Characterizing Multi-Decadal Trends in Streamflow and Design Floods
in the Southeastern United States
By
Sarah Brannum
Senior Honors Thesis
Department of Geological Sciences
University of North Carolina at Chapel Hill
April 29, 2021
Approved:
______
Dr. Antonia Sebastian, Thesis Advisor
Characterizing Multi-decadal Trends in Streamflow and Design Floods in the Southeastern United States
Sarah Brannum
Abstract
Design floods serve an important role in environmental planning and management; however, flood frequency analyses often assume that historical records are stationary despite anthropogenic changes across the watershed. Such changes are especially prevalent in the southeastern United States where rapid population growth coupled with climate change is dramatically altering catchment response. To understand how design floods have changed over time, this study investigates historical records of daily river discharge at over 5,800 USGS gauges in the Southeastern USA. When looking at trends in daily discharges, we find that 40% experienced a significant (p<0.05) increase in daily discharge, 50% experienced significant decrease, and 10% experienced no significant change in daily discharge. We observe that, in general, gages exhibiting increasing daily discharge are spatially concentrated east of the Appalachian Mountains and gages exhibiting decreasing daily discharge are spatially concentrated to the west. When looking at trends in extreme discharges using both the annual maxima and a peak-over-threshold with discharges above the 90th and 99th percentiles, we find that less than 20% of gages had a significant trend in the extreme discharges. We then conducted a flood frequency analysis at gages with the most significant (positive and negative) trends in daily discharge to estimate the 25- 50- and 100-year design flows using the Gumbel distribution based. We compare the modeled results using the annual maxima over the entire period of record and for every 30-year segment of the record. For all return periods, we find that about 75% of gages experienced a significant trend, with 50% of gages experiencing an increasing trend in the magnitude of the design flood. Future work will look to attribute our observed trends to changes in the watershed including urbanization and climate change. Understanding non-stationary trends in river discharge, especially in coastal zone, is critical for local government planning and adaptation in light of changing coastal hazards.
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1. Introduction
Floods are the natural disaster that occur at the highest frequency and can cause damage and loss of life almost anywhere around the world (UNISDR 2017). The Southeastern United States (U.S.) is particularly vulnerable to flooding due to risk of both tropical and wave cyclones, as well as orographic lifting from the Appalachian Mountains which can cause extreme rain events on the eastern side of the mountains (Lecce 2000). In fact, recent tropical cyclone events, including Hurricanes Matthew (2016), Irma (2017), and Florence (2018), as well as major precipitation events, have demonstrated the vulnerability of Southeastern U.S. communities to flooding and the catastrophic damage that can ensue (Smith 2020). Because floods can be so costly, there is a critical need to accurately quantify flood risk and plan for future events based on that risk. Scientists and engineers use models to understand and quantify flood hazards, which can provide local governments with information needed to best protect their communities. These models are often based on historical events and their frequencies in order to gauge how likely these events will occur in the future. However, if flood hazards are changing over time, not accounting for this change could lead to false assumptions about the frequency of major flood events and undermine preparedness, leaving communities vulnerable to flood damage (Beighley and Moglen, 2002). Thus, quantifying and effectively communicating flood hazards and how they are changing is vital for community resilience and has the potential to save both money and lives.
It is important to observe and quantify trends in river discharge to understand and predict future flood events and recognize the characteristics that impact the damage a future flood event may have. One useful approach is to evaluate whether the magnitude of the design flood has changed over time (Blum et al. 2020). A design flood is a flood of a certain magnitude that has a specific probability of occurring (FEMA). The magnitude of the design flood can tell city planners how close to have development to a river, insurance rates, or how at risk a building is to flooding given an event of a particular return period (FEMA). The 100-year-flood is the primary design flood used by government agencies because it is severe enough to cause damage, but statistically not likely to occur in a given year (FEMA). Government flood standards use the 100-year-flood in order to avoid frequent flood exposure but avoid setting a superfluous standard that limits any development along rivers (FEMA). If the magnitude of the 100-year-flood or other design floods is changing, then flood risk for certain locations could be underestimated (Blum et al. 2020).
