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# Statistical Analysis of Two Flooding Loss Datasets for California: National Flooding Insurance Program (NFIP) and Spatial Hazard Events and Losses Database (SHELDUS)

Madeleine Kremer, Weiming Hu, Tom Corringham

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Madeleine Kremer, Weiming Hu, Tom Corringham. Statistical Analysis of Two Flooding Loss Datasets for California: National Flooding Insurance Program (NFIP) and Spatial Hazard Events and Losses Database (SHELDUS). 2024. hal-04718897

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# Statistical Analysis of Two Flooding Loss Datasets for California: National Flooding Insurance Program (NFIP) and Spatial Hazard Events and Losses Database (SHELDUS)

Madeleine Kremer¹,², Tom Corringham³, Weiming Hu¹

¹James Madison University (JMU), Harrisonburg, Virginia, USA

²Hochschule für Technik und Wirtschaft des Saarlandes, Saarbrücken, Germany

³Center for Western Weather and Water Extremes, Scripps Institution of Oceanography, University of California, San Diego, California, USA

Corresponding author: Weiming Hu (huwx@jmu.edu)

## Key Points:

* Low insurance coverage in high-risk areas leads to substantial uninsured flood damage.

* Machine learning improves flood prediction, informing better flood resilience strategies.

* Outdated NFIP tools contribute to insufficient data and low insurance penetration.

## Abstract

Floods are a major natural disaster in the United States, causing billions of dollars in damage each year. In the western US, atmospheric rivers significantly drive flood damage, which is expected to worsen with climate change. The National Flood Insurance Program (NFIP) provides insights into insured flood losses, but low insurance coverage in high-risk areas leaves substantial damage uninsured. Understanding the statistical relationship between insured and total flood damage is crucial for developing effective flood resilience strategies. This paper investigates this relationship, focusing on California, by analyzing flood damage data and employing machine learning algorithms. Our findings aim to enhance flood prediction models and inform policy decisions to reduce future economic impacts of floods. Despite the NFIP's efforts, its outdated tools, such as Flood Insurance Rate Maps (FIRMs) and Special Flood Hazard Area (SFHA) designations, have led to low insurance penetration and limited data on flood damages. This research seeks to address these gaps and contribute to more accurate and effective flood risk management.

## 1 Introduction

Flooding in the United States (US) causes billions of dollars in damage every year (Collins et al., 2020). Atmospheric rivers are the main drivers of flood damage in the western US, with damage increasing a lot with storm intensity and duration (Corringham et al., 2019). Climate change is expected to make atmospheric rivers stronger, leading to more flood damage in the
future (Corringham et al., 2020). The National Flood Insurance Program (NFIP) gives some understanding of insured flood losses, but not many people have insurance, even in high-risk areas, resulting in significant uninsured damage (Gall, 2015; Kousky, 2018). Understanding the statistical relationship between insured and total flood damage is important for making good flood resilience strategies and reducing future risks.

Predicting flood damage is important for improving flood resilience, and recent studies have shown that machine learning algorithms can give good results in this area. For example, Yang et al. (2020) made a flood property insurance claims model using random forest classification. Similarly, Mobley et al. (2021) used random forest classification to predict flood probability across a large area and found three times more structures at risk of flooding than current FEMA floodplains. A literature review by Mosavi et al. (2018) showed that machine learning methods have greatly improved flood prediction models, giving better performance and cost-effective solutions.

Flooding (often due to tropical storms) is among the leading causes of natural disaster damage in the US, with billions of dollars spent every year on government payouts, property damage, and agricultural losses (Collins et al., 2020). The NFIP gives some information about insured flood losses, but the low insurance coverage in high-risk areas leaves a lot of damage uninsured (Gall, 2015; Kousky, 2018). This paper aims to investigate the statistical relationship between insured and total flood damage in the US, with a focus on California. By analyzing flood damage data and using machine learning algorithms, we hope to give a better understanding of flood damage. This research will help make more accurate predictive models and inform policy decisions to reduce the economic impact of floods in the future.

## 2 Methods

### 2.1 Inflation Adjustment

Inflation adjustment is very important to analyze financial data over a long period. It allows monetary values to be comparable over time by removing the effects of inflation. In this document, we will explain the method used to adjust the flood damages data in California for inflation up to the year 2023. By using a Price Index as the base for our adjustment, we can compare monetary values in a meaningful way and get a better understanding of the financial impact of flood damages in California over time.

