Chronic and Acute Coastal Flood Risks to Assets and Communities in Southeast Florida

69 years of hourly SWL data at the Key West tidal station over the 1950–2018 period (Tidesandcurrents.noaa.gov 2019a) were used for coastal flood frequency analysis. The hourly sea-level data are reported relative to the latest National Tidal Datum Epoch (NTDE), which references the 1983–2001 period with mean higher high water (MHHW) as the tidal datum. It should be noted that the Virginia Key and South Port Everglades tidal stations are closer to the County, however, both stations have been operational for less than 30 years. The datum for the Virginia Key tidal station was used to adjust SWL data in Key West tidal station (Tidesandcurrents.noaa.gov 2019b).

HAZUS-MH, FEMA’s standardized modeling tool for estimating potential losses from flood events, was used to estimate monetary losses to buildings associated with different SWLs. First, HAZUS coastal flood hazard modeling was used to determine flood extent and depth corresponding to different SWL exceedances above MHHW (i.e., 0.3–3 m with equidistant steps of 0.3 m). Coastal flood hazard modeling in HAZUS is similar to that presently used by FEMA to produce coastal Flood Insurance Rate Maps (FIRMs) (Scawthorn et al. 2006a, b). The approach considers lands that are adjacent to the sea and are situated below the stillwater flood surface to be inundated areas. Low-lying areas without a hydraulic connection to the flood source are identified during overlaying the stillwater flood surface over a digital elevation model (DEM) in order to identify disconnected areas that should not be considered as floodplains (i.e., bathtub method without hydrological connectivity) (Yunus et al. 2016). The approach neglects the effects of terrain roughness and vegetation on the spread of floodwater flow (Ramirez et al. 2016). In addition, the duration of the flood event is not considered, and it is assumed that the flood propagation is only limited by topography. These limitations and assumptions are the reason that the bathtub model could overestimate flood extents (Mcleod et al. 2010; Allen et al. 2010; Bates et al. 2010). Regardless of the shortcomings of the bathtub method, the simplicity of the algorithm and low computational complexity of this model has made it a valuable method to create regional to large scale potential coastal inundation maps (e.g., Mokrech et al. 2014; Lloyd et al. 2016). The bathtub method is primarily based on topography, and the quality of DEM can significantly affect the inundation area (Van de Sande et al. 2012). In this study, we used $1/9$ arc-second (approximately 3-m) DEM data.

The produced flood hazard maps (i.e., flood extent and depth) were subsequently used in the HAZUS flood loss estimation module to calculate physical damages, which were interpreted in direct dollar values of building replacement cost (i.e., the cost of replacement by an identical object) (Scawthorn et al. 2006a; FEMA 2018). Consequently, monetary losses to buildings were estimated at the Census block scale for different SWL exceedances above MHHW (i.e., 0.3 to 3 m with equidistant steps of 0.3 m). The losses were estimated based on the general building stock inventory data aggregated at the Census block scale in HAZUS level 1 analysis (Scawthorn et al. 2006b). This approach provides an estimate of the direct losses to buildings and the immediate impact of building damages on the community such as business interruption and job losses are not incorporated.

The available datums in HAZUS-MH are NAVD88 and NGVD29. Thus, the reference datum for Key West tidal station was used to change the datum for SWL data from MHHW to NAVD88. The estimated damages from HAZUS were used to develop a loss function [i.e., losses versus SWL of $h$, $C_i(h)$] for each Census block ($i$) in the region, which accounts for spatial variability. It was assumed that losses value is linearly changed between consecutive SWLs.

Historical adjusted SWL data from the Key West tidal station was used to estimate the annual exceedance probability of SWL of $h$ under current and future conditions using a nonstationary mixture normal-GPD probability distribution (Ghanbari et al. 2019). The mixture model uses the normal distribution to characterize the nonextreme (i.e., bulk) component of the SWL data and the extreme component of the data (i.e., upper tail) is represented by the GPD. The nonstationarity of SWL data is incorporated by expressing the location parameters of the normal and GP distributions as functions of SLR instead of time. Thus, the future risk of coastal flooding under alternative SLR levels can be evaluated regardless of projected time to certain sea-level conditions. Following Ghanbari et al. 2019, the mixture cumulative distribution function ($F$) of SWL ($h$) is defined aswhere $u$, $\alpha$, and $\xi$ denote the location (i.e., threshold), scale, and shape of the GPD; variables $\mu$ and $\sigma$ represent location and scale of the normal distribution; $\varphi$ denotes the probability of independent exceedances over threshold; and $erf$ = error function.

