Hydrologic Data

The study area’s hydrologic network consists of two streamgages (fig. 1B; table 1); USGS streamgages 03238785 and 03238798 have been in operation since February 23, 2017. The upstream streamgage (station number 03238785; Grays Crossing streamgage) is operated as a stage-discharge gage, and the downstream streamgage (station number 03238798; Highway 8 streamgage) is operated as a stage-only gage. Because the NWS does not issue forecasts for Fourmile Creek, another regional streamgage is critical for this study. The Cincinnati streamgage (station number 03255000) is a stage-only gage on the Ohio River at Cincinnati, Ohio, and is designated as the NWS AHPS site CCNO1 (fig. 1A; table 1). The NWS issues forecasts year round for the Ohio River at Cincinnati. The forecasts show estimated river stage up to 5 days into the future. At all three streamgages, stage is measured every 15 minutes, transmitted hourly by a satellite radio in the streamgage, and made available on the internet through the USGS National Water Information System (U.S. Geological Survey, 2021b, c, d). Stage data from these streamgages are referenced to local datums but can be converted to water-surface elevations referenced to NAVD 88 by adding the stage measurement and its respective datum shown in table 1. The Cincinnati streamgage has a gage datum currently (2022) referenced to the National Geodetic Vertical Datum of 1929 (NGVD 29), but this study references all elevations to NAVD 88, so the gage datum was converted to NAVD 88 by computing the difference in orthometric height between NAVD 88 and NGVD 29 (in this case −0.65 ft) using the North American Vertical Datum Conversion (VERTCON) (Milbert, 1999; National Geodetic Survey, 2021) and adding the difference to the NGVD 29 elevation. Continuous records of streamflow for the Grays Crossing streamgage are computed from a stage-discharge relation (rating curve) developed and periodically updated as additional discharge measurements are made. Stage and discharge data from the Grays Crossing streamgage were used for calibration of the model and comparison of model results.

The streamflows used in the model simulations (table 3) were obtained from either the current stage-discharge relation (USGS rating number 1.1, effective May 7, 2020, and current at the time of this investigation [2022]) or a theoretical rating for the Grays Crossing streamgage, and the streamflows corresponded with the target (incremental) stages. The current stage-discharge relation is based on discharge values with known stages from actual streamflow measurements at the streamgage. Flow events down Fourmile Creek happen so quickly that it is difficult to complete an actual streamflow measurement during the peak. Additionally, the period of record for this streamgage is relatively short (about 5 years), and large, less frequent events have not occurred since the streamgage was installed. The maximum discharge recorded to date at the Grays Crossing streamgage was 2,350 ft³/s on May 18, 2020 (table 1). A theoretical rating needed to be used because the current stage-discharge relation only goes up to a stage of 8.54 ft (2,560 ft³/s), and this study required a maximum input flow rate of at least a 2-percent AEP flood (8,000 ft³/s; table 2). Additionally, although rating number 1.1 for the Grays Crossing streamgage includes an extension from 6.50 to 8.54 ft (6.50 ft is approximately the highest modeled value based on actual streamflow measurements), the theoretical rating developed for this study was used instead of the extended portion of rating number 1.1. Because the theoretical rating was developed by using a hydraulic model that incorporates topographic and bathymetric data, it is considered more accurate than the extension that was used for rating 1.1. Three major tributaries join Fourmile Creek within the 3.4-mi study reach (the drainage area increases 80 percent from the upstream end to the downstream end; fig. 1B; table 1); therefore, the discharges were adjusted for tributary inflows by means of drainage area ratios with coefficients (exponents) for Region 1 from Hodgkins and Martin (2003). This was done in the hydraulic model with a flow-change location just downstream from each tributary confluence.

Topographic and Bathymetric Data

All topographic data used in this study are referenced vertically to NAVD 88 and horizontally to the North American Datum of 1983. Cross-section elevation data for the land surface were obtained from a 5- by 5-ft-resolution digital elevation model (DEM) that was derived from light detection and ranging (lidar) data collected as part of a larger statewide mapping effort during 2010–17 by Photo Science, Inc. The lidar data for Campbell County were collected in 2012. The DEM was obtained from the KyFromAbove website at https://kyfromabove.ky.gov. The lidar data were collected at a 2.3-ft (0.7-meter) or better nominal pulse spacing (horizontal resolution) and have a vertical accuracy of 0.30-ft (9.25-centimeter) root-mean-square error. With that resolution and accuracy, the lidar data support production of 1-ft contours (Dewberry, 2012). The USGS created 1-ft contour lines from the DEM data for use in floodplain-boundary delineation using ArcGIS.

Because lidar data cannot provide ground elevