Edited by: Eva Thelisson, AI Transparency Institute, Switzerland
Reviewed by: Hongxiang Yan, Pacific Northwest National Laboratory (DOE), United States; Zihan Lin, Boston University, United States; Ashraf Dewan, Curtin University, Australia
This article was submitted to Data-driven Climate Sciences, a section of the journal Frontiers in Big Data
†These authors have contributed equally to this work and share first authorship
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Model output of localized flood grids are useful in characterizing flood hazards for properties located in the Special Flood Hazard Area (SFHA—areas expected to experience a 1% or greater annual chance of flooding). However, due to the unavailability of higher return-period [i.e., recurrence interval, or the reciprocal of the annual exceedance probability (AEP)] flood grids, the flood risk of properties located outside the SFHA cannot be quantified. Here, we present a method to estimate flood hazards that are located both inside and outside the SFHA using existing AEP surfaces. Flood hazards are characterized by the Gumbel extreme value distribution to project extreme flood event elevations for which an entire area is assumed to be submerged. Spatial interpolation techniques impute flood elevation values and are used to estimate flood hazards for areas outside the SFHA. The proposed method has the potential to improve the assessment of flood risk for properties located both inside and outside the SFHA and therefore to improve the decision-making process regarding flood insurance purchases, mitigation strategies, and long-term planning for enhanced resilience to one of the world's most ubiquitous natural hazards.
The perilous and expensive nature of flood hazards calls for concurrent improvements in the ability of scientists to measure their risk (Kron,
One component of flood hazard quantification that is of particular importance in planning for development is the accurate estimations of return-period-based flood depths (Yang et al.,
Not surprisingly given the paucity of updated scientific work on flood, few if any historical records of such estimates may exist to guide construction, protection, or restoration efforts. Thus, reliance on hydrologic and hydraulic modeling of flood events as a function of AEP is necessary (Mostafiz et al.,
Previous research has focused on estimating flood hazard and risk for properties located inside the Special Flood Hazard Area (SFHA—areas exposed to 1% or greater annual chance of flooding), where flood insurance is mandatory (e.g., Posey and Rogers,
The overarching goal of this research is to characterize flood hazards at locations both inside and outside the SFHA. More specifically, the research addresses the question, “If no modeled flood data exist for some or all return periods, what are the flood characteristics?” To that end, this research introduces a method for describing flood hazards whereby the flood is characterized using the Gumbel extreme value distribution (Waylen and Woo,
The contribution of this research is the development of a novel method to estimate flood hazard characteristics based on existing hydrologic-modeled flood surfaces. Ultimately, this technique will help government agencies and community officials to formulate policies and homeowners to make more informed decisions regarding insurance purchase (Rahim et al.,
The method consists of extrapolating flood depths using the Gumbel extreme value distribution at the locations where a Gumbel fit is possible because flood depths for at least two return periods are known. Extreme return periods are selected where most of the study area is assumed to be submerged (
Schematic representation of the concept behind the flood depth surface estimating method.
Schematic summary of the flood hazard characterization method.
A frequently-flooded residential neighborhood in Metairie, Louisiana (Jefferson Parish), bounded by the area shown in
Study area in Metairie, Louisiana.
The grid cells located within SFHA have at least two flood depth values (i.e., 100– and 500-year return periods) for which the Gumbel distribution can be fit initially (described in Section 2.3). For the grid cells located in shaded-X zone (i.e., only 500-year flood depth is available) or unshaded-X zone (i.e., no flood information available), spatial interpolation is conducted to characterize flood in these grids (described in Section 2.4).
The study area consists of 44 census blocks with a total area of ~1.126 km2. The mean elevation in this below-sea-level, levee-protected area is −5.5 feet with a standard deviation of 0.71 and a range of −9.0 to −2.9 feet. Descriptive statistics of the Risk MAP-output flood depths by return period are shown in
Descriptive statistics of preliminary (uncleaned) flood depths (feet) by return period for the Metairie, Louisiana, study area.