Recent studies have begun to analyze how the magnitude of the design flood has changed (Griffin et al 2019; Slater et al 2021). For example, Griffin et al (2019) studied how the magnitude of the 30- and 50-year design flood has changed at stream gages in the UK using a moving window approach. They found that a sizeable fraction of gages showed trends in the magnitude of a specific design flood. Although this paper was specific to the UK, many of the characteristics that affect streamflow persist around the world, making it plausible that other areas could have trends in the magnitude of the design flood. Slater et al. (2021) performed a similar analysis on discharges at the global scale. Globally, for the 20- and 50-year return periods, they found that the magnitude of the design flood increased in temperate zones but decreased in arid, tropical, polar, and cold zones. However, for the 100-year return periods, they found decreased magnitudes in arid and temperate zones and an increase in tropical areas. They note that differences could also be attributed to site record length. For the Southeastern U.S. specifically, Slater et al. 2021 found no overarching spatial trend in how the magnitude of the 20-
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, 50-, or 100- year design floods have changed. However, since this study was performed for the global scale, the finer details are often neglected in favor of a discussion the larger trends observed.
In addition, several prior studies have investigated trends across stream gages in the continental U.S. in daily discharge (Sagarika et al 2014; Rice et al 2015; Rice et al 2016; Boggs et al 2011), annual maxima (Berg et al 2018; Villarini et al 2016; Aryal et al 2018), and extreme events above a specific threshold or discharge percentile (Slater et al 2016; Neri et al 2020; Lins et al 1999; Debbage et al 2018; Aryal et al 2018). Studies which focus on median, low-percentile events, or mean discharge have found statistically significant increases in discharge (Patterson et al 2013; Naz et al 2018; Sagarika et al 2014) whereas studies which analyze extreme events, or high discharge scenarios, reach conclusions which are more nuanced, with some studies finding increases in the magnitudes of extreme discharge events (Naz et al 2018; Groisman et al 2001) and others finding decreases or no change in the magnitudes of extreme discharge events (Lins et al 1999; Rice et al 2015; Blum et al 2020). In general, previous studies have attributed changes in discharge (whether positive or negative) to anthropogenic factors such as urbanization and climate change.
Discharge can change due to a variety of factors affecting the hydrologic cycle or hydraulic response at any given river station. It is well understood that changes in urbanization, precipitation, land use/land cover, climate, and antecedent rainfall conditions all contribute to changes in streamflow (Neri et al 2020). For example, urbanization can lead to increases in impervious surfaces which results in increased in runoff volume and reduced time to peak (Rose and Peters, 2011; MongollΓ³n et al 2016; Beighley et al 2002). Similarly, global warming associated with anthropogenic climate change has led to increases in precipitation intensity in certain places which can drive higher streamflows during storm events (Sagarika et al 2014). However, interactions between urbanization and observed increases in precipitation are highly non-linear, leading to even more complex streamflow responses (Sebastian et al. 2019). While it is difficult to attribute trends in streamflow to one of these variables, and it is equally difficult to predict how changes in any one of these variables will impact streamflow. It is vitally important to understand where these changes are occurring and the magnitude of the change.
In this study, we collect daily discharge records at over 5,000 U.S. Geological Survey (USGS) gages at locations in the Southeastern U.S. and use them to quantify both historical trends in river discharges and the magnitude of the design flood. We used this data in order to see if there are trends in daily discharges, extreme discharges, and in the magnitude of the design flood. Additionally, we hope to see if there are any spatial trends in gages that have trends in discharges. In performing these analyses, we hope that this study will contribute to the conversation around flood risk and management in the Southeastern U.S.
2. Background
Flood risk is a function of hazard, vulnerability, and exposure (UNISDR 2017). The hazard is the depth or velocity of water caused by either extreme rainfall, dam failure, coastal storm surge, or other events (UNSIDR 2017). Exposure refers to the presence of development and people that are susceptible to flood damages, while vulnerability refers to the susceptibility of infrastructure and people to flooding (Kron 2005). Examples of factors that can impact vulnerability and
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exposure to floods include number of buildings at risk, quality of infrastructure, socio-economic status, and social inequalities (UNSIDR 2017). Given that the majority of the worldβs major cities are built along rivers, millions of people and buildings are at risk of flooding, and this risk is only rising as population growth and development in flood-prone areas is increasing (Jongman et al. 2012).
