# The FLOod Probability Interpolation Tool (FLOPIT): A Simple Tool to Improve Spatial Flood Probability Quantification and Communication

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

^{FEMA}(i,j) − AEP

^{FLOPIT}(i,j)

## 3. Results

## 4. Discussion

## 5. Conclusions

## Supplementary Materials

**Figure S1**. Map of a roughly 3 km reach of the Susquehanna River and tributaries at Muncy, PA. Panel 1 shows the location Lycoming County and Muncy, PA. Panel 2 shows the FEMA floodplains, derived from FEMA flood surface elevation data for the 1% and 0.2% annual chance (1 in 100-year and 1 in 500-year) floods. Panel 3 shows the FLOPIT interpolated flood probabilities, from 10% to 0.2% annual chance (1 in 10-year to 1 in 500-year). Flood probabilities are almost always higher than the flood zone communicated probabilities. The Borough of Muncy is located in the center of the map, with large northern sections inside the flood zones;

**Figure S2**. Map of a roughly 1.5 km reach of the Sims Bayou in Houston (TX). Panel (a) shows the location of Harris County and the Sims Bayou. Panel (b) shows the FEMA floodplains, derived from FEMA flood surface elevation data for the 1% and 0.2% annual chance (1 in 100-year and 1 in 500-year) floods. Panel (c) shows the FLOPIT interpolated flood probabilities, from 10% to 0.2% annual chance (1 in 10-year to 1 in 500-year). Flood probabilities are always greater than or equal to the flood zone communicated probabilities;

**Figure S3**. Box and whisker plot of the interpolated return period versus the FEMA flood zone return period for each map pixel of the Muncy map. Return periods in the 100 (1%) year flood zone range from 10 (10%) to 100 (1%), and the average return period is roughly 20 years (4%). Return periods in the 500-year zone range from 100 (1%) to 500 (0.2%), and the average is roughly 250 (0.4%) years. Whiskers extend to maximum and minimum of data;

**Figure S4**. Box and whisker plot of the interpolated return period versus the FEMA flood zone return period for each Sims Bayou in Houston (TX), map pixel. Flood probabilities in the 1 in 100 (1% annual chance) flood zone range from 1 in 10 (10% annual chance) to 1 in 100 (1% annual chance), with an average flood probability of roughly 1 in 30 (3.3% annual chance). Flood probabilities in the 1 in 500 (0.2% annual chance) zone range from 1 in 100 (1%) to 1 in 500 (0.2%), and the average is roughly 1 in 300 (0.33% annual chance). The solid green line illustrates a hypothetical perfect relationship. Whiskers extend to maximum and minimum of data;

**Figure S5**. Box and whisker plot of the interpolated return period versus the FEMA flood zone return period for each map pixel of the Selinsgrove map. Return periods in the 100 (1%) year flood zone range from 10 (10%) to 100 (1%), and the average return period is roughly 20 years (4%). Return periods in the 500-year zone range from 100 (1%) to 500 (0.2%), and the average is roughly 250 (0.4%) years. Whiskers extend to maximum and minimum of data.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Disclaimer