10 | 0.67 | 0.45 | 0.00 | 3.40 | 51,937 |
50 | 0.75 | 0.50 | 0.00 | 3.70 | 68,937 |
100 | 0.90 | 0.58 | 0.00 | 4.10 | 91,163 |
500 | 0.93 | 0.58 | 0.00 | 4.10 | 100,705 |
Initial quality checks of the source data are performed to identify cells with unrealistic flood depths. The three types of spurious source data are: (1) any cell with a reported flood depth less than or equal to zero for any return period; (2) any cell in which a flood depth for a shorter return period equals or exceeds that for any longer return period; and (3) any cell in which a shorter-duration return period has a reported flood depth but a longer return period has a null (i.e., flood-free) value. Flood depth values for all return periods at any cell that violate any of the three rules above are characterized as “missing.” Flood depth values for cells in which the depth is known (i.e., non-null) for only the 500-year return period are removed here temporarily, but the regression parameters derived are used later to project flood depth as a function of return period for such cells.
The Gumbel distribution is a widely accepted method for flood frequency analysis (e.g., Kumar and Bhardwaj,
The Gumbel extreme value probability density function (PDF) as a function of flood depth (
where α and
The cumulative distribution function (CDF) is equal to the non-exceedance probability,
Solving for
For each cell having non-null
The cells that flood at all four (i.e., 10-, 50-, 100-, and 500-year) return periods are examined first. Such cells that represent a water body are distinguished from those that represent a (flood-prone) terrestrial surface. Each cell that is actually terrestrial and has a negative
The cells flooded at only three (i.e., 50-, 100-, and 500-year) return periods and having null
The cells having known, positive
At each cell flooded by the 100-year return period event, the unique α and
Several spatial interpolation techniques are applied to the study area, separately for each extreme return period (i.e., 5,000-, 10,000-, 15,000, and 20,000-year). A moving average filter is used to impute all missing flood elevation cells in the study area, by experimenting with different window sizes. The dimensions of the final window selected are determined as the smallest that can impute all missing cells, with the same-sized window used for all return periods. Then, because the flood elevation surface of a completely flooded surface should be smooth, a 3 × 3 moving window is run to smooth the flood elevation surface (i.e., reduce undulations over the flooded terrain). Along with the moving average-smoothing, IDW, natural neighbor, and ordinary kriging spatial interpolation techniques are also used (separately) to impute the missing cell values. Assessment of the relative effectiveness of each technique is conducted. The result of the spatial interpolation procedure is a complete set of flood elevations at each extreme return period for each cell in the study area, including those cells for which the values were expunged at the shorter return periods.
After deducting the ground elevation,
A second scenario occurs for cells that have a null
Likewise, the third scenario involves cells with null (i.e., flood-free)
The fourth scenario involves correcting any cells for which the spatially interpolated 5,000-year depth is spuriously less than the Risk MAP-modeled 500-year
Model validation is then performed by statistically comparing the estimated
Then, four spatial interpolation methods are implemented (one at a time, separately) to estimate Gumbel parameters (i.e., α and
A sensitivity analysis is performed, cell by cell, to check the extent to which the success of the estimation procedure, based on the Gumbel parameters, hinges on the number of “known”
The data cleaning process described in Section 2.2 is run on the 121,215 cells in the study area. Data cleaning identifies 32 cells with
Number of cells in the study area removed by each data cleaning criterion.
10-year flood depth ≤ 0 | 13 |
50-year flood depth ≤ 0 | 16 |
100-year flood depth ≤ 0 | 1 |
500-year flood depth ≤ 0 | 2 |
10-year flood depth ≥ 50-year flood depth | 776 |
10-year flood depth ≥ 100-year flood depth | 0 |
10-year flood depth ≥ 500-year flood depth | 2 |
50-year flood depth ≥ 100-year flood depth | 530 |
50-year flood depth ≥ 500-year flood depth | 4 |
100-year flood depth ≥ 500-year flood depth | 2,263 |
10-year flood depth ≥ 0 and 50-year flood depth is NULL | 7 |
10-year flood depth ≥ 0 and 100-year flood depth is NULL | 0 |
10-year flood depth ≥ 0 and 500-year flood depth is NULL | 0 |
50-year flood depth ≥ 0 and 100-year flood depth is NULL | 4 |
50-year flood depth ≥ 0 and 500-year flood depth is NULL | 1 |
100-year flood depth ≥ 0 and 500-year flood depth is NULL | 2,353 |
Descriptive statistics for the scale (α) and location (
Descriptive statistics of α and
α | 0.24 | 0.08 | 0.08 | 0.82 |
−0.33 | 0.37 | −3.16 | 0.00 |
The smallest possible moving-average window that interpolates all flood elevation values at extreme return periods is 31 × 31 cells. Descriptive statistics for the spatially interpolated and smoothed Gumbel parameters are shown in
Descriptive statistics for α and
α | 0.28 | 0.22 | 0.07 | 2.08 |
−1.72 | 1.41 | −12.96 | −0.39 |
The procedure described in Section 2.5 regarding validation of the distribution is implemented for the case study area.