Flood risk emerges from the interaction of flood hazard probability, exposed values, and their vulnerability (Crichton 1999; Merz et al. 2010). A commonly used risk indicator for flood risk assessment is average annual losses (AAL) (Kron 2005; Purvis et al. 2008). AAL can be estimated by integrating the area under a loss exceedance function, which is a function that presents the relationship between exceedance probability of SWL of $h$ [here $p(h)=1-F(h)$] and the value of losses that the level of water inflicts on property and assets [here $C_i(h)$] (Jonkman et al. 2008; Grossi et al. 2005). In this study, risks from coastal flooding were categorized into two types: (1) chronic risk from frequent nonextreme (i.e., minor) flooding events with multiple occurrences per year, which are largely driven by tidal fluctuations rather than storm surge; and (2) acute risk from infrequent extreme flood events with less than one event per year frequency that usually arise from hurricanes and extreme weather conditions. Annual losses as a function of the exceedance probability of the daily SWL (i.e., loss exceedance function) were estimated for each Census block aswhere $n_y$ denotes the number of SWL observations per year; $C_i$ represents the loss function corresponding to the $i$th Census block; $F^{-1}$ = inverse cumulative distribution function of the SWL from Eq. (1); and $p$ represents the daily SWL exceedance probability. Subsequently, acute AAL was estimated as follows:where $L_i(p)$ = loss exceedance function corresponding to the $i$th Census block; $k$ = number of census blocks in Miami-Dade County; ${\tau }_1$ denotes the upper bound of daily exceedance probability for estimation of acute AAL; and ${\tau }_1$ may be determined such that acute risk encompasses occasional extreme flooding events with an annual return period larger than 1 year.

Similarly, chronic AAL was estimated bywhere ${\tau }_2$ represents the upper bound of daily exceedance probability in the estimation of chronic AAL; and ${\tau }_2$ may be determined such that the chronic damages from frequent minor flooding events are independent. Thus, ${\tau }_2$ represents the inverse of the smallest expected length (i.e., number of days) between two consecutive minor flooding events that lead to independent damages (i.e., the smallest daily exceedance probability). For example, if damages that are at least 1 day or 5 days apart are assumed to be independent, ${\tau }_2$ would be equal to 1 or $1/5{\mathrm{d}\text{ay}}^{-1}$, respectively. Schematic representation of the relationship between losses and exceedance probability of SWL of $h$ is shown in Fig. 1.

The coastal flood risk assessment was limited to the eastern part of Miami-Dade County because the preliminary results using the bathtub method provided unrealistic flooding in response to SLR in western regions. It is possible that the western regions could experience flooding due to reduced drainage capacity when the existing extensive canal and pumping infrastructure system is compromised as sea level rises. However, the determination of the potential flooding in western portions of the county requires the application of a comprehensive hydrologic/hydraulic routing model, which also simulates the rising groundwater levels due to both rainfall and SLR. Such a modeling task was beyond the scope of this study. Moreover, coastal flooding induced by tidal or storm surge currents is likely to be concentrated in the coastal regions.

The regional SLR projections for the Key West tidal station from the report by Sweet et al. (2017) were used to perform an assessment of expected time to certain changes in MSL by 2100. The available projections include low, intermediate-low, intermediate, intermediate-High, high, and extreme SLR scenarios, which correspond to 0.3, 0.5, 1, 1.5, 2, and 2.5-m global SLR, respectively. While the intermediate low scenario has a 73% chance of being exceeded under representative concentration pathway (RCP) 4.5 climate change scenario, the intermediate and intermediate-high scenarios have 17% and 1.3% chances of being exceeded under the RCP 8.5 climate change scenario, respectively (Kopp et al. 2014; Sweet et al. 2017). The chance of exceedance of more extreme scenarios (i.e., high or extreme scenario) is extremely low.

