Estimating the change in the rational runoff coefficient through history in Jefferson County, Texas

Jefferson County in Texas has experienced devastating storms in recent years resulting in billions of dollars in damages. The county has gone through temporal milestones in terms of population growth and industrial development. Many studies have shown that urban development increases the risk of flooding by decreasing the soil infiltration capacity. The current study focuses on estimating the extent to which the urban development in the county has led to increased imperviousness using a combination of historical and current spatial data. Rational runoff coefficients of the County were estimated and compared at three different times over a span of 120 years. A land survey map for 1898, an aerial imagery map for 1966 and a land parcel map for 2019 were obtained from various sources. The three maps available, each in different format, were analyzed to determine the land use and land cover type for the respective years. The runoff coefficient increased by 21% from 1898 to 1966 and remained the same from 1966 till 2019. The estimates are in correlation with industrial and population growth patterns of the county. These preliminary spatial analyses are useful in estimating the contributions of recent major flooding from overall development, or if they may be more impacted from other factors such as changes in weather patterns.


Introduction
The changes in land use, especially the ones associated with urban development affect flooding in many ways.Urbanization frequently replaces natural vegetation and topsoil with construction elements such as concrete and asphalt to construct roads and buildings or even drainage structures.However, these building elements do not typically have the same infiltration capacity as the natural soil cover and therefore may increase the surface water runoff into waterbodies or neighborhoods resulting in increased flood hazards [1].The effect of urbanization on runoff has been reinforced by many scientific studies across the world.A study in the Houston metropolitan area showed a clear relationship between the extent of urbanization and the amount of runoff, where areas with increased urbanization showed an increase in runoff and areas with less urbanization had relatively low runoff [2].A study conducted in Whiteoak Bayou watershed in Texas showed that with 10% increase in imperviousness, the runoff depth and peak flow increased by 77% and 32% respectively [3].
A wide range of literature also exists on the change in surface runoff on a temporal scale based on land use and land surface change.These studies can be divided into two categories: (1) studies in surface runoff change through history and (2) studies predicting future change in runoff in an area.Most of these studies use extensive use of hydrological modeling coupled with land use maps generated using mapping software to calculate runoff.However, the availability of advanced hydrological software and weather (including precipitation) monitoring and tracking equipment are recent developments and were not universally available historically.Therefore, different studies have tried calculating the historical runoff using different methods.One study introduced two new methods, where one involved generating maps of fractional impervious surfaces for direct computation of catchment-level imperviousness and the other method involved generating maps of urban land use for subsequent computation of estimates of catchment imperviousness based on an urban extent index.Both of these methods required topographic maps to carry out the process and the existence of true color aerial photographs for validation [4].A study in India used a soil and water assessment tool (SWAT) to calculate streamflow from 1979 to 2012 and to predict the future flow from 2012 to 2030.That study showed that streamflow increased from 1.8 to 9.96% due to urbanization and 31% to 56% due to increases in agriculture [5].
This current study is interested in estimating the historical change in runoff coefficient based on land use and land surface changes in Jefferson County in Texas.The surface runoff can be estimated by the rational runoff coefficient.The Rational Method is one of the simplest and the oldest methods in estimating peak runoff.It depends on predetermined values for land use and land surfaces based on the runoff coefficient represented by "C" [6].
Jefferson County is located in the southeastern region of Texas, and collectively with other counties is known as Southeast Texas (SETX).The county shares a border with Louisiana on the east, Orange  [7].
