Homeowner flood risk and risk reduction from home elevation between the limits of the 100- and 500-year floodplains

Abstract

Floods inflict significant damage even outside the 100-year floodplain. Thus, restricting flood risk analysis to the 100-year floodplain (Special Flood Hazard Area (SFHA) in the United States of America) is misleading. Flood risk outside the SFHA is often underestimated because of minimal flood-related insurance requirements and regulations and sparse flood depth data. This study proposes a systematic approach to predict flood risk for a single-family home using average annual loss (AAL) in the shaded X Zone–the area immediately outside the SFHA (i.e., the 500-year floodplain), which lies between the limits of the 1.0- and 0.2-percent annual flood probability. To further inform flood mitigation strategy, annual flood risk reduction with additional elevation above an initial first-floor height () is estimated. The proposed approach generates synthetic flood parameters, quantifies AAL for a hypothetical slab-on–grade, single-family home with varying attributes and scenarios above the slab-on-grade elevation, and compares flood risk for two areas using the synthetic flood parameters vs existing spatial interpolation-estimated flood parameters. Results reveal a median AAL in the shaded X Zone of 0.13 and 0.17 percent of replacement cost value () for a one-story, single-family home without and with basement, respectively, at and 500-year flood depth <1 foot. Elevating homes one and four feet above substantially mitigates this risk, generating savings of 0.07–0.18 and 0.09–0.23 percent of for a one-story, single-family home without and with basement, respectively. These results enhance understanding of flood risk and the benefits of elevating homes above in the shaded X Zone.

1 Introduction

Flood is considered the costliest natural hazard worldwide (Wang & Sebastian, 2021). Between 1980 and 2021, the United States of America was affected by 36 catastrophic floods that caused a total $173.3 billion (consumer price index adjusted) in direct losses (NOAA, 2022). FEMA’s floodplain maps are used to determine flood risk zones and their base flood elevations (BFEs), which have been used to define flood risk regions around the United States of America (Xian et al., 2015). FEMA’s 100-year floodplain–the area that has at least a one-percent chance of experiencing flood in a given year–has been used to define high-risk flood zones, known as the Special Flood Hazard Area (SFHA). Many efforts have been made to quantify flood risk (Habete & Ferreira, 2017; Armal et al., 2020; Mostafiz et al., 2021a), determine minimum first-floor elevation requirements (American Society of Civil Engineers (ASCE), 2014; FEMA, 2019) and identify the benefit of applying mitigation strategies in the SFHA (Rath et al., 2018), including regulations on development such as the mandatory purchase of flood insurance for those with a federally-backed mortgage (Wing et al., 2022).

Areas outside the SFHA, generally known in the United States of America as X Zones, have received significantly less attention because they have been considered as moderate-to-low flood risk areas, with less than a one-percent annual chance of flood occurrence (Technical Mapping Advisory Council, 2015). However, average annual flood losses outside the SFHA have mounted to $19.1 billion and are projected to increase by 21.2 percent in the United States of America by 2050 because of climate change (Wing et al., 2022). Thus, significantly more attention must be devoted to understanding flood risk in these areas in order to reduce flood losses.

The area between the limits of the one-percent (bordering the SFHA) and 0.2-percent (bordering the “non-shaded X Zone”) annual flood probability inundation areas—the 500-year floodplain, known in the United States of America as the “shaded X Zone”—is particularly preferred for dense development and is considered an area of likely population growth (Association of State Floodplain Managers, 2020). Clearly, it is important to assess the flood risk outside the SFHA, particularly in the shaded X Zone. Notable examples of research on flood hazards in the shaded X Zone include that of Hagen and Bacopoulos (2012), who identified tropical storm characteristics that induce flooding in Florida’s Big Bend Region. Likewise, Ferguson and Ashley (2017) evaluated residential development in Atlanta, Georgia. Kiaghadi et al. (2020) investigated the relation between hurricane events and the housing price depreciation in Miami-Dade County. Goldberg and Watkins (2021) analyzed flood risk among three watersheds in the lower St. Johns River basin landscape, and Hemmati et al. (2021) examined how flood risk assessment affects residents’ location choices. However, there is a dearth of research focusing on flood risk evaluation for residential buildings in the shaded X Zone. Without a better understanding of flood risk for areas in the shaded X Zone, the true costs and benefits of flood mitigation strategies cannot be realized (Mostafiz et al., 2022c).