As Price Index, we use the Consumer Price Index (CPI) as the reference to measure inflation. The CPI is a measure of the average change over time in the prices paid by consumers for a basket of goods and services. Then adjustment factors are calculated by dividing the CPI of the reference year (2023) by the CPI of each previous year. This gives us a factor that indicates how much prices have increased from that year until the reference year.

$$Inflation Factor = \frac{IPC_{2023}}{IPC_{year}}$$
Each payment and damage amount are multiplied by the adjustment factor corresponding to the year of the claim. This converts the amounts into constant US dollars of 2023. We can now inspect the data as wanted.

$$Payment_{inflation adjusted} = Payment \times Inflation Factor$$

$$Damage_{inflation adjusted} = Damage \times Inflation Factor$$

## 2.2 Linear Regression

Linear regression is a powerful tool used to analyze and predict trends in data over time. Here, we applied linear regression to analyze flood damages in California over the years. By applying this method to flood damage in California, we can better understand how damage has evolved over the years and particularly predict the daily damage amount of flood for the SHELDUS database, which represents total flooding damage.

We defined the NWM rain rate and the NFIP damage as our independent variables (X) and our dependent variable (Y) as the predicted SHELDUS flood damages. This sets up our regression model to predict. We used the Linear Regression model from the scikit-learn library on Python to fit our data. This step calculates the best-fit line that minimizes the error between the predicted and actual values, which gave the fitted model. Using this fitted model, we can predict the flood damages for any given year. This helps us understand the trend and project total flood damage on a daily scale for the SHELDUS database.

## 2.3 Proportional Distribution

Proportional distribution analysis is an effective method for understanding the relationship between different datasets. In this study, we applied this technique to analyze flood damage in California using the SHELDUS and NFIP databases. This approach helps us better understand the distribution of insured versus total flood damages and improves our flood prediction models.

We began by loading the necessary modules and datasets. The NFIP dataset contains daily records of insured flood damages, while the SHELDUS dataset provides monthly aggregated flood damage data. Next, we prepared the data by aligning the two datasets by month and county. This step was crucial for comparing the damage reported in each database. We then performed a proportional distribution analysis to compare the monthly aggregated data from both datasets. For example, for each day of a particular month, a damage proportion can be calculated based on NFIP daily and monthly aggregated data. This value is assumed to remain constant when applied to the SHELDUS dataset to calculate daily damage from the monthly aggregates. This helped us understand how insured damages (NFIP) relate to the total reported damages (SHELDUS).
## 2.4 Evaluation Metrics

Using this fitted model, we predicted the total flood damage. This step allowed us to assess the accuracy of our model and understand the relationship between insured and total flood damages. We evaluated the model's performance using metrics such as Root Mean Square Error (RMSE) and bias calibration with the following equation.

$$RMSE_{linear regression} = \sqrt{\frac{1}{n}\sum_{i=1}^{n}(damage_{lr,i} - damage_{gt,i})^2}$$

$$RMSE_{proportional distribution} = \sqrt{\frac{1}{n}\sum_{i=1}^{n}(damage_{pd,i} - damage_{gt,i})^2}$$

$$Bias_{linear regression} = \frac{1}{n}\sum_{i=1}^{n}(damage_{lr,i} - damage_{gt,i})^2$$

$$Bias_{proportional distribution} = \frac{1}{n}\sum_{i=1}^{n}(damage_{pd,i} - damage_{gt,i})^2$$

The results demonstrated a significant relationship between insured and total flood damages, highlighting the importance of improving insurance coverage in high-risk areas. The proportional distribution analysis provided valuable insights for enhancing flood prediction models.

# 3 Data

## 3.1 NFIP

The National Flood Insurance Program (NFIP), administered by the Federal Emergency Management Agency (FEMA), provides flood insurance and collects data on insured flood losses, offering a unique source of information on flood damages since 1978 in the USA. The NFIP database contains daily county-level data on insured flood losses, making it a vital resource for flood risk assessment despite the low insurance penetration rate across the country (Gall, 2015; Kousky, 2018). For this study, we utilized NFIP data from 1979 to 2021, although the database extends from 1978 to 2022 at the time we are conducting this study. Focusing on California, we found high-quality data providing detailed information on state, county, date, and event type, as well as various damage categories and claims data (Collins et al., 2020). The NFIP data is comprehensive, including details such as the number of policies in force, the number of claims,
the total claim amount, and specific damage categories like building and content damage. The
data quality is considered high due to the rigorous reporting and verification processes followed
by FEMA. However, it is important to note that the data is only representative of insured
properties, which may introduce some bias due to the low insurance penetration rate,
particularly in high-risk areas (Gall, 2015).

