in this study and the bridge names are shown in (b).Areas of approximate flooding compiled from a number of sources including the Santa Clara Valley Water District's 1998 Report on Flooding and Flood Related Damages in Santa Clara County.Photos courtesy of Valley Water.(b) Locations of infrastructure modification during the Reach 1 Downstream Project, highlighted with green, and proposed infrastructure modification in the Reach 2 Urban Project, highlighted in orange.Purple colors indicate the % of non-white persons per census block group.

Figure 2 .
Figure 2. Flowchart of hybrid model.White boxes represent models, arrows pointing towards a box indicate a required model input, while arrows pointing out of a box indicate a model output.Bold text describes a generic input or output, while normal text indicates the specific models used in this application.Italicized words indicate the specific datasets used as inputs.The model works in the following steps: Step 1: prepare input data, Step 2: synthetically simulate boundary conditions, Step 3: model a subset of boundary conditions covering sample space through numerical model, Step 4: develop surrogate models of along-river water level from numerical model output of boundary condition subset, and Step 5: input synthetic boundary conditions from statistical model to surrogate models to produce along-river water levels for any joint condition.

Figure 3 .
Figure 3. Impact of infrastructure updates on the probability of flood initiation for present-day climate conditions.(a) Baseline probability of flood initiation for the urban portion, river kilometers 1-8.(b) Probability of flood initiation for the urban portion, river kilometers 1-8, if infrastructure updates were implemented as originally planned.Across both panels, the bold line represents the ensemble mean and the light blue areas represent the variability across 50 simulations.The red stars indicate the locations of flood initiation for the design event.Vertical grey dashed lines indicate the locations of bridges within the model.(c) Map view of the baseline return period shown as the probability of flood initiation in (a).(d) Map view of the return period after infrastructure updates shown as the probability of flood initiation in (b).Circles represent averaged ensembles of the locations of flood initiation, with larger radii corresponding to more frequent events.The background color is the social vulnerability index from the Center for Disease Control (CDC SVI) using American Community Survey (ACS) dat data for 2017-2021 by block group with dark colors indicating higher vulnerability.

Figure 4 .
Figure 4.The change in the return period of flood initiation for the original infrastructure plans due to climate change.(a) Map depicting the return period averaged across the 50 simulations for the original infrastructure plans due to climate change.Circles represent locations of flood initiation with larger radii corresponding to more frequent events.The background color is the social vulnerability index from the Center for Disease Control (CDC SVI) using American Community Survey dat data for 2017-2021 by block group with dark colors indicating higher vulnerability.(b) Boxplots depicting the spatial variation across transects for the average return period in the University Avenue Bridge area, for present-day and a future climate where river discharge is increased.The dashed box in (a) highlights the transects plotted in (b).

Figure 5 .
Figure 5.The risk trajectory for different communities in a changing climate and considering infrastructure modifications.Panels (a)-(c) display risk amplification due to increases to discharge and panels (d)-(f) display risk amplification due to sea level rise.Green and purple arrows indicate a risk reduction or a risk amplification, respectively.We emphasize that a flood amplification factor of zero does not mean an absence of flood risk but rather the absence of an amplification of risk.For the sake of easier comparison, we plot these flood amplification factors for historic return periods, keeping in mind that these may no longer accurately describe current climatic conditions.