Flood risk is assessed as the product of flood occurrence probability and the associated consequences (Šugareková & Zeleňáková, 2021). Average annual loss (AAL) has been used in past research to represent flood risk (Hallegatte et al., 2013; Armal et al., 2020; Rahim et al., 2021; 2022; Mostafiz et al., 2022a; Bowers et al., 2022; Wing et al., 2022; Yildirim & Demir, 2022; Al Assi et al., 2023b; Friedland et al., 2023) in terms of costs associated with direct building loss, direct contents loss, and indirect losses such as use loss while the building is being renovated (Al Assi et al., 2023a). AAL is calculated as the integral of flood loss as a known function of the flood probability (or flood return period), and the Gumbel distribution function is one of the most widely accepted probability functions (Singh et al., 2018; Patel, 2020). The Gumbel parameters are the regression coefficients (slope and y-intercept, respectively) in the relationship between flood depth above the ground () and the double natural logarithm of probability of non-exceedance probability () (Gnan et al., 2022a; 2022b).

Calculating flood risk in the shaded X Zone can be challenging due to data limitations. As the shaded X Zone lies between the limits of the one-percent and 0.2-percent annual chance of flood, land in this zone is by definition unflooded until the 100-year flood event is exceeded. Therefore, in the shaded X Zone, is zero or null (i.e., would be negative and is therefore undefined) for flood events with return periods less than 100 years. Given that return period depth grids typically include the 10-, 50-, 100-, and 500-year events, all locations within the shaded X Zone have a value that is therefore zero or “null” for return periods shorter than the 500-year event. Thus, locations within the shaded X Zone have a value for only one return period (i.e., 500 years), with the consequence that the Gumbel flood parameters cannot be generated from the Gumbel distribution for any location within the shaded X Zone. Without the Gumbel parameters, annual flood risk (or even the probable range of annual flood risk) cannot be estimated in the shaded X Zone. Further, although flood loss has been often observed in the shaded X Zone, risk reduction from elevation cannot be estimated due to the lack of flood risk estimates. Therefore, comparison of benefits and costs to support mitigation decision making in the shaded X Zone is not possible.

To overcome these challenges, this paper presents a systematic approach to 1) provide a meaningful estimate of the range of expected annual flood risk in the shaded X Zone; and 2) calculate the reduction in annual flood risk via elevation for homes in the shaded X Zone. The lack of flood hazard data in the shaded X Zone is addressed by developing a library of combinations of synthetic, regression-derived Gumbel parameters that meet the mathematical definition of the shaded X Zone. These are used here by hypothetical type of single-family homes in the United States of America (i.e., one vs two-plus stories, with vs without basement) as input to the framework methodology presented in Al Assi et al. (2023a). The results of two case studies are compared with the results generated from the Gumbel regression parameters produced using Mostafiz et al.’s (2021b, 2022b) method, which extrapolated the Gumbel parameters in the shaded X Zone using spatial interpolation, to confirm the results of this method for a range of 500-year flood depths in inland and coastal areas.

The contribution of this research is a novel conceptualization and implementation of annual flood risk assessment in the shaded X Zone–a location where little flood risk information has been generated. This improved risk assessment provides a clearer perception of the advantages of applying mitigation strategies in those areas. The methodology and results generated in this paper will benefit homeowners, builders, developers, community planners, and other partners in the process of enhancing resilience to the flood hazard via risk-informed construction techniques.

