### Expected annual exposure

To show the impact of spatial zone selection on estimates of populations uncovered as an indicator of flooding impacts to SLR for coastal communities, we mixed two main fashions: a small-area demographic projection mannequin and a flood danger chance mannequin.

### Small-area demographic projection mannequin

Following^{40}, we produced a set of small-area demographic projections utilizing a proportional becoming algorithm to produce spatiotemporally constant Census Block Groups (CBGs) for the interval 1940–2010 and employed a blended, linear/exponential projection for the interval 2010–2100. We included solely CBGS (*n* = 81,815) situated in counties (n = 406) anticipated to expertise any chance of flooding.

We produce these projections utilizing the ‘Year Structure Built’ query, group quarters rely (*GQ*), and persons-per family (PPHU) from the 2013–2018 Census Bureau’s American Community Survey and the rely of housing models on the county-level from historic censuses. Following^{41}, the population in time *t* in county *i* in CBG *j* is given as ({P}_{{tij}}=H* {{{{{{rm{PPHU}}}}}}}+{GQ}).

We calculate *H* within the interval 1940–2010 utilizing ({hat{H}}_{ij}^{v}=frac{{C}_{j}^{v}}{{sum }_{i=1}^{n}{sum }_{t=1939}^{v-1}{H}_{ijt}^{v}}) (* {sum }_{t=1939}^{v-1}{H}_{{ijt}}^{v}), the place ({C}_{j}^{v}) is the rely of housing models from the historic census within the set of time durations (vin {1940,1950,…,2010}) in county *j* and ({H}_{{ijt}}^{v}) refers to the estimate of housing models in time *t* from the American Community Survey for block group *i* in county *j*. For instance, to estimate the variety of housing models in block group I in county j for the 12 months 1960, the quantity counted within the 1960 census (({C}_{j}^{1960})) is split by the variety of HUs in county j as estimated within the ACS for the interval 1939–1959 (({sum }_{i=1939}^{1959}{H}_{j}^{1960})) and multiplied by the variety of HUs for every block group for a similar interval (({sum }_{i=1939}^{1959}{H}_{{ij}}^{1960})),

We mission *H* within the time durations 2020–2100 utilizing ({H}_{{ij}}^{t+z}=left(alpha +beta zright)+[{H}^{t}-left(alpha +beta tright)]) for any CBGs experiencing population progress and ({H}_{{ij}}^{t+z}={e}^{beta }* {z}^{alpha }+[{H}^{t}-left({e}^{alpha }* {t}^{beta }right)]) for CBGs experiencing population decline. We subset our projections for the time durations 2000–2100.

We then management our projections to the Shared Socioeconomic Pathways (SSPs)^{42,43}. Out of pattern validations counsel fairly good match for this strategy^{40,42}. Controlling our projections to the SSPs permits a close to direct translation of our small-area outcomes to national-level SSPs and different nation-level SLR assessments.

### Digital elevation mannequin

To classify exposure classes, we employed airborne lidar-derived digital elevation fashions (DEMs) distributed by NOAA^{44} supplemented with the USGS Northern Gulf of Mexico Topobathymetric DEM^{45} in Louisiana and the USGS National Elevation Dataset^{46} within the small fraction of land not lined by the opposite sources. These elevation information are vertically referenced to NAVD88 and transformed to the MHHW datum utilizing NOAA’s VDatum grid (model 2.3.5)^{47}. Following a tub mannequin, we assessed uncovered land space utilizing a given water top towards the elevation mannequin to generate binary inundation surfaces. The DEM information are high-resolution, high-accuracy, LiDAR-derived digital terrain (bare-earth) fashions with the bottom uncertainty related to estimates of flood exposure^{11,48,49}.

In previous literature^{28,50,51}, it’s common to use linked parts evaluation on binary inundation surfaces to implement hydrological connectivity to the ocean. While this strategy works with a small variety of elevation thresholds, it turns into computationally intractable when assessing tens of 1000’s of SLR situations (mixtures of years + emissions situations + Monte Carlo simulations), as is finished on this work. Instead, we observe the framework described in^{52} to immediately refine the DEMS. First, we generated inundation surfaces from 0–10 m above MHHW, at 0.25 m increments, denoting the *i*’th such top on this sequence by ({h}_{i}), and denoting every such binary floor as ({{{{{{{rm{ThresholdWaterSurface}}}}}}}}_{i}({{{{{{rm{lat}}}}}}},{{{{{{rm{lon}}}}}}})). For every pixel within the DEM under 10 m, we famous the minimal worth of *i* for which ({{{{{{{rm{ThresholdWaterSurface}}}}}}}}_{i}({{{{{{rm{lat}}}}}}},{{{{{{rm{lon}}}}}}})) is 1 (i.e., the place its elevation is under ({h}_{i})), which we saved in a brand new index floor *ThresholdIndexSurface(lat,lon)*. We then integrated levee information from the Mid-term Levee Inventory (FEMA/USACE, acquired September 2013) and used linked parts evaluation to take away remoted areas inside every inundation floor, thus producing absolutely linked binary masks ({{{{{{{rm{ConnectedWaterSurface}}}}}}}}_{i}({{{{{{rm{lat}}}}}}},{{{{{{rm{lon}}}}}}})). As earlier than, for every pixel within the DEM under 10 m, we discovered the bottom worth of *i* for which ({{{{{{{rm{ConnectedWaterSurface}}}}}}}}_{i}({{{{{{rm{lat}}}}}}},{{{{{{rm{lon}}}}}}})), which we once more saved in an index floor LinkedIndexSurface(lat,lon).