Jefferson County was founded in 1835.The first recorded population was in 1850 and was recorded as 1769, and as of 2019 it was 254,340.There had been a huge uptick of population between 1900 and 1960 increasing from 14,239 to 249,659 which could be attributed to the Spindletop oil boom in 1901.Since 1960, the population has been rather constant [8].Lumber has been a major industry since the county's founding paving the way to its industrial development based on the oil boom.These in turn developed the transportation services such as shipping and the railways so much so that currently there are two major public ports in the area, many private docks and three major railways [9].
Many studies use spatial analyses such as geographical information systems for analyzing changes in land cover over time, especially as the population changes.The data may come from various sources.Mundhe and Jaybhaye [10] studied land surface changes in Pune City India using satellite data available from LandSat.The changes are from 1973 to 2011 as this type of satellite data are available during those timeframes.Similarly, Yang et al. [11] also used satellite data for estimating imperviousness from 1993 to 2001 in western Georgia.In the United States Levien et al. [12] used satellite data to evaluate land cover changes in California over a five-year period in the 1990s.Sinha et al. [13] used similar methods combined with hydrologic modeling to analysis surface runoff characteristics from 1971 to 2015.
But what if major land changes may be related to earlier dates in time?In the case of Jefferson County, the major growth in population is from around 1900 to the mid-1960s, with a much lower increase over the next decades to recent years.Thus, different sources of data might be needed for studying the land cover changes.
The altitude of Jefferson County ranges from 0 to 49 ft.The combination of being a coastal plain and a low-lying area makes it prone to flooding.The main streams of the county are Taylors Bayou, Hillebrandt Bayou and Pine Island Bayou, in addition to the Neches River.The mean annual temperature is 69° F and the mean annual rainfall is 53 inches.Along the coast, the soils are beachy sand and towards the north, soils are light-colored loamy over deep reddish clayey or loamy subsoils with hardened calcium deposits.The rest of the county has light to dark loamy surfaces over clayey subsoils.The climate is subtropical, humid featuring warm moist summers with gulf breezes [14].
Jefferson County has been plagued by storms in recent years resulting in multiple flooding events in a short period of time.Some of the notable storms are Hurricane Harvey in August 2017, Tropical Storm Imelda in September 2019 and Hurricane Laura in August 2020 followed by Tropical Storm Delta in October of the same year.These storms have caused destruction of property, loss of lives and cost billions of dollars.However, the county is not new to storms, and has experienced over 25 storms between 1851 and 2001 [15].According to Brody et al. (16), Jefferson County is found to have the highest percentage of its land area in a 100-year flood plain of any county in Texas and had over $10 billion in property loss over 12 floods between 1997 and 2001.This makes the county one of the important areas for mitigation efforts in Texas.Drainage District 6, one of the three drainage districts in the county, has been constantly developing drainage enhancing projects in the areas [17].
Due to the extreme flooding in Jefferson County in the past decade, there are questions as to its many possible causes.One cause is obviously the intense rainfall of recent events such as Hurricane Harvey and Tropical Storm Imelda.But there are other possible causes.One is an increase in runoff due to urbanization.This current study offers insight into whether the urbanization of the county has led to increased runoff based on historical spatial maps.
Three years were chosen to calculate the rational runoff coefficient, "C", for the county based on the availability of maps and trends in population growth.As noted previously, the County was sparsely urbanized prior to the oil boom in 1901, which then resulted in a large population increase over the next several decades.Thus an 1898 map was available and was chosen as the baseline for looking at runoff trends.Then from the mid-1960s, just at the end of the baby boom, till recently the population did not change very much.Thus, the second point in time was chosen as 1966.Finally, recent Fig. 1 1898 Land Survey Map overlaid with current county boundaries and watersheds [7,18] maps from 2019 representing the times of the extreme weather events were chosen for further analysis of the possible changes in runoff despite smaller population growth, since development practices may have also contributed to changes in land coverage.

Methodology
The three maps based on availability of the data and the developments patterns of the County are the 1898 land survey map, the 1966 areal imagery and the 2019 land parcel map.The process for estimating the rational runoff coefficient for the three maps is outlined in the following sections.

1898 map
A land survey map from 1898 was obtained from the Library of Congress [18].The map is probably one of the temporally closest maps of the county since its founding and is very close in time to the start of the oil boom in Texas in 1901, thus a valuable starting point to evaluate land cover changes.The first step was to overlay the map with the current boundary of Jefferson County [7].The 1898 map is available in an image format and is not spatially referenced.The georeferencing tool in ArcGIS [19] was used to align the 1898 map with the county's current boundary.The 1898 map with current county boundaries was then overlaid with current watershed boundaries of Jefferson County, obtained from the county's engineering department, as shown in Fig. 1.The current watersheds do not necessarily represent historical watersheds and is merely used to divide the county into smaller areas to calculate the rational runoff coefficients.The county areas were then classified as rural based on the population and the extent of development in 1898.
The Texas Department of Transportation (TxDOT) Hydraulic Design Manual was used to correlate the land use types of the map [20].The rational runoff coefficients rural watersheds are shown in Table 1.The overall runoff coefficient for a rural watershed is given by Eq. 1.
where C = runoff coefficient for rural watershed, C r = com- ponent of coefficient accounting for watershed relief, C i = component of coefficient accounting for soil infiltration, C v = component of coefficient accounting for vegetal cover, C s = component of coefficient accounting for surface type.
As Jefferson County is typically flatland with average slopes less than 1% [21], watershed characteristic was determined to be low.Clayey and loamy soils with calcium deposits towards the northern part of the county imply that the northern watershed soil infiltration characteristic is high and sandy soils on the south of the county imply that the watershed soil infiltration characteristic is normal to low.Since much of the county was considered grasslands, with little to no development, the watershed vegetal cover characteristic was estimated as low in most cases and watersheds with high concentrations of railroad development were considered normal.Due to the county being in a flood plain area with some lakes and ponds and marshes, the surface storage characteristic was estimated as normal to low.The areas of the watershed along with the identified watershed characteristics are shown in Table 2.

1966 map
Aerial images of Jefferson County from 1966 developed by the US Department of Agriculture (USDA) and with the image tiles in polygon shape file were obtained from the Texas Natural Resources Information Systems (TNRIS) datahub [22].These aerial images have been collated and collected by this datahub, making detailed land cover information for this year readily available.These images are in black and white and are spatially referenced.A total of 201 images in the County shown in Fig. 2 were overlaid with the current county boundary, and tiles.The tiles were used as a reference for identifying the images and to calculate the area.The overlapping polygons of the shapefiles of these tiles were edited to remove the overlapping areas using ArcGIS [19].Each tile in the map is numbered for tabulating purposes in the format "x.y".Number x represents the column starting from the left and number y represents the row starting from the top of column x.The current tiles are numbered from 1.01 (first column, first row) to 17-03 (seventeenth column, third row).Based on visual analysis, each of these images were divided into rural or urban for further classification.The categorized images with areas of each tile representing the image are shown in Table 3.The rural watershed types were further categorized into Jefferson County natural watersheds to identify the characteristic using the runoff coefficient for rural and mixed land use table from the TxDOT hydraulic manual as shown in Table 1 and for urban as shown in Table 4 [20].The urban watershed areas were broadly divided into commercial and residential areas.
The areas of rural and urban watersheds were then compiled from the tiles and characteristics estimated and the compilation is shown in Table 5.

2019 map
For the most recent estimation of runoff coefficients, a land parcel map from 2019 Jefferson County was obtained from the TNRIS datahub [23].The map contains detailed information of land parcels including land use type.The 2019 land parcels map of Jefferson County is shown in Fig. 3.The land use data were exported to a spreadsheet for further classification of the land use type using a property assessment guide developed for tax purposes [24].The identified land use type and their areas are shown in Table 6.The rational runoff coefficients for each of these classifications were assigned using the TxDOT hydraulic design manual and the values as listed in Tables 1 and 4 [20].

Results
Overall estimated runoff coefficients for the 1898 land survey map, the 1966 USDA aerial image map and the 2019 land parcel map are calculated and shown in Tables 7, 8 and 9 with values of 0.28, 0.34 and 0.34 respectively.The extent of urbanization for the three years is shown in Fig. 4. The coefficient components of C r, C i , C s and C v are defined in Eq. 1 and the corresponding values are provided in Table 1.
The estimated values for the watersheds in Jefferson County showed an increase in the rational runoff coefficient from 1898 to 1966.There was no increase in the estimated overall runoff coefficient from 1966 to 2019.However, rural and urban methods for estimating the rational runoff coefficient are not frequently averaged.Therefore, in Tables 8 and 9, estimated values separately for more rural versus more urban areas are also provided.
The number of tiles in each watershed of the 1966 Aerial Image Map were classified into either rural or urban watersheds and the number of tiles in each watershed and their classification are provided in Table 5.There are a total of 45 tiles classified as urban with a total tile area of 131,200 acres and 156 tiles classified as rural with a total tile area of 406,300 acres.The urban tiles are depicted in a shade of pink in Fig. 4. The component coefficients used for rural watersheds are the same as the 1898 Land Survey Map and are shown in Table 8.The overall rational runoff coefficient for the rural watershed area which is around 406 thousand acres of the county is 0.28.The urban portion of the county which is around 131 thousand acres has a rational runoff coefficient of 0.52.The urban watershed runoff coefficient is higher than the rural watersheds of the county.However, the rational runoff coefficient for the whole county is 0.34 as previously stated.
The land use type of the 2019 Land Parcel Map shown in Table 6 are broadly categorized into rural and urban types as shown in Table 9.The total rural area is around 698 thousand acres, and the urban area is around 87 thousand acres.The urban area of the County is depicted in a shade of pink in Fig. 4. The rational runoff coefficient for rural areas is 0.30 which is slightly higher than 1898 and 1966.The rational runoff coefficient for urban areas is 0.51 which is slightly lower than 1966.The overall runoff coefficient is 0.34 and is the same as 1966.

Discussion
The availability of data was a major consideration for the study as the analysis was over a period of more than 120 years.All the maps that were obtained are of a different format.Therefore, three different approaches were used for these three maps, but all three approaches were based on the same simple formula for estimating runoff, the rational runoff coefficient.The rational runoff coefficient was established before the mid-1920s and yet is still used today by state departments of transportation including Texas, particularly for smaller land areas [20].Although there may be many more advanced models for estimating runoff, the rational runoff coefficient method is still a valid approach for estimating a particular characteristic of the land, that is the potential for runoff based on development and a few other variables.
The 1898 map is one of the earliest manually created land survey maps that is available.The only available information from the map is the legend present in the map itself which showed that most of the land was either undeveloped or agricultural.The map showed the land as divided into land parcels and the presence of rail roads.The legend of the map and the soil information of the County were used to determine the land use type which was then used to estimate the rational runoff coefficient.
The second map from 1966 was an areal imagery map.It was georeferenced from aerial photographs developed by the US Department of Agriculture.The type of information available for this map is different from the 1898 land survey map.The 1966 map does not have an associated meta data file with it.However, the resolution offered much insight into the type of land cover.Dividing the area into tiles facilitated the visual analysis of the area and may be useful to decision makers and modelers as they explore changes in smaller areas of the County.
The land parcel map from 2019 has metadata with information helpful in identifying the land cover.Hence, it did not require visual analysis.The land parcel shapefiles were simply grouped into different land cover types based on the data.The rational runoff coefficient values for estimated using TxDOT hydraulic design manual.As with the 1966 map, these shapefiles are also useful to decision makers  The estimated rational runoff coefficients might be correlated to the population and industrial growth of the county.There had been a more than 1500% increase in population from 1900 to 1960 but the population has remained the same from 1960 to 2019.Post the Spindletop Oil Boom in 1901, the County saw a tremendous increase in industrial development and population.Comparison of the three maps showed that there had been a dramatic increase in urban areas, mostly along the Neches River from 1898 to 1966.However, a further increase in urbanized areas was minimal from 1966 to 2019.An overall timeline of the periods investigated in this research is depicted in Fig. 5.
Even though the rational runoff coefficients correlate with the development pattern of the county, they are not an accurate indicator of the surface imperviousness of detailed portions of the County.The current method has limitations such as the determination of land use type by visual analysis is prone to human error.The accuracy of the method is also heavily dependent on the grid sizes or subdivisions of the areas for visualization purposes.Choosing larger grid sizes offers an easy approach, but not accuracy.Dividing the maps into smaller grid sizes may generate more accurate results.
For instance, although the average rational runoff coefficient has not changed significantly from the 1960s to the 2010s, various smaller areas have.Some new neighborhoods have been built as the socioeconomics vary over time, while other areas may have been converted to greener spaces, perhaps due to environmental or other considerations.Two examples are in Figs. 6 and 7. Figure 6 depicts the Blossom Drive neighborhood in Beaumont that was heavily inundated with flood waters during Tropical Storm Imelda, even though it is not near the Neches River nor in a storm surge area, and therefore more representative of urban flooding.As can be seen, the neighborhood was developed between the years of the two more recent maps. Figure 7 shows an industrial area of the County, where many of the industrial structures have been removed and are now green spaces during this same period.
In addition, the rational method is rarely used for large areas for which more advanced hydrological methods have been developed to estimate runoff for various storm events [20].However, due to the complexity and additional spatial, rainfall, soil, storm system characteristics and other data needed for a more comprehensive evaluation, an initial estimate with the rational runoff coefficient is a valuable starting point.These preliminary spatial analyses are useful  in estimating the contributions of recent major flooding from overall development, or if they may be more impacted from other factors such as changes in weather patterns.Further research is required to establish the relationship between precipitation and land changes through history and flooding risk.