2 Background

Recent catastrophic events and studies regarding projected trends under environmental change scenarios reveal that the area outside the presently designated SFHA is subjected to rapidly increasing flood risk. For example, in 2005 Hurricane Katrina inflicted severe damage outside the SFHA across Louisiana, Mississippi, and Alabama, including massive structural damage (Xian et al., 2015). Likewise, only 7 years later Hurricane Sandy caused flooding far above the BFE and beyond the SFHA in New York and New Jersey (FEMA, 2013). Only 5 years later, amazingly, 68 percent of the 31,000 homes that Hurricane Harvey flooded in the Houston, Texas, area were outside the SFHA (Kousky et al., 2020b). In the next year, 24 percent of the area flooded and 43 percent of the residential structures damaged in North Carolina by Hurricane Florence were outside the SFHA (Pricope et al., 2022). And in 2019, 62 percent of the 1,000+ Texas homes flooded in Tropical Storm Imelda were outside the SFHA (Kousky et al., 2020b). Kennedy et al. (2020) reported that Hurricane Michael in Florida caused major wave and surge damage in X Zones. In a more general sense, a trained model to predict flood damage probability in the conterminous United States of America using a suite of geospatial predictors and the location of historical reported flood damage revealed that an astounding 68 percent of flood damage was outside of FEMA’s high-risk zone (Collins et al., 2022). Significant attention has been devoted to reducing flood damage exacerbated by climate change and sea level rise (Botzen & van den Bergh, 2008; Hino & Hall, 2017; Kousky et al., 2020a; Xian et al., 2017). Therefore, a need exists to evaluate flood risk in the shaded X Zone more comprehensively through improved assessment of economic consequences to better identify and mitigate the risk.

Recent studies show that using the refined numerical integration method shows promising results to predict AAL because it accounts for losses across the full range of exceedance probabilities, and it addresses the limitations of other approaches (Gnan et al., 2022a). This refined numerical integration method models the annual probability of exceedance for the expected flood depth using available flood depth data. The Gumbel distribution is used to determine the annual probability of exceedance at each given depth. AAL is then estimated using trapezoidal Riemann sums to aggregate the area under the loss-exceedance probability curve (Meyer et al., 2009; Gnan et al., 2022a).

Specifically, the refined numerical integration method has been used to estimate annual flood risk for multiple home elevation scenarios above the initial first-floor height to determine flood risk reduction (Gnan et al., 2022a). Optimizing the effectiveness of the elevation strategy using such scenarios is important for maximizing the benefit of federal government grants, such as from FEMA or the U.S. Department of Housing and Urban Development (HUD), for elevating such homes, to as many people as possible. These elevation scenarios conform to or surpass the National Flood Insurance Program (NFIP) requirement that the minimum lowest-floor elevation is at the BFE, which is approximately equal to the 100-year flood elevation () (FEMA, 2019). However, because ASCE (2014) national technical standard stipulates that adding one foot above as the minimum recommended elevation requirement for residential buildings in the United States of America, higher elevation scenarios must also be considered in assessing flood risk and risk reduction.

Elevating above is often cost-effective (Taghinezhad et al., 2021), especially at the time of construction (Rath et al., 2018). It is already well-established that increasing first-floor heights in A and V Zones (i.e., inundation and high-velocity zones within the SFHA, respectively in the United States of America) at the time of construction is wise, with costs recoverable in as few as 6 and 3 years, respectively, through insurance premium reduction (Rath et al., 2018). The value of implementing a “smart” flood risk mitigation strategy (Taghinezhad et al., 2020) applies equally to homes in the shaded X Zone, especially now that it is becoming apparent that these homes are not as flood safe as was recently assumed, by using the refined numerical integration technique. Flood risk reduction in dollars, represented as the difference between the AAL before and after applying the mitigation strategy, can be promulgated as a means of increasing awareness for homeowners and communities in the shaded X Zone regarding the flood risk and the importance of considering the mitigation strategies to decrease that risk.

3 Methodology

The computational framework to quantify AAL in the shaded X Zone consists of three major steps (Figure 1). First, synthetic flood parameters are generated based on shaded X Zone properties. Second, AAL is quantified using the computational framework developed by Al Assi et al. (2023a). In that approach, AAL is partitioned to homes (I = 1 through n) separately for building, contents, and use, with the AAL reduction calculated for M increases of increment J in first-floor height above the (Al Assi et al., 2023a). Third, the results are confirmed using two separate areas by comparing the AAL computed from synthetic data in this framework against that calculated using the flood parameters generated through the Mostafiz et al. (2021b) method.

FIGURE 1

3.1 Generate synthetic flood parameters

This research uses the two-parameter Gumbel distribution function to estimate flood depth. Equation (1) shows the cumulative distribution function (CDF) of the Gumbel distribution, which represents the annual non-exceedance probability ().