One way that hazard is measured is by quantifying the magnitude of the design flood and mapping the associated depth and extent of inundation. The design flood refers to the discharge that corresponds to a flood with a certain probability of occurrence. The design flood is calculated using the statistical probability that a certain river discharge is likely to occur. This analysis is done by using historical river gage data in order to determine the frequency at which certain events in the past occurred. To calculate the probability of the design flood, the following equation is used (Thomason 2019, p 4-3 β 4-4):
1 1 = = 1 π¦π¦ ππ β οΏ½ οΏ½ where P is the probability of the design floodππ occurringππ in a given year, T is the return period, and y is the number of years that we are interested in looking at. For example, the magnitude of the 100-year flood refers to a magnitude of an event that has a 1% chance of occurring in one year. In most cases, streamflow dynamics are assumed to be stationary over the period of record. But, given changes in channel morphology, land use and climate, this stationary assumption could result in an under or over prediction of the design flood (Stephens and Bledsoe, 2020). For example, if a channel was dredged or if rainfall increased for a given river, the frequency of a flood event of a specific magnitude would change. Similarly, for a given flood frequency, the magnitude of the design flood would increase.
Flood hazard maps indicate the depth and extent of flooding that occurs as a result of flood of a particular magnitude, i.e., a design flood. Flood hazard maps can also be intersected with information about exposure and vulnerability to estimate flood risks (de Moel et al. 2009). In the U.S., the Federal Emergency Management Agency (FEMA) delineates special flood hazard areas (SFHAs) based on the 100-year design flood. (FEMA 2005). These maps highlight the areas that would be flooded if an event with a 1% annual chance occurs. The SFHA is used by the National Flood Insurance Program (NFIP) in order to determine which properties need flood insurance and by city planners in order to determine which places would be most suitable for new development (UNISDR 2017). Recent studies suggest that upwards of 13.3% of the U.S. population may be exposed to the 100-year-flood (Wing et al. 2018). Yet, FEMA flood hazard maps are often 10-15 years old (Birkland et al. 2003), and increasing evidence suggests that an increasing proportion of losses are occurring outside of the mapped flood hazard areas (Brody et al. 2013).
To plan for and mitigate future changes in streamflow, it is important to understand large-scale shifts in design floods and where they are occurring. Communicating flood risk to the public is important for facilitating smart development and preparing for flood events when they occur. Flood frequency is the most important way that hydrologists communicate flood risk to city governments.
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3. Data and Methods
3.1. Data Collection
We obtained discharge records at 5,855 USGS gages located on rivers and streams within the USGS South Atlantic-Gulf Region (Figure 1). This region encompasses the states of Alabama, Florida, Georgia, North Carolina, South Carolina, and Tennessee (see, e.g., https://www.usgs.gov/media/images/usgs-regional-map). We subset the dataset to include only gages that included at least 30 years of consecutive daily discharge data. Prior studies have also used 30 years as a record long enough to be able to show a trend, but short enough to include as many gages as possible (Slater et al 2021; Griffin et al 2019). In addition, we wanted to ensure that we were using a window that was long enough where individual large years did not obscure any long-term trend. This resulted in 1,322 USGS gages that met our criteria (shown in black on Figure 1).
Figure 1. This figure shows the locations of all USGS river gages in the study area and a histogram showing the distribution of gages by record length. The black dots represent gages with records longer than 30 years and the grey dots represent gages with records less than 30 years. Only gages with records longer than 30 years (black dots) were included in the trend analysis.
3.1.1. Extreme Event Analysis
We consulted the literature to determine how to quantify an extreme event. Prior studies have used either the annual maxima (Berg et al 2018; Villarini et al 2016; Aryal et al 2018) or discharges above a certain threshold (Slater et al 2016; Neri et al 2020; Lins et al 1999; Debbage et al 2018; Aryal et al 2018). The annual maxima ensure that each year in the record is represented. However, the latter approach allows the research to account for instances in which more than one major flood event occurred in a given year. This could increase the number of extreme events observed in the record, leading to a higher estimate of the design flood than if only annual maxima were considered (Bezak et al. 2014). In most peak-over-threshold studies, authors identify discharges associated with major flood events based on records that exceed a
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certain percentile discharge (Lins et al 1999; Slater et al 2016; Debbage et al 2018). However, there is recognition that the selection of percentile is subjective to the researcher, which could affect the statistical significance if the number of data points is lower because of a higher threshold (Bezak et al. 2014). Some papers avoid this by setting a threshold that includes a specific number of data points per year (Neri et al 2020, Aryal et al 2018). Thus, in this study, we created three datasets to study extreme events: (1) annual maxima; (2) peak event discharge exceeding the 90th percentile of daily discharge records; and (3) peak event discharge exceeding the 99th percentile of daily discharge records. By using different ways to quantify an extreme event, we hope to understand more fully how these peak discharges are changing in the Southeastern U.S.