## References

- Strömberg, D. Natural Disasters, Economic Development, and Humanitarian Aid. J. Econ. Perspect.
**2007**, 21, 199–222. [Google Scholar] [CrossRef] - (IFRC) International Federation of Red Cross and Red Crescent Societies. World Disasters Report 2016; IFRC: Paris, France, 2016; Available online: https://www.ifrc.org/Global/Documents/Secretariat/201610/WDR 2016-FINAL_web.pdf (accessed on 3 July 2020).
- Winsemius, H.C.; Aerts, J.C.J.H.; Van Beek, L.P.H.; Bierkens, M.F.P.; Bouwman, A.; Jongman, B.; Kwadijk, J.C.J.; Ligtvoet, W.; Lucas, P.L.; Van Vuuren, D.P.; et al. Global drivers of future river flood risk. Nat. Clim. Chang.
**2016**, 6, 381–385. [Google Scholar] [CrossRef] - Wing, O.E.J.; Bates, P.D.; Smith, A.M.; Sampson, C.C.; Johnson, K.A.; Fargione, J.; Morefield, P. Estimates of present and future flood risk in the conterminous United States. Environ. Res. Lett.
**2018**, 13, 034023. [Google Scholar] [CrossRef] - Hallegatte, S.; Green, C.; Nicholls, R.J.; Corfee-Morlot, J. Future flood losses in major coastal cities. Nat. Clim. Chang.
**2013**, 3, 802–806. Available online: http://www.nature.com/nclimate/journal/v3/n9/full/nclimate1979.html%5Cnhttp://www.nature.com/nclimate/journal/v3/n9/pdf/nclimate1979.pdf (accessed on 1 July 2020). [CrossRef] - Hirabayashi, Y.; Mahendran, R.; Koirala, S.; Konoshima, L.; Yamazaki, D.; Watanabe, S.; Kim, H.; Kanae, S. Global flood risk under climate change. Nat. Clim. Chang.
**2013**, 3, 816–821. [Google Scholar] [CrossRef] - Godschalk David, R. Urban Hazard Mitigation: Creating Resilient Cities. Nat. Hazards Rev.
**2003**, 4, 136–143. [Google Scholar] [CrossRef] - Kjellgren, S. Exploring local risk managers’ use of flood hazard maps for risk communication purposes in Baden-Württemberg. Nat. Hazards Earth Syst. Sci.
**2013**, 13, 1857–1872. [Google Scholar] [CrossRef] - Zarekarizi, M.; Srikrishnan, V.; Keller, K. Neglecting uncertainties biases house-elevation decisions to manage riverine flood risks. Nat. Commun.
**2020**, 11, 1–11. [Google Scholar] [CrossRef] - (FEMA) The Federal Emergency Management Agency. Percent Annual Chance Data; FEMA: Washington, DC, USA, 2015. Available online: https://www.fema.gov/media-library-data/1522157767608-ed99f04df13b5b7239922b3e77b7f8ea/FactSheet-PercentAnnualChanceData.pdf (accessed on 3 July 2020).
- Ludy, J.; Kondolf, G.M. Flood risk perception in lands “protected” by 100-year levees. Nat. Hazards
**2012**, 61, 829–842. [Google Scholar] [CrossRef] - Smith, D.I. Floodplain management: Problems, issues and opportunities. Floods
**2000**, 1, 254–267. [Google Scholar] - Alfieri, L.; Salamon, P.; Bianchi, A.; Neal, J.C.; Bates, P.D.; Feyen, L. Advances in pan-European flood hazard mapping. Hydrol. Process.
**2014**, 28, 4067–4077. [Google Scholar] [CrossRef] - Jafarzadegan, K.; Merwade, V.; Saksena, S. A geomorphic approach to 100-year floodplain mapping for the Conterminous United States. J. Hydrol.
**2018**, 561, 43–58. [Google Scholar] [CrossRef] - Woznicki, S.A.; Baynes, J.; Panlasigui, S.; Mehaffey, M.; Neale, A. Development of a spatially complete floodplain map of the conterminous United States using random forest. Sci. Total. Environ.
**2019**, 647, 942–953. [Google Scholar] [CrossRef] - (FEMA) The Federal Emergency Management Agency. Guidance for Flood Risk Analysis and Mapping; FEMA: Washington, DC, USA, 2018. Available online: https://www.fema.gov/media-library-data/1523562952942-4c54fdae20779bb004857f1915236e6c/Flood_Depth_and_Analysis_Grids_Guidance_Feb_2018.pdf (accessed on 3 July 1998).
- Luke, A.; Sanders, B.F.; Goodrich, K.A.; Feldman, D.L.; Boudreau, D.; Eguiarte, A.; Serrano, K.; Reyes, A.; Schubert, J.E.; AghaKouchak, A.; et al. Going beyond the flood insurance rate map: Insights from flood hazard map co-production. Nat. Hazards Earth Syst. Sci.
**2018**, 18, 1097–1120. [Google Scholar] [CrossRef][Green Version] - Soden, R.; Sprain, L.; Palen, L. Thin Grey Lines. In Proceedings of the 2017 CHI Conference on Human Factors in Computing Systems, Denver, CO, USA, 6–11 May 2017; pp. 2042–2053. [Google Scholar]
- McClelland, G.H.; Schulze, W.D.; Coursey, D.L. Insurance for low-probability hazards: A bimodal response to unlikely events. J. Risk Uncertain.
**1993**, 7, 95–116. [Google Scholar] [CrossRef] - Oberholzer-Gee, F. Learning to Bear the Unbearable: Towards an Explanation of Risk Ignorance; Mimeo, Wharton School, University of Pennsylvania: Philadelphia, PA, USA, 1998. [Google Scholar]
- (FEMA) The Federal Emergency Management Agency. Guidance for Flood Risk Analysis and Mapping; FEMA: Washington, DC, USA, 2020. Available online: https://www.fema.gov/sites/default/files/documents/fema_flood-depth-and-analysis-guidance.pdf (accessed on 3 July 2020).
- Yamazaki, D.; Ikeshima, D.; Sosa, J.; Bates, P.D.; Allen, G.H.; Pavelsky, T.M. MERIT Hydro: A High-Resolution Global Hydrography Map Based on Latest Topography Dataset. Water Resour. Res.
**2019**, 55, 5053–5073. [Google Scholar] [CrossRef][Green Version] - Fritsch, F.N.; Carlson, R.E. Monotone Piecewise Cubic Interpolation. SIAM J. Numer. Anal.
**1980**, 17, 238–246. [Google Scholar] [CrossRef] - Gesch, D.; Oimoen, M.; Greenlee, S.; Nelson, C.; Steuck, M.; Tyler, D. The National Elevation Dataset. Photogramm. Eng. Remote. Sens.
**2002**, 68, 5–32. [Google Scholar] - (PAMAP, 2020) Pennsylvania Spatial Data Access. PAMAP Program. Available online: https://www.dcnr.pa.gov/Geology/PAMAP/Pages/default.aspx (accessed on 3 July 2020).
- Taheri, S.; Briggs, I.; Burtscher, M.; Gopalakrishnan, G. DiffTrace: Efficient Whole-Program Trace Analysis and Diffing for Debugging. In Proceedings of the 2019 IEEE International Conference on Cluster Computing (CLUSTER), Albuquerque, NM, USA, 23–26 September 2019; pp. 1–12. [Google Scholar]
- Taheri, S.; Devale, S.; Gopalakrishnan, G.; Burtscher, M. ParLoT: Efficient Whole-Program Call Tracing for HPC Applications. In Computer Vision; Springer International Publishing: Dallas, TX, USA, 2019; pp. 162–184. [Google Scholar]
- Kron, W. Flood Risk = Hazard ×·Values ×·Vulnerability. Water Int.
**2005**, 30, 58–68. [Google Scholar] [CrossRef] - Schumann, G.; Hostache, R.; Puech, C.; Hoffmann, L.; Matgen, P.; Pappenberger, F.; Pfister, L. High-Resolution 3-D Flood Information From Radar Imagery for Flood Hazard Management. IEEE Trans. Geosci. Remote. Sens.
**2007**, 45, 1715–1725. [Google Scholar] [CrossRef] - Cohen, S.; Brakenridge, G.R.; Kettner, A.; Bates, B.; Nelson, J.; McDonald, R.; Huang, Y.-F.; Munasinghe, D.; Zhang, J. Estimating Floodwater Depths from Flood Inundation Maps and Topography. JAWRA J. Am. Water Resour. Assoc.
**2018**, 54, 847–858. [Google Scholar] [CrossRef] - Scorzini, A.R.; Radice, A.; Molinari, D. A New Tool to Estimate Inundation Depths by Spatial Interpolation (RAPIDE): Design, Application and Impact on Quantitative Assessment of Flood Damages. Water
**2018**, 10, 1805. [Google Scholar] [CrossRef][Green Version] - Frazier, T.; Boyden, E.E.; Wood, E. Socioeconomic implications of national flood insurance policy reform and flood insurance rate map revisions. Nat. Hazards
**2020**, 1–18. [Google Scholar] [CrossRef] - Karamouz, M.; Fereshtehpour, M.; Ahmadvand, F.; Zahmatkesh, Z. Coastal Flood Damage Estimator: An Alternative to FEMA’s HAZUS Platform. J. Irrig. Drain. Eng.
**2016**, 142, 04016016. [Google Scholar] [CrossRef] - Kousky, C.; Kunreuther, H.; LaCour-Little, M.; Wachter, S. Flood Risk and the U.S. Housing Market. J. Hous. Res.
**2020**, 29, S3–S24. [Google Scholar] [CrossRef] - Thaler, T.; Hartmann, T. Justice and flood risk management: Reflecting on different approaches to distribute and allocate flood risk management in Europe. Nat. Hazards
**2016**, 83, 129–147. [Google Scholar] [CrossRef][Green Version]