For this study, we extracted key variables such as location (state and county), date of the
event, and damage data (building and content damage). To ensure consistency and comparability
with other data sources, we summed the building and content damage into a single category
labeled as "insured damage." This approach allowed us to align the NFIP data with the property
damage data from the Spatial Hazard Events and Losses Database for the United States
(SHELDUS). One limitation of the NFIP data is the lack of adjusted damage costs to current dollars.
Unlike SHELDUS, which provides inflation-adjusted damage costs, the NFIP data is reported in
nominal terms. To address this issue, we adjusted the insured damage costs to 2023 USD to
ensure that all damage figures are comparable over time (Yang et al., 2020; Mobley et al., 2021).

3.2 SHELDUS

The Spatial Hazard Events and Losses Database for the United States (SHELDUS) is a
database providing modeled data on various hazards, including wildfires, droughts, and flooding.
Developed by the University of South Carolina and currently maintained by the Arizona State
University (ASU) Center for Emergency Management and Homeland Security, SHELDUS offers a
monthly-county-level dataset for the contiguous United States (CONUS) and other U.S.
territories, such as Puerto Rico and the Virgin Islands. The dataset includes essential information
such as the date of the event, location (state and county), and direct losses (property, crop losses,
injuries, and fatalities). SHELDUS relies heavily on data from the National Centers for
Environmental Information (NCEI), though the processing methods differ, resulting in potential
discrepancies between the two databases. Despite these differences, SHELDUS remains a
valuable resource for analyzing hazard impacts over time and across regions.

For this study, we extracted data on winter weather, severe storms/thunderstorms, and
flooding, focusing specifically on property flood damage while excluding crop damage. One of
the key advantages of SHELDUS is that it provides damage costs adjusted for inflation, expressed
in 2023 US Dollars (USD). This feature enables direct comparison and analysis over different time
periods without the need for additional inflation adjustments. While SHELDUS records damage
due to natural hazards monthly, this temporal resolution can be a limitation for detailed flood
event analysis. To enhance this resolution and improve flood event detection, we integrated data
from the National Water Model (NWM). The NWM provides high-resolution hydrological data,
including variables such as rain rate, which can help identify days with abnormal precipitation.
By incorporating the NWM's rain rate variable, we aimed to pinpoint specific days with significant
rainfall, allowing us to identify flood days more accurately. This approach helps to complete the
monthly SHELDUS data and provides a more precise temporal alignment with the flood events.
The integrated dataset can then be cross-referenced with the National Flood Insurance Program (NFIP) data to offer a comprehensive understanding of flood events and associated damages.

The National Centers for Environmental Information (NCEI) database, also known as the Storm Events Database, is a key resource for environmental data in the United States, offering extensive information on a wide array of natural hazards, including floods, wildfires, droughts, and severe storms. Unlike SHELDUS, which provides modeled data and adjusts damage costs for inflation, NCEI focuses on raw, observational data collected from various federal, state, and local sources. The database includes detailed information on the date, location, and type of events, as well as the associated impacts such as property damage, crop losses, injuries, and fatalities. NCEI data is widely used for climate and environmental research, policymaking, and disaster response planning. Despite its comprehensive nature, we did not utilize the NCEI database for our study, as our research required the inflation-adjusted and processed data provided by SHELDUS, which better suited our analytical needs.

## 3.3 National Water Model

To facilitate downscaling SHELDUS data from monthly to daily resolution, we incorporated a variable from the National Water Model (NWM), maintained by the National Oceanic and Atmospheric Administration (NOAA) and the Office for Water Prediction (OWP). The NWM is a hydrologic model covering the USA, simulating streamflow across the territory through stream gauges. This database offers high accuracy, with over 2.7 million river reaches and hourly records for the contiguous United States (CONUS) through various variables such as river velocity, snow depth, elevation features, and rain rate.

For this study, we used only the rain rate variable, which provides hourly precipitation rates for every point on a 1km grid across CONUS since 1979. This variable enabled us to detect abnormal rain precipitation and identify specific flood days, thereby refining the monthly SHELDUS data (Yang et al., 2020). By combining these datasets, we aimed to enhance the temporal resolution of SHELDUS and improve flood event detection.

To facilitate the comparison between insured flood damages, total flood damages, and precipitation rate data, we conducted our analysis across the entire Californian territory, excluding San Bernardino, Santa Barbara, and Riverside counties due to data unavailability. This integration enabled us to achieve a more accurate and comprehensive understanding of flood events. We processed the data with spatial aggregation (using the mean) and temporal
aggregation (using the sum) to effectively analyze the statistical relationship between insured and total flood damage in California (Mobley et al., 2021; Mosavi et al., 2018).