Descriptive statistics and root-mean-square error for Risk MAP-modeled minus predicted
10-year | 0.17 | 0.21 | −0.25 | 1.58 | 0.27 |
50-year | −0.01 | 0.09 | −0.33 | 0.53 | 0.09 |
100-year | 0.13 | 0.07 | −0.00 | 0.85 | 0.15 |
500-year | −0.10 | 0.11 | −0.95 | 0.57 | 0.14 |
For cells having only a 500-year Risk MAP-modeled
Descriptive statistics and root-mean-square error for Risk MAP-modeled minus predicted 500-year
Moving average and smoothing | −1.14 | 1.30 | −11.43 | 6.90 | 1.73 |
Inverse distance weighting | −1.12 | 1.32 | −11.43 | 6.92 | 1.73 |
Natural neighbor | −1.11 | 1.33 | −11.43 | 6.92 | 1.73 |
Ordinary kriging | −1.12 | 1.32 | −11.43 | 6.93 | 1.73 |
The sensitivity analysis described in Section 2.6 quantifies the rationality of using Gumbel extreme value distribution even as the number of known points decreases to two (
Descriptive statistics and root-mean-square error of the difference (Δ) between the Gumbel model-based flood depth (
Δ 500-year depth using 10-, 50-, and 100-year depth as predictors | 0.32 | 0.22 | −0.26 | 1.87 | 0.39 |
Δ 100-year depth using 10- and 50-year depth as predictors | −0.02 | 0.20 | −0.46 | 1.09 | 0.20 |
Δ 500-year depth using 10- and 50-year depth as predictors | 0.28 | 0.38 | −0.46 | 2.65 | 0.47 |
This method offers a means for circumventing the ever-present dilemma of how to ensure high-quality modeling to support planning for preventing, mitigating, and/or adapting to future flood events when little measured data are available, for locations where advanced hydrological and hydraulic modeling has been conducted to determine estimate
If it can be assumed that the Risk MAP-modeled data are the “correct” values, the Gumbel distribution-generated flood parameters are shown to be remarkably stable for simulating and imputing
Validation and sensitivity analysis confirm that the method is relatively insensitive to the spatial interpolation technique chosen, at least for this study area. The relatively small errors, as evidenced by the small RMSE values (see
As with any research, there are limitations to the analysis and interpretation of results. Flood hazard estimation is, by necessity, based on such a limited number of data points, but the availability of model output at only a small number of locations and return periods necessitates use of this technique. Moreover, the rounding of original FEMA-modeled values to the tenth of a foot restricts the precision with which the results can be presented. This method was applied to a relatively limited geographical extent with homogeneous topography. Future work should evaluate the performance of the method across a larger geographical extent with more heterogeneous topography. In addition, the effect of climate change on flood hydroclimatology is not considered (Zhou et al.,
Existing
Overall, the method performed well across the study area. The specific findings of the case study include that:
the presented method is able to characterize flood hazards in areas of low to moderate flood risk; for example, 100-year
spatial interpolation of extrapolated surfaces functioned well, regardless of technique; for example, 500-year
using 10-, 50-, and 100-year
Future availability of longer-return-period
The datasets presented in this study can be found in online repositories. The names of the repository/repositories and accession number(s) can be found below:
RM and MR developed the methodology. RM collected and analyzed the data and developed the initial text. MR prepared the code, run the analysis, and edited the text. CF provided original ideas and advice on the overall project methodology and edited the text. RR edited early and late drafts of the text. NB expanded the literature review and edited the text. FO prepared
This research was funded by the USDA National Institute of Food and Agriculture, Hatch project LAB 94873, accession number 7008346, U.S. Department of Homeland Security (Award Number: 2015-ST-061-ND0001-01), the Louisiana Sea Grant College Program (Omnibus cycle 2020–2022; Award Number: NA18OAR4170098; Project Number: R/CH-03; Omnibus cycle 2022–2024; Award Number: NA22OAR4710105; Project Number: R/CH-05), the Gulf Research Program of the National Academies of Sciences, Engineering, and Medicine under the Grant Agreement Number: 200010880, The New First Line of Defense: Building Community Resilience through Residential Risk Disclosure, and the U.S. Department of Housing and Urban Development (HUD; 2019-2022; Award No. H21679CA, Subaward No. S01227-1).
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
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