Solving Eq. (1) for yields:

In Eqs (1), (2), is flood depth, u represents the location parameter or y-intercept of the Gumbel-generated regression line (noting that Eq. (2) takes the form where x is ; is ,; is ) of as a function of the double natural logarithm of , and is the scale parameter or slope of the same Gumbel-generated regression line. is expressed as a function of flood return period () by:

To overcome the absence of and values in shaded X Zone, synthetic values of and are generated to estimate the range of these parameters expected in the shaded X Zone.

Generating the synthetic, unique and for the shaded X Zone begins with substituting for from Eq. (3) into Eq. (2), for the 100 (i.e., )-year return period, for which is assumed to be less than or equal to zero in the shaded X Zone, as shown in Eq. (4):

Likewise, if it is assumed that a point within the shaded X Zone does flood within the 500 (i.e., )-year flood, the generalized Eq. (2) can be expressed for this specific scenario as:

Solving Eqs (4)–(5) yields the ratio between and in the shaded X Zone:

Thus, the range of the ratio of to in the shaded X Zone is known, but the range of and the range of remain unknown. By definition, (i.e., the slope of the Gumbel-generated regression) must be positive because longer-return-period flood events always have higher than shorter-return-period . The upper limit of is assumed to occur in coastal areas. Therefore, this study updates values from flood events in Bohn’s (2013) data set that expresses stillwater elevation at 10-, 50-, 100-, and 500-year return periods for 13 counties along the Gulf and Atlantic coasts (Supplementary Table S1). This data set is then used to identify the upper limit of (Supplementary Table S2).

Because is positive, by Eq. (6), must be negative. A negative meets expectations, as this value represents the y-intercept of the Gumbel-generated regression, with an equivalent return period of 1.58 years. The maximum allowable value of is therefore determined, subject to the restraints of Eq. (6).

Each combination of and values within the acceptable range of each variable, as described above, at increments of 0.1 feet for each, is initially considered as potentially acceptable values to describe the vs return period relationship. Those simultaneous combinations that have a vs ratio that falls outside the range of acceptability (Eq. (6)) are discarded. The remaining combinations of and are used to calculate , with the result considered potentially acceptable for inclusion, as described in the next section.

Each combination of and that is derived and potentially acceptable is used to determine possible values at the 2-, 10-, 50-, 100-, 500-,1,000-, 5,000-, and 10,000-year return periods (Eq. (2)), noting that values for the 100-year and shorter return periods are negative or zero. A plot of vs the double natural logarithm of return period based on these calculations is then used to confirm the assumption that is less than or equal to zero for the 100-year and more than zero for the 500-year flood events, in addition to visualizing at longer return periods (i.e., 500-, and 1,000- year).

3.2 Quantify annual flood risk and flood risk reduction

3.2.1 Refined numerical integration method

AAL represents the sum of the expected annual flood risk to a building (), its contents (), and its loss of use while unoccupied due to flood (). While , , and likely differ based on owner-occupant category (i.e., homeowner, landlord, tenant), this study considers only AAL from the perspective of a homeowner.

The method of Gnan et al. (2022a, 2022b, 2022c) is used to calculate and as a proportion of home replacement cost value () by integrating the flood loss over all probabilities of exceedance, as shown in Eqs. (7)–(8):where and represent the building and contents losses as a proportion of , which is the unit replacement cost per square foot () multiplied by the home area ():

By contrast, is calculated from the number of months that the building is inoperable, as shown in Eq. (10):where represents the use loss in months.

Then, the three components of AAL are converted to absolute currency values (in USD) for building (), contents (), and use (), as described by Eqs (11)–(13):where is the monthly rent incurred by the homeowner, calculated by assuming that 1 year of rent is equal to one-seventh of (Amoroso & Fennell, 2008; Eq. (14)).

These values are then summed to give the total AAL as a proportion of () as shown in Eqs (15–16):

To quantify the economic benefit of elevating above , AAL is calculated with and without elevation, to reveal the annual flood risk reduction, as generally expressed by Eq. (17):

3.2.2 Data processing

The MATLAB algorithm developed by Al Assi et al. (2023a) is utilized here to analyze all simultaneously valid and combinations; these combinations remain constant by home type (i.e., one or two-or-more stories, with and without basement). The input data include number of stories (1 or 2+), basement existence (0 = No, 1 = Yes), living area in square feet (), unit cost per square footage (, in USD/sf), , and flood parameters (; ). United States Army Corps of Engineers (USACE, 2000) depth damage functions (DDFs) are incorporated by home type (i.e., number of stories and basement existence). The AAL reduction is calculated for each additional elevation through feet (Figure 1) above .

3.3 Confirm results

Spatial interpolation is used to characterize the flood hazard (; ) in the shaded X Zone (Mostafiz et al., 2021b; 2022b) for a known location where multiple return period flood depth data are available. The flood parameters (; ) are used to calculate annual flood risk by using Eq. (2) and (7)–(17) and confirming the result produced from the synthetic data.

4 Case study

Jefferson Parish, Louisiana, and Santa Clarita, California, are selected as these areas have multiple return period (10–, 50–, 100–, and 500–years) flood depth data, which are needed to estimate flood parameters using spatial interpolation (Figure 2). Flood depth grids were developed at a scale of 3.048 m x 3.048 m, by FEMA through its Risk Mapping, Assessment and Planning (Risk MAP) program (FEMA, 2021). To demonstrate all possible scenarios for synthetic and estimated flood parameters to quantify annual flood risk and flood risk reduction in the shaded X Zone, a hypothetical slab-on-grade, single-family home with 2000 sq. ft. of living area is used, with the four scenarios of home type (i.e., one or two-or-more stories, with and without basement) calculated separately. Each combination in the collection of synthetic and estimated Gumbel parameters is input to evaluate the range of annual flood risk for each home type. is assumed to be $135 according to the projected 2022 average construction cost of single-family homes in the United States of America (Doheny, 2021), and is assumed to be 0.5 feet above the ground for slab-on grade foundations. This assumption is made because there is no regulatory BFE in the shaded X Zone and it is assumed that most homes are built on non-elevated slab foundations. The flood damage initiation point in the DDF is assigned at a fixed flood depth of zero in the structure, as suggested by Pistrika et al. (2014). Annual flood risk for homes with basements is calculated in the same way; thus, it is assumed that the basement is not flooded until water is above the FFH. The annual flood risk reduction is calculated for each additional first-floor height of 1–4 feet above .

FIGURE 2

5 Results

5.1 Generate synthetic flood parameters

The ratio of flood parameters (Eq. (6)) along with the updated stillwater elevation for coastal data are used to determine the flood parameters’ range and combinations that satisfy shaded X Zone properties. The analysis updating the results of Bohn (2013) suggests that the maximum is 4.60 (Eq. (18)). Thus, the range of , subject to the constraints of Eq. (6), is shown in Eq. (19).

A total of 1740 combinations of and satisfies the flood parameter ratio for the shaded X Zone (Eq. (6)). Table 1 shows the descriptive statistics for and values resulting from all possible combinations. Because the dataset is very large and is not normally distributed, percentiles are provided along with the minimum and maximum values. Possible values of and fall between 28.58 and 0.48 feet and between 0.10 and 4.60, respectively.

The flood depth-return period relationships generated at the 2-, 10-, 50-, 100-, 500-, 1,000-, 5,000- and 10,000-year return periods for these 1740 scenarios are shown in Figure 3. The at return periods less than or equal to 100-year is negative or zero, and at 500-year and longer return periods is positive, as expected. Descriptive statistics of at the 500-, 1,000-, 5,000-, and 10,000-year return periods are shown in Table 2.

FIGURE 3

5.2 Quantify annual flood risk and flood risk reduction

For the 1740 scenarios of valid and combinations, annual flood risk and flood risk at additional elevations above are calculated as a proportion of by using = 0.5 foot, and the corresponding DDF for each home type. The results are presented for the shaded X Zone for homes without and with basement by categories of 500-year flood depths for one- and two-plus-story homes (Table 3; Table 4, respectively), and by categories of for one- and two-plus-story homes (Table 5; Table 6, respectively). The annual flood risk reduction is considered as the mean avoided AAL, calculated at each additional increment above for each single-family home type (Table 7; Table 8). Because the data set is not normally distributed, the percentiles are provided along with the minimum and maximum values to describe the annual flood risk (Tables 3–6) and flood risk reduction (Tables 7 and 8) at each category.