## 4 Results

### 4.1 Major Flooding Events as Characterized by NFIP, SHELDUS, and NWM

* 1986 Flooding Event: Valentine's Day Flooding in Sonoma County

<figure><img src="image_2.png" /><figcaption>Fig. 1: Flooding damage amount and rain rate in California in 1986</figcaption></figure>

In the figure 1, the total damage is higher than the insured one. February 1986 is sadly known as the “Valentine’s Day Flooding” in Sonoma and Napa Counties. Although Sonoma County appears to be the highest NFIP damage in California, this flooding event touched Napa County too but there’s a difference in terms of population. Sonoma county had around 345k
211 inhabitants with one NFIP policy count and only a third of that represents the population of Napa
212 the same year with only 104k inhabitants, also with one NFIP policy count.

213 • 2005 Flooding Event: Marin County

<figure><img src="image_3.png" /><figcaption>Fig. 2: Flooding damage amount and rain rate in California in 2005</figcaption></figure>

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215

216 The flooding of December 2005 in Marin County, see figure 2, is the third most important
217 damage in the NFIP records in California. Here SHELDUS' records are a lot higher than the NFIP
218 one for every flooding event of the year and particularly in December. This flooding event
219 happened in the Marin County at the end of December 2005 and continued through January
220 2006.

221

• Selected Missing Events

222 A further analysis of flooding damage data from the NFIP and SHELDUS databases reveals
223 notable discrepancies for Sonoma County. In the first instance, the NFIP database reports a
224 significant damage amount of $69,950,289 for a flooding event in January 1995, while SHELDUS
225 records a damage figure of $6,914,110.29 for an event in March 1995. The differences in both
226 the dates and amounts suggest that these might be distinct events rather than a single
227 occurrence. This discrepancy highlights potential issues in data consistency and reporting
228 between the two sources. Similarly, another mismatch is observed for 2019. The NFIP database
229 lists damages amounting to $34,623,251 for February 2019, while SHELDUS records zero
230 damages for a flooding event in January 2019. It is important to note that SHELDUS acknowledges
231 the flood event in January 2019 but records no damage. These differences suggest potential
232 challenges in synchronizing event dates and reported damages between NFIP and SHELDUS,

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233 underscoring the need for careful cross-verification when utilizing these databases for comprehensive flood damage assessment.
234

<figure><img src="image_4.png" /><figcaption>Fig. 3: Monthly comparison of total and insured flood damage in California in 2020</figcaption></figure>

The figure 3 shows that, on a state level, NFIP damage is consistently higher than SHELDUS damage for each month of 2020. This trend highlights the discrepancy between insured and total flood damages, demonstrating that the insured damages reported by NFIP surpass the total damages recorded by SHELDUS across all counties. Over 44 years of flooding data (1978-2022), so 528 months, we have a total of 113 months where the insured flood damage is higher than the total damage recorded by SHELDUS.
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The five largest SHELDUS flood damages in California correspond to specific flooding events documented in the NFIP records. These events occurred in the same month and county as listed. Furthermore, in each case, the total damage reported in the SHELDUS database exceeds the insured damage recorded by the NFIP, indicating a successful cross-validation between the databases. The five largest events took place in the following counties: Butte in February 2017 (figure 4) with $665.49 million in damage, Los Angeles in February 1980 (figure 5) with $548.05 million in damage, Santa Barbara in January 1995 with $181.74 million in damage, Napa in January 2006 with $171.74 million in damage, and Marin in December 2005 with $166.66 million
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in damage. Notably, the event in Marin is recorded as the third largest NFIP damage event in California (see figure 2 above).

<figure><img src="image_5.png" /><figcaption>Fig. 4: Flooding damage amount and rain rate in California in 2017</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>Fig. 5: Flooding damage amount and rain rate in California in 1980</figcaption></figure>

## 4.2 Cross Validation of monthly Flooding Damages from NFIP and SHELDUS
<figure><img src="image_7.png" /><figcaption>Fig. 6: Total and insured damages in 2023 USD across the years in California</figcaption></figure>

The main difference between the two databases is the kind of flood damage recorded and their corresponding timeline. NFIP records date back to 1978 only for insured flood damage while SHELDUS goes back to 1958 for all kinds of flood damage, representing total damage.

<figure><img src="image_8.png" /><figcaption>Fig. 7: Count in month of every possible scenario between NFIP and SHELDUS damage per county in California from 1978 to 2022</figcaption></figure>

Only the 20 counties with the most scenario count are represented here. As we can see, the most common scenario is scenario C, where there is flood damage recorded by the two
databases while the amount in USD of total damage is higher than the insured damage. See Figure 2 in the annex for the complete figure with every county. Not every county has the same amount of scenario because of the lack of data. For a lot of dates across the timeline we were working on, we didn't have any damage recorded, not even 0.00$. Moreover, it is also possible that some damage doesn't match the dates and/ or the county of the other database. The matching is not really accurate, and it explains why there is such a difference of scenario counts between every county.