To find the maxima per year, we wrote a simple script in R to iterate through all the daily discharge values and extract the maximum observed discharge in each water year. A water year extends from October 1st to September 30th and accounts for seasonal variations in surface water supply due to seasonal influences on discharge such as precipitation patterns or snowmelt (USGS). To generate 90th and 99th percentile, we used the entire record of daily discharge at each gage to determine how many events would fall within the defined percentile. For the 90th percentile, we used the top 10% of discharge values, and for the 99th percentile, we used the top 1% of discharge values. For each list of discharges above the threshold, we looked at the dates to filter out observations that may have been from a single event. If a major storm event produced significant rainfall, the river discharges could be elevated for numerous days. In order to not count any flood events more than once, for dates that were directly next to each other, we only took the highest discharge of those because we considered dates with high discharges directly next to each other to be a result of the same event. For example, if there are three consecutive days that have discharges above our threshold, we considered those high discharges to be associated with one event, and therefore only added the day with the highest of those discharges to our dataset.
3.1.2. Design Flood Analysis
Herein, we used the magnitude of the design flood that corresponds to the 25-, 50-, and 100- year return periods. We used a moving window of 30 years and iterated through the entire length of the gage record. We started by taking the first 30 years of the record and finding the annual maxima for each year in the window. Once we had a time series of the year versus annual maximum, we fit the data to the Gumbel distribution and used the fit data to find the magnitude of the discharge for each return level: 25-, 50- and 100-year. We then repeated the same process for years 2 through 31 of the record. We stepped through the entire length of the record annually until we had obtained a time series of magnitude of flood and plotted them relative to the final year of moving window.
To fit the Gumbel distribution, we used the R package βfevdβ (Gilleland and Katz 2016). The Gumbel distribution is often used in hydrology because it can account for the peak discharges having a positive skew (U.S. Dept. of Agriculture 2007). It can be used to estimate the expected discharge for a given return period using the following equation (U.S. Dept. of Agriculture 2007, p. 5-11):
= +
πΊπΊ ππ οΏ½ πΊπΊ ππ ππ ππ πΎπΎ ππ 6
where XG,T is the predicted discharge, XΜ is the average annual peak discharge, KG,T is the constant dependent on the return period and sample size, and S is the standard deviation of the annual peak discharge (U.S. Dept. of Agriculture, p. 5-11). Other distributions we could have used include the Weibull, Gamma, Lognormal, and generalized extreme value (GEV) distributions (Slater et al 2021). Once we fit the data to the distribution, we can calculate the magnitude of the discharge for different return periods. We created a dataset of all stream gages in the Southeastern U.S. using the last year of the window as the date associated with the magnitude of the 25-, 50-, and 100-year design floods based on the previous 30 years of the record.
3.2. Mann Kendall Test
After generating the datasets described above including our daily discharge dataset, a Mann Kendall statistical test was applied whether there were statistically significant trends in the data. The Mann-Kendall test is non-parametric test that can be applied to data without a particular distribution and one that has missing data points (Gilbert 1987). The hypothesis test has a null hypothesis that there is no trend in the data, and to reject the null would be to assume that there is a trend. To find whether the null hypothesis is accepted or rejected, the Mann-Kendall statistic is calculated using the following equation (Gilbert 1987, p. 209):
= ππβ1 ππ ( )
ππ οΏ½ οΏ½ π π π π π π π₯π₯ππ β π₯π₯ππ where is the Mann Kendall Statistic, ππ= is1 ππthe=ππ+ day1 the observation was taken, and represents the number of observations in the time series data. In plain terms, this equation takes a list of observationsππ in chronological order andπ₯π₯ finds the difference between directly adjacentππ data points. Then, it takes the sum of how many of the differences are negative versus positive. The magnitude of the Mann Kendall Statistic, , correlates to the magnitude of the trend. If is negative, later observations are smaller than earlier ones, meaning there is a decreasing trend in the magnitude of the observations over time.ππ Conversely, if is positive, later observationsππ are larger than earlier ones, meaning there is an increasing trend in magnitude over time. Larger magnitude values would mean that we would reject the nullππ hypothesis and assume that there is a significant trend. However, if is close to zero, we would not have enough confidence to reject the null hypothesisππ and would assume no trend. The threshold of what value of is deemed significant is dependent on whatππ confidence level (i.e., p-value) is used. ππ The Mann-Kendall test was performed in R using the R package βKendallβ (McLeod 2011). For our analysis, we applied a p-value of less than 0.05 to determine statistical significance (EPA Statistical Analysis for Monotonic Trends). Another output of the Mann-Kendall test in R is a tau value that signifies the magnitude of the trend. The sign of the tau value is either negative or positive and corresponds to a negative or positive trend respectively. Interpreting the outputs from the test, we used the tau value to determine the direction and magnitude of the trend and the p-value to determine whether the trend was statistically significant.
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4. Results
4.1. Daily Discharge
Our results indicate that there is a statistically significant increase in the magnitude of daily discharge at 533 (40%) gages in the Southeastern U.S. and a statistically significant decrease in discharge at 648 (49%) gages (Table 1). At the remaining 145 gages, we detected no significant trend in daily discharge. We map the magnitude of the trend at the gages where statistically significant trends were detected (Figure 2). In general, we observe a stark contrast in trends at gages east of the Appalachian Mountains versus west where the majority of gages to the east of the mountains show a decreasing trend in daily discharges, while the majority of gages west of the mountains show an increasing trend in daily discharges. Our trend in daily discharges overall agreed with the literature (Fig. 2). For example, Rice et al (2015) found that gages in the Southeast generally decreased, specifically east of the mountains.
Figure 2. Figure showing all gages with records larger than 30 years colored and sized by the sign and magnitude of trends in daily discharges. Increasing trends are shown in red, while
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decreasing trends are shown in blue. Non-significant trends are represented by smaller black dots.
Statistically significant trends in daily discharge values provides evidence of changing watershed dynamics across the region. Changes in watershed dynamics can be attributed to climate change, urbanization, and other variables that can affect river discharge (Neri et al 2020). The Appalachian Mountains act as a dividing line between gages that are predominately increasing in discharge (west) versus gages that are predominately decreasing in discharge (east). This stark spatial trend could be due to a number of factors. Given that the natural mountains show a trend, we can postulate that there is a natural phenomenon to explain why there is a stark spatial trend confined by a natural feature. As a result, we might infer that a natural or anthropogenic climate change in the form of rain amounts changing could be responsible for the trends in daily discharge we are seeing. Many studies have observed trends in rainfall throughout the U.S. (Bartels et al, 2019; Hoerling et al 2016). In general, it is found that the Southeastern US is experiencing decreases in precipitation (Bartels et al. 2019). However, there are gages that do not align with the zoning east versus west of the mountains. Because there are outlier gages, we can assume that other factors could be playing a role. Some of the areas that contain the most outliers are in the vicinity of major cities in the Southeastern U.S. such as Raleigh, NC, Nashville TN, and Tampa, FL. Urbanization could explain why the outliers are clustered in major metropolitan areas. It is important to recognize that our gages data has a spatial bias where more gages are located in urban areas, which could be affecting how interpretation of spatial trends.
4.2. Extreme Event Analysis
Using either annual maxima or peak-over-threshold method, there are far fewer gages that show significant trends compared to the daily discharges. While over 90% of gages had a significant trend in daily discharges, only 19% (annual maxima), 20% (events above the 90th percentile), or 12% (events above the 99th percentile) showed significant trends in discharges (Table 1). Neither discharge trends for individual gages using annual maxima (Fig. 3) or peak-over-threshold (Fig. 4) show obvious spatial trends across the Southeast. Our findings are in line with other studies that examined trends in annual maxima. For example, Lins et al. (1999) found more significant trends in not as extreme events (such as the annual median flow) compared to the annual maxima.
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Figure 3. Figure showing all gages with records larger than 30 years colored and sized by the sign and magnitude of trends in annual maxima.
For either method of quantifying extreme events, we did not seem to find any major spatial trends in gage trends. We attribute this to a limited number of gages that show a significant trend. However, for the peak-over-threshold specifically, we saw that between the 90th and 99th percentile events, the number of gages that showed significant trends decreased from 20.3% of gages down to 12.2% of gages. Without results, we can say that as event become more extreme, the number of gages that show trends in the extreme magnitudes decreases. There are few gages that are experiencing changes in the magnitude of the most extreme discharges in the Southeastern US. Lins et al (1999) found that as events throughout the entire U.S. become more extreme and intense for a given gage, the trend in discharge associated with those events decreased. Specifically, for the Southeastern U.S., very few gages showed significant trends, with the majority of the gages decreasing in magnitude of the most extreme events (Lins et al 1999).
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Figure 4. Figure showing all gages with records larger than 30 years colored and sized by the sign and magnitude of trends in 90th percentile events (left) and 99th percentile events (right).
Comparing the results of the annual maxima and peak-over-threshold approaches to look at trends in extreme discharges, we noticed that a reduced number of gages showed trends in discharges compared to the daily discharges (Table 1). For the annual maxima, we noticed that 80% of gages that showed a significant trend were decreasing. Conversely, using the peak-over- threshold, we noticed that the majority of gages showing a significant trend were increasing. For the events above the 90th percentile discharge, 70% of the gages with significant trends had increasing trends. For events above the 99th percentile discharge, 62% of gages with significant trends had increasing trends. As noted previously, using the peak-over-threshold can overestimate the discharges and could exaggerate trends (Bezak et al, 2013). This discrepancy between annual maxima versus extreme discharges above our thresholds could be evidence of this flaw in the peak-over-threshold. Again, by using both the annual maxima and peak-over- threshold approaches, we hope to more accurately convey trends in extreme discharges and the nuances that could exist in these trends.
4.3. Return Period of Design Flood
Using our dataset generated by the moving window approach, we were able to see how the magnitude of the design flood changed over time. For each point on the time series (Fig 5), one year is removed while one year is added to the window. Then, when calculating the magnitude of the design flood using that specific window, large changes in magnitude correspond to either the inclusion or removal of an abnormal annual maxima in the record.
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Figure 5. Example gages show a time series of how the magnitude of the design flood is changing at (a) Tar River at Tar River, NC; (b) Cape Fear River at Lillington, NC; (c) Neuse River at Kinston, NC, as well as a map showing where the example gages are located. Each line represents a different return interval, with green being 100 years, blue being 50 years, and purple being 25 years. These time series show the discharge of the design flood versus the last year in the 30-year window that were generated for each gage and were used to quantify trends in the magnitude of the design flood.
We looked at the change in magnitude of the 25-year-flood, 50-year-flood, and 100-year-flood (Fig 6). We found that the majority of gages showed a significant trend in the magnitude of the design flood given different return periods (Fig. 6). Around 75% of gages show a significant trend in changing magnitude of the design flood for each return period (Table 1). Similarly, around 50% of gages saw a significantly increasing trend in the magnitude of the design flood given either of the return periods (Table 1). Between the different return periods, the number of gages that showed trends in the magnitude of the design floods did not vary greatly (Table 1). We do not observe stark spatial patterns in the trends of the magnitude of the 25-year, 50-year, or 100-year design flood. There were no gages where changing the return interval yielded the opposite trend; in other words, for every gage, all of the return intervals showed trends in magnitude of the design flood with the same sign.
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Figure 6. Figure showing all gages in the Southeastern U.S. with significant trends in the magnitude of the 25-year, 50-year, and 100-year design floods.
Table 1: Table displaying the values represented in the figures above.
Significant Increasing Significant No Significant Trend Trend Decreasing Trend
Daily Discharge 533 (40.2%) 648 (48.8%) 145 (10.9%)
Annual Maxima 41 (3.5%) 173 (14.7%) 966 (81.9%)
90th Percentile Events 170 (14.4%) 70 (5.9%) 939 (79.6%)
99th Percentile Events 88 (7.5%) 54 (4.6%) 1036 (87.9%)
25-Year Design 497 (50.9%) 234 (24.0%) 245 (25.1%) Flood Magnitude
50-Year Design 495 (50.7%) 229 (23.5%) 252 (25.8%) Flood Magnitude
100-Year Design 495 (50.7%) 224 (23.0%) 257 (26.3%) Flood Magnitude
4.4. Discrepancy between annual maxima and return period
One of the most interesting findings was the discrepancy between the number of gages that showed trends in the annual maxima versus the number of gages that showed trends in the magnitude of the design flood. For annual maxima, we found that 18.2% of gages showed a significant trend, while for the design floods with a return period of 25-, 50-, and 100-years, we found that 74.9%, 74.2%, and 73.7% of gages showed statistically significant trends (Table 1). Our methods of finding the magnitude of the design flood involved using the annual maxima for 13
each gage and fitting that data to the Gumbel distribution. Since they both use the same annual maxima dataset, we did not expect to see a large difference in the number of gages that show statistically significant trends. However, this is not the case since the return period analysis yielded many more gages with significant trends than the annual maxima alone. We can attribute some the differences to the fitting of the data to the Gumbel distribution. Another key difference between our annual maxima analysis versus the return period is the number of data points for each gage. For the return period analysis, since we used a moving window approach, each gage would have 30 less data points compared to the annual maxima. Differences in the amount of data points could explain why there are major differences in the number of gages that show significant trends. Future work would suggest that we use different distributions to fit our data to see which one is the best (Slater et al 2021).
5. Discussion
Although we performed a fairly comprehensive review of different approaches to looking at trends in streamflow, there are a few items that could be beneficial for us to further this work. First, in our return period analysis, we used the annual maxima and fit that data to a Gumbel distribution. To compare different methods, we could use a peak-over-threshold approach and fit that data not only to the Gumbel distribution, but other distributions as well. Also, for our return period analysis, we were unable to fit gages that had years missing to the distribution. In order to include more gages that were only missing a couple years in a row, we could fill in the missing years using either the average of the years around it, fit a curve and use a value that corresponds to the slope of the line, or another gap filling approach. Additionally, we could examine how the inclusion or removal of events of a certain type (e.g. hurricanes) impacts the magnitude of the design flood.
To examine flood risk, we decided to look at stream gage discharge records for major streams and rivers in the Southeastern U.S. When a major rain event occurs where the river is more likely to flood and potentially cause flood damage, the discharge increases. This relationship is slightly complicated when a river overflows its banks. Discharge is a function of both water velocity and cross-sectional area of a river. When the river overtops its banks, the cross-sectional area is drastically increased. The velocity decreases in response to the overtopping of banks. Using discharge solely, it is difficult to estimate the volume of water that will overtop the banks and cause flood damage to nearby structures. Other tools such as stage-discharge curves and floodplain maps are used to complete the picture of relating specific river discharges to amount of flood damage. In the field of hydrology, discharge data is predominately used to examine flood trends and risk. However, it is important to recognize that discharge alone does not paint a full picture of flood damage as a whole.
Nonetheless, our research question has important implications for the field of hydrology and planning for major flood events in the future. Today, city managers rely on floodplain maps and the 100-year-flood as a metric for determining what locations are at risk of flood damage (National Flood Insurance Program). However, the floodplain maps rely on the stationarity of the magnitude of the 100-year flood, which our analysis has proven to not be the case (Figure 6; Table 1). When determining how at risk a location is from flooding, it is important to recognize that the frequency of flood events is changing, and therefore be conservative when determining how likely a place is to flood.
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6. Conclusion
In this study, we used various methods (historical gage data and return period analysis) and created three discharge datasets (daily discharges, annual maxima, and discharges over a specific threshold) to examine how river discharges have changed across the Southeastern U.S. The take- aways are three-fold. First, our analysis of daily discharge suggests that there are stark spatial trends where daily discharge is decreasing at gages located to the east of the Appalachian Mountains and increasing to the west. Second, we also looked at trends in major events, where we defined major events as either the annual maxima or events above a certain discharge threshold. For both of these analyses, we found that a small percentage (about 20%) of gages showed a significant trend in magnitude discharge. Third, we also looked at the magnitude of the design flood at different return intervals. We used a moving window in order to see how the magnitude is changing over time, and to see how the inclusion and removal of specific events change the magnitude of the design flood. We found that the majority (75%) of gages showed a significant trend in the magnitude of the design flood at the 25-year, 50-year, and 100-year return intervals. By using different methods to determine how discharge is changing for rivers across the Southeastern U.S., we hope to recognize that streamflows are dynamic, and recognizing flood risk for a location cannot be done under the assumption of stationary streamflows.
7. References
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