We assumed that pixels the place ThresholdIndexSurface(lat,lon)= LinkedIndexSurface (lat,lon) will not be remoted, and subsequently their elevations within the refined DEM are unchanged. However, places the place ThresholdIndexSurface (lat,lon) < LinkedIndexSurface’(lat,lon) had been remoted. To guarantee connectivity when thresholding towards new water surfaces, we adjusted such pixels’ elevations to equal ({h}_{{{{{{rm{LinkedIndexSurface}}}}}}}) (({{{{{{rm{lat}}}}}}},{{{{{{rm{lon}}}}}}})).

### Sea level rise projections and flood occasion chance surfaces

To produce an internally constant mannequin of flooding, given each pixel within the adjusted DEM, and any SLR projection, we calculated the annual chance that not less than one close by excessive flood occasion would exceed every pixels’ elevation. Here we used the probabilistic SLR projections printed beforehand^{53}, which incorporate native non-climatic elements resembling isostatic adjustment and human-caused land subsidence, and are carefully aligned with latest IPCC findings^{54,55}.

We use historic storm surge information at particular person tide stations to estimate their return level curves, and apply them to all pixels between the tide stations utilizing a tub mannequin. Unlike research that carry out hydrodynamic simulations on artificial storms (e.g., FEMA’s base flood elevation maps), these curves don’t think about elements resembling native topography, rainfall, or waves. While the station-distance sensitivity evaluation carried out in^{28} means that the distances between tide stations used on this work are sufficiently shut to assess EAE within the US, exposure estimates on the <1% chance threshold could also be notably delicate to these elements.

We specified our mannequin following earlier approaches^{22,28,52,56} which maintain storm surge fixed, becoming the parameters of a generalized Pareto distribution (GPD) to historic heights and frequencies of utmost coastal flood occasions at NOAA tide stations alongside the US shoreline with not less than 30 years of hourly information via 2013. This specification permits us to estimate (P(Hge Y=2000)), the annual chance of the utmost water top, *H*, exceeding elevation, *E*, within the 12 months 2000 (the baseline 12 months, the place SLR=0). We expanded a framework described beforehand^{28,52} to estimate *whole* per-pixel annual chance of exceedance of any water top in any 12 months, unconditional to SLR sensitivity to emissions. Published SLR projections^{53} are supplied as a set of probabilistic distributions, every with 10,000 Monte Carlo samples of SLR for every tide-gauge station and for annually. Below we denote every pattern because the operate ({{{{{{rm{SLR}}}}}}}_{j}(y)) for (jin [1,ldots ,10000]). From the legislation of whole chance, we are able to estimate the annual chance of the utmost water top, *H*, exceeds elevation *E* in 12 months *Y* from

$$P(Hge E{{{{{rm}}}}}Y=y)approx frac{1}{10,000}mathop{sum }limits_{j=1}^{10,000}P((H+{{{{{{rm{SLR}}}}}}}_{j}left(yright))ge E{{{{{rm}}}}}Y=2000)$$

(1)

We computed this operate below every emissions pathway (RCPs 2.6, 4.5, and eight.5) for every decade (2000–2100), for elevations between 0 and 10 m at 0.1 m increments. We saved these chances in lookup tables for environment friendly queries.

For each pixel within the DEM with elevation *E(lat,lon)*, we decided its closest NOAA tide-gauge station and used the related lookup tables to estimate its annual water top exceedance chance for each SLR projection listed above. We saved the leads to a big raster database, producing chance surfaces (P(Hge E({{{{{{rm{lat}}}}}}},{{{{{{rm{lon}}}}}}})Y=y)) for all three emissions situations and a long time alongside the complete US shoreline.

Recent research counsel that the tub mannequin employed right here possible overestimates exposure, because it doesn’t incorporate wave attenuation nor the time it takes for water to attain their full extent^{57,58}. Given the excessive spatial decision and large distributions of water heights utilized in our EAE evaluation, it isn’t but computationally possible to make use of a hydrodynamic mannequin to refine these outcomes.

### Exposure computation

To assess population exposure inside a US Census Block Group below any water top (together with all exposure approaches described above, specifically, MHHW, LECZ, in addition to 100-year storm surge adjusted for SLR), we generated a linked inundation floor. For the MHHW and LECZ layers, we merely thresholded the adjusted DEM to discover pixels under SLR(y) and for (10+SLR(y)), respectively. For the 100-year storm layer, we thresholded the chance floor to discover pixels the place (Pleft(Hge E,|,Y=yright) < 0.01). For every block group, we counted the proportion of its pixels on dry land (as outlined by the National Wetland Inventory^{59}) lined by the inundation floor, and multiplied by its whole population, as predicted by every SSP. To compute anticipated annual exposure (EAE), outlined because the anticipated variety of individuals on land under the utmost native storm surge top in a given 12 months^{28}, we multiplied the worth of every pixel inside the chance floor (P(Hge E({{{{{{rm{lat}}}}}}},{{{{{{rm{lon}}}}}}})Y=y)) by the block group’s (per-pixel) population density and computed the sum.