5.3 Confirm results

Table 9 demonstrates and parameters, and the 500-year flood depths, in the shaded X Zone located in Jefferson Parish, Louisiana, and Santa Clarita, California, using spatial interpolation (Mostafiz et al., 2021b). The parameter and 500-year flood depth for Jefferson Parish are less than 1 while these values range from 0.97 to 1.37 and 1.00–1.70 feet, respectively, in Santa Clarita. The AAL (i.e., annual flood risk) results for a hypothetical home located in Jefferson Parish and Santa Clarita, calculated through spatially interpolated and synthetic parameters, are summarized in Table 10 and Table 11, respectively.

6 Discussion

The derivation of the synthetic flood parameters (i.e., ; ) for the shaded X Zone (Table 1) for establishing the relationship between flood depth and return period (Figure 3) is useful for providing decision-makers (e.g., construction specialists and regional planners) sufficient information across a range of return periods. Results suggest that generating ; is obviate the need for representing the relationship between flood depth vs building, contents, and use loss separately, as in most conventional DDF-based flood risk analyses. Instead, the approach shown here provides estimates for total loss (i.e., building, contents, and use) for wide range of 500-year flood depths (Table 2) and thus the flood risk assessment (Tables 3; 4, 5,; 6) in the shaded X Zone. The applications are even more valuable for risk assessment for construction with long expected life spans and/or grave consequences for flooding, such as sites of cultural or historical importance, hospitals, nursing homes, and bridges, in which partitioning the loss into its components is less important than estimating the long-term total loss.

Another strength of this approach is that it overcomes complications associated with the changing value of assets over time. This is because the total annual flood risk (building, contents, and use) for single-family homes in the shaded X Zone is expressed proportionally to . It is anticipated that providing the results in this format will garner more attention to the long-term flood risk in the shaded X Zone with the actionable outcome of increasing awareness of the benefits of applying mitigation actions.

The results show that the median AAL at falls between only 0.097 and 0.172 percent of , for a single-family home with 500-year flood depth less than one foot, regardless of home type. These results are mainly affected by the unique DDFs based on home type (Mostafiz et al., 2021c).

Not surprisingly, flood depth is the primary factor involved flood risk, with greater depth causing more damage. Thus, elevating the home is the primary strategy for flood risk reduction, but the improvements vary by 500-year flood depth. For example, while the flood risk reduction is approximately 36, 57, 71, and 81% for one through four feet above , respectively, when the 500-year flood depth less than 1 foot for all home types (Tables 3; 4), that risk is reduced by less and less with additional feet of elevation in 500-year categories (i.e., 1–2 feet above , 2–3 feet, etc.,; Tables 3; 4).

The AALs for the case study subsets of Jefferson Parish (Louisiana) and Santa Clarita (California) generated by spatial interpolation-estimated flood parameters are within the range of AAL results using synthetic flood parameters. In the case of Jefferson Parish, the mean AAL values of $39, $61, $30, and $49 for one-story without basement, one-story with basement, two-plus-story without basement, and two-plus-story with basement single-family home, respectively, calculated using the spatial interpolation-estimated flood parameters, are between the minimum and 25th percentile AAL for the appropriate 500-year flood depth and values. For Santa Clarita, the mean AAL values of $584, $839, and $658 for one-story without basement, one story with basement, and two-plus-story with basement single-family home, respectively, calculated using the spatial interpolation-estimated flood parameters, are between the 75th quartile and maximum AAL for the appropriate 500-year flood depth and values, while the mean AAL value of $432 for two-plus-story without basement single-family home is between the 50th and 75th quartiles. While both techniques lead to similar results, the spatial interpolation method requires multiple return period flood depth data and is computationally intensive. Additional work to confirm the range of areas for which synthetic flood parameters is appropriate will further justify the use of this technique.

7 Conclusion

Although this study provides an important first step for predicting and enhancing community understanding of the flood risk in the shaded X Zone, some cautions need to be considered. First, the numerical results will differ from those suggested here in areas where the parameter exceeds 4.60. Also, the spatial interpolation-estimated flood parameters derived here require depth grids for 10-, 50-, 100-, and 500-year events; these results would be refined if 200- or 250- year depth grids are available. Furthermore, location-specific and recent inflationary trends may result in being much higher than the assumed $135/sf, but AAL could be updated easily for future work. Despite these cautions, this research contributes to the mitigation of the damage and loss experienced outside the SFHA and to improved awareness of the magnitude of flood risk in this region and the benefit of applying mitigation strategies.

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