Coastal planners and decision makers should evaluate and implement various adaptation strategies to manage and reduce enhanced future flood risk due to uncertain SLR (Hinkel et al. 2013; Baxter 2013). All three elements of flood risk (i.e., flood hazard probability, exposed values, and their vulnerability) can be altered by different strategies (Baxter 2013). For example, technical engineering measures such as sea walls, forward pumps, flood barriers, and levees lower the chance of flooding and spatial zoning regulations limit the number of people and values at risk. Other measures such as elevating houses and wet or dry flood proofing (Baxter 2013) may reduce flood risks by lowering the vulnerability of buildings (Kreibich et al. 2005; Kreibich and Thieken 2009). Although the choice among these solutions requires diligent planning, deployment of any of these measures ultimately leads to an increase in the SWL at which a community begins to flood (i.e., increase in the flood threshold).

In this study, chronic and acute AAL were estimated under different SLR levels when hypothetical adaptation strategies (e.g., seawall, flood barriers, levee, and coastal retreat) were adopted to increase the level at which the region begins to flood (i.e., increase in the flood threshold). The flood adaptation was incorporated in the analysis by truncating the loss exceedance function at the exceedance probability of the new flood threshold (i.e., revised ${\tau }_2$) and estimating the AAL as the area of the remaining part of the loss exceedance function. Chronic and acute AAL from coastal flooding events were calculated under continuous SLR levels (i.e., 0–60 cm) and increase in flood threshold (i.e., 0–90 cm) with equidistant steps of 3 cm.

The upper limit (${\tau }_1$) in the estimation of acute AAL is approximately $1/365{\mathrm{d}\text{ay}}^{-1}$, because acute risk is defined as risks from infrequent extreme flood events with a frequency of less than one event per year. The precise estimation of expected time between independent damages (i.e., $1/{\tau }_2$) requires information about the relation between the building recovery time (e.g., number of days) and the functionality reached for a given damage level (i.e. building restoration functions) (Lin and Wang 2017). However, this information specific to the study region is rarely available. Thus, in the current study, in order to approximate the upper limit (${\tau }_2$), the sensitivity of chronic AAL to the lengths between independent damages (i.e., 1–90 days) was explored under three SLR levels (Fig. 2).

The results show that the number of days between independent losses does not affect chronic AAL under 15-cm SLR because the expected length between flood events would remain greater than 90 days. However, under higher MSL values (e.g., 45 and 60 cm SLR) the number of days between independent losses affects the estimated chronic AAL. Clearly, as the length of time between independent events decreases, the chronic AAL increases. However, the rate of change becomes less steep when the number of days is more than about 21. Thus, it was assumed that losses should be at least 21 days apart to be considered as independent. Furthermore, it may be assumed that buildings are protected and losses are negligible when SWL is lower than the flood threshold. Thus, ${\tau }_2$ should be less than the daily exceedance probability of the flood threshold, which is 0.52 m above MHHW at the Key West station (Sweet et al. 2018). Hence, ${\tau }_2$ was set as the minimum of $1/21$ ($0.048{\mathrm{d}\text{ay}}^{-1}$) and the daily probability of exceedances over the flood threshold, which for instance is equal to 0.0005, 0.003, and 0.84 under current condition, 15 and 60 cm SLR, respectively.

Fig. 3. (left panel) illustrates changes in the return periods of future coastal flooding at the Key West tidal station under four SLR values. The year when the indicated SLR values are anticipated to occur is presented in Table 1 under all regional SLR scenarios (Sweet et al. 2017). The future return periods of coastal flooding could decrease and even under the smallest indicated SLR level (15 cm), a considerable decrease in return periods might happen. For example, the 100-year flood will become a 5-year flood under 15 cm SLR, which may happen by 2035 or 2045 under the intermediate or intermediate-low SLR scenarios, respectively.

This sensitive response to SLR can be attributed to small extreme sea-level variance at the Key West station (Church et al. 2006; Hunter et al. 2013). The empirical and simulated relationships between return periods and the corresponding flood heights are depicted in Fig. 3 (right panel). The relationship between flood levels and corresponding annual return periods will change if sea levels continue to rise (Rahmstorf and Coumou 2011; Ray and Foster 2016).