Conclusion
The rational runoff coefficient was estimated for three different years over the span of 120 years using detailed study and visual analysis of the available maps.The estimated runoff coefficients are in correlation with population growth pattern and industrial growth pattern of the county with 21% increase from 1898 to 1966 and no change from 1966 to 2019.Therefore, the increase in flooding may not be entirely attributed to the increase in urbanization of the County.Other factors such as climate changes may be responsible for the increase in flooding disasters.Further studies are required to validate the current study and to create a correlation between increased flooding and climate changes.

Fig. 3
Fig. 3 Land parcel map of Jefferson County overlaid with the county boundary

Fig. 4
Fig. 4 Maps from 1898, 1966 and 2019 showing the extent of rural and urban areas in Jefferson County.a 1898 land survey map, b 1966 USDA areal imagery map and c 2019 land parcel map

Fig. 5
Fig. 5 Timeline map showing the pattern of population growth, rational runoff coefficient and major developmental milestones

Fig. 6 Fig. 7
Fig. 6 Blossom Drive neighborhood in and after 1966 showing a developed area.a 966 USDA areal imagery map b 2018 NAIP image map (Tile number 10.04 and 11.03) County on the northeast, Hardin County on the north, Liberty County on the west and Chambers County on the southwest.The Neches River on the east separates Jefferson County from Orange County and Louisiana, whereas on the north, Pine Island Bayou separates Jefferson County from Hardin County.There are eight incorporated municipalities in Jefferson County: Beaumont, Bevil Oaks, China, Groves, Nederland, Nome, Port Arthur, and Port Neches

Table 2
Estimated watershed characteristics of 1898 land survey map Fig. 2 1966 Aerial Map Compilation of Jefferson County Overlaid with Grids

Table 3
Areas and watershed types of image tiles from 1966 Tile code

Table 5
Compilation of land use types of Jefferson county, 1966

Table 6
Land use types of Jefferson County, 2019

Table 9
Rational runoff coefficient for 2019 land parcel map