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## 4.3 Temporal Resampling of Total Flooding Damages

Temporal resampling is a technique used to convert data from one time resolution to another, providing a finer or coarser temporal granularity. In our study, we applied temporal resampling to the SHELDUS dataset to better align it with the NFIP data and to enhance the temporal resolution of total flooding damage records.

The SHELDUS dataset provides monthly aggregated flood damage data, while the NFIP dataset offers daily records of insured flood damages. We began by extracting the necessary flood damage data from both datasets, ensuring that the data was aligned by location (county) and time (month and year). To achieve daily resolution from the monthly SHELDUS data, we utilized the rain rate variable from the National Water Model (NWM).

The rain rate data, which provides hourly precipitation rates on a 1km grid across the contiguous United States (CONUS), helped us identify days with significant rainfall within each month. We distributed the total monthly flood damages from SHELDUS proportionally across the identified flood days, thereby creating a daily flood damage dataset. The resampled daily SHELDUS data was then compared with the NFIP daily records. This step involved aligning the resampled data with the exact dates and locations of flood events as recorded in the NFIP dataset.

The temporal resampling of the SHELDUS data allowed us to achieve a precise temporal alignment with the NFIP data. This enhanced temporal resolution provided a better understanding of the distribution and timing of flood events, as well as the relationship between insured and total flood damages. This approach underscores the need for integrating high-
resolution hydrological data with damage records to better understand and mitigate the impacts of flooding.

<table><caption>Fig. 8: Table of the results from the RSME and bias calculations in USD</caption><thead><tr><th></th><th>Linear Regression</th><th>Proportional Distribution</th></tr></thead><tbody><tr><th>RMSE</th><td>98, 721, 940.63 $</td><td>26, 698, 265.30 $</td></tr><tr><th>Bias</th><td>-18, 256, 430.28 $</td><td>-688, 905.95 $</td></tr></tbody></table>

<figure><img src="image_9.png" /><figcaption>Fig. 9: Comparison of actual damage with Linear Regression and Proportional Distribution results with the RMSE method</figcaption></figure>

The results of our analysis clearly indicate that the proportional distribution method outperforms linear regression in predicting flood damages. This is evidenced by the lower Root Mean Square Error (RMSE) of 26,698,265.30$ for the proportional distribution, compared to 98,721,940.63$ for linear regression. A lower RMSE signifies better accuracy in predictions. Additionally, both methods exhibit a negative bias, indicating an underestimation of flood damage. However, the bias for the proportional distribution (-688,905.95$) is much closer to zero than that of the linear regression (-18,256,430.28$), further demonstrating its superior performance. Therefore, while still an underestimation of flood damage, the proportional distribution method provides more reliable and precise estimates than linear regression.

## 5 Conclusions

This study provides a comprehensive analysis of flood damages in California, leveraging data from the National Flood Insurance Program (NFIP) and the Spatial Hazard Events and Losses
Database for the United States (SHELDUS). Through the application of machine learning algorithms and statistical methods, we have identified significant discrepancies between insured and total flood damages, highlighting the critical gaps in insurance coverage, particularly in high-risk areas. The findings underscore the limitations of the current NFIP tools, which contribute to insufficient data and low insurance penetration. By refining flood prediction models and integrating more accurate damage estimates, this research offers valuable insights for enhancing flood resilience strategies. Future efforts should focus on improving data collection and coverage, as well as updating predictive models to better inform policy decisions aimed at reducing the economic impacts of floods in California and beyond. This work lays the groundwork for a more resilient approach to flood risk management, one that can adapt to the increasing challenges posed by climate change.

## Acknowledgments

I would like to express my gratitude to, Pr. Weiming Hu (James Madison University, VA, USA) and Pr. Tom Corringham (UC San Diego, CA, USA) for their valuable feedback and guidance throughout this work and also to Pr. Alpaslan Yörük (HTW Saar, Germany) for accepting to evaluate this project. I also wish to thank Pr. Steven Frysinger (James Madison University, VA, USA) and Mrs. Vera Müller (HTW Saar, Germany) for providing the resources and continuous support for this exchange abroad.

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<figure><img src="image_10.png" /><figcaption>Fig. 7: Complete count in months of possible scenarios between NFIP and SHELDUS damage per county in California from 1978 to 2022</figcaption></figure>

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