Without the implementation of adaptation strategies, based on the bathtub approach used here, the total AAL could increase to almost $12 billion as a result of SLR (Fig. 4). Under the current condition, acute extreme coastal flooding accounts for most of the expected annual losses. However, cumulative chronic AAL from frequent minor flood events could exceed the acute AAL from extreme events under future MSL conditions. With a 15-cm increase in MSL, chronic flooding events would account for almost 50% of total AAL. Under 30-cm SLR value, the chronic and acute AAL could be approximately $1.6 and $0.9 billion, respectively. Chronic coastal flood risks in Miami-Dade County could be highly sensitive to even small shifts in sea-level due to low topography and densely populated coastal areas (Chakraborty et al. 2014; Genovese and Green 2015). Therefore, if sea level continues to rise, appropriate adaptation strategies might be needed to protect the region against cumulative losses from frequent nonextreme flooding events. The spatial distribution of chronic and acute AAL under current condition and 30- and 60-cm SLR is presented in Fig. 5. The City of Miami Beach has potentially the highest chronic and acute flood risks under 30- and 60-cm SLR. The low-lying areas in the western part of the city are highly vulnerable in particular to chronic risks from minor flooding induced by tidal fluctuations.

The relationships between SLR and total AAL under different flood threshold levels could be used to specify the magnitude of SLR beyond which current adaptation plans may no longer be effective to meet policy targets (i.e., tipping point) (Kwadijk et al. 2010). The analysis can subsequently provide information to develop a sequence of adaptation measures over time to meet predefined targets under an uncertain future (e.g., adaptation pathways) (Haasnoot et al. 2013; Zandvoort et al. 2017).

In this study, the current coastal flood risk ($170 million) is used as the acceptable AAL risk target (i.e., policy target) to maintain the current level of flood risk. Fig. 6 illustrates the estimated total AAL versus SLR for four flood threshold levels. As sea-level rises, total AAL could exceed the target (the current flood threshold line relative to the dashed line). Thus, it could be necessary to change the adaptation strategy level to meet the target under higher MSL conditions. The analysis also suggests the expected time at which the new adaptation strategies are needed based on different SLR projections. For example, in the case of a 30-cm increase in flood threshold, the tipping point would be reached within approximately 30, 20, and 15 years (i.e., the year 2050, 2040, and 2035) under the intermediate-low, intermediate, and intermediate-high SLR projections, respectively.

The potential impacts of different SLR values on chronic and acute AAL under varying flood threshold levels are illustrated in Fig. 7. The $x$-axis represents the primary driving force (i.e., SLR), while the $y$-axis represents the adaptation strategy levels (i.e., increase in flood threshold). This analysis could be used to estimate minimum adaptation levels in terms of increases in the flood threshold to prevent increases in chronic, acute, and total AAL at varying SLR levels in order to maintain the current level of flood risk. The slope of isolines indicates that the least adaption level that would be needed to compensate the negative impacts of SLR varies by SLR. The least adaptation level that would be needed to keep the current flood risk at the same value is higher than the value of SLR itself. For example, an approximately 45-cm increase in flood threshold is needed to offset a 30-cm SLR. The vertical isolines in the middle panel illustrate the level of increase in flood threshold that might not be effective in decreasing acute AAL under different SLR values. For example, under 30-cm SLR, a 30-cm increase in flood threshold might not be effective to compensate the negative impact of SLR on acute AAL. However, they could be effective in decreasing chronic AAL.

While quantification of losses using HAZUS analysis may provide reasonable first estimates for flood risk analysis, deploying a comprehensive hydrologic/hydraulic routing model could improve the flood hazard mapping. Moreover, management of surface waters in the region via the existing extensive canal and pumping infrastructure system were not considered in the current study, which likely leads to overestimation of flood risks. Furthermore, indirect losses such as traffic disruptions, business interruption, road closures, economic losses, and public inconvenience (Sweet and Park 2014; Moftakhari et al. 2018) were not included in the analysis and should be taken into account in future studies. Risks from pluvial flooding and heavy precipitation may also increase due to alterations in groundwater (Groves et al. 2018) and weather conditions. Thus, the compounding effect of pluvial/fluvial and coastal flooding (Nadal et al. 2010; Karamouz et al. 2015; Moftakhari et al. 2017b) should also be considered in future work.