**Figure 1.**Schematic diagram of flood hazard communication via flood zone maps compared to the true hazard. The upper left y-axis represents the flood hazard. This is highest near the river and decreases as the elevation rises. The lower right y-axis represents elevation, in this simple illustration increasing with increasing distance from the river. Due to the way flood zones “bin” flood hazard into discrete zones, the communicated flood hazard is almost always lower than the true flood hazard.

**Figure 2.**Conceptual diagram illustrating the FLOPIT flood surface elevation-probability interpolation approach. Flood surface elevation-probability data are not available for all flood probabilities. FLOPIT interpolates a water surface elevation to return period relationship between existing flood surface elevation-probability data. The continuous relationship is then used to interpolate flood probabilities for elevations between two flood surface elevations, producing a continuous flood probability map.

**Figure 3.**Comparison of the Annual Exceedance Probability (AEP) map provided by FEMA (

**A**) as part of the Flood Risk Database with the AEP map generated by FLOPIT (

**B**). The lower panels show the spatial distribution of bias (

**C**) and the histogram of biases over all cells (

**D**). FLOPIT’s interpolation method is log-linear. The map is for roughly 1.5 km reach of the Sims Bayou in Houston (TX). Longitude bounds are [−95.302, −95.281] and latitude bounds are [29.672, 29.675].

**Figure 4.**Map of a roughly 3 km reach of the Susquehanna River and tributaries at Selinsgrove, PA. Panel 1 shows the location of Snyder County and Selinsgrove, PA. Panel 2 shows the FEMA floodplains, derived from FEMA flood surface elevation data for the 1% and 0.2% annual chance (1 in 100-year and 1 in 500-year) floods. Panel 3 shows the FLOPIT interpolated flood probabilities, from 10% to 0.2% annual chance (1 in 10-year to 1 in 500-year). Flood probabilities are almost always higher than the flood zone communicated probabilities. The Borough of Selinsgrove stretches from the north and west edges of the map to the river and just above the Selinsgrove Speedway, with large northern and eastern sections inside the flood zones.

**Figure 5.**Comparison of the 100-year map provided by FEMA (

**A**) as part of the Flood Risk Database with the 100-year water surface elevation map generated by FLOPIT (

**B**). The lower panels show the spatial distribution of bias (

**C**) and the histogram of biases over all cells (

**D**). FLOPIT’s interpolation method is log-linear. The map is for roughly 1.5 km reach of the Sims Bayou in Houston (TX). Longitude bounds are [−95.302, −95.281] and latitude bounds are [29.672, 29.675].

**Table 1.**Average bias in estimating the water surface elevation for all interpolation algorithms. The number indicated in bold has the lowest overall bias. Units are in meters.

Log-Linear | Log-Spline | Linear | Spline |
---|---|---|---|

0.766 | 0.729 | 1.414 | 1.313 |

**Table 2.**FLOPIT run times for three case studies as a function of the interpolation method. The reported numbers are wall times on a virtual Amazon Web Services (AWS) instance with 24 cores and 185 GB memory. Units are in seconds.

Study Area | Sims Bayou | Muncy | Selinsgrove | |
---|---|---|---|---|

Resolution (Total Area) | 10 m (18 km^{2}) | 16 m (400 km^{2}) | 6 m (100 km^{2}) | |

Interpolation Method | Log-Linear | 12.55 | 119.75 | 233.13 |

Spline | 21.61 | 117.40 | 311.67 | |

Log-Spline | 25.04 | 140.97 | 364.26 | |

Linear | 10.07 | 97.92 | 179.83 |

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**MDPI and ACS Style**

Zarekarizi, M.; Roop-Eckart, K.J.; Sharma, S.; Keller, K.
The FLOod Probability Interpolation Tool (FLOPIT): A Simple Tool to Improve Spatial Flood Probability Quantification and Communication. *Water* **2021**, *13*, 666.
https://doi.org/10.3390/w13050666

**AMA Style**

Zarekarizi M, Roop-Eckart KJ, Sharma S, Keller K.
The FLOod Probability Interpolation Tool (FLOPIT): A Simple Tool to Improve Spatial Flood Probability Quantification and Communication. *Water*. 2021; 13(5):666.
https://doi.org/10.3390/w13050666

**Chicago/Turabian Style**

Zarekarizi, Mahkameh, K. Joel Roop-Eckart, Sanjib Sharma, and Klaus Keller.
2021. "The FLOod Probability Interpolation Tool (FLOPIT): A Simple Tool to Improve Spatial Flood Probability Quantification and Communication" *Water* 13, no. 5: 666.
https://doi.org/10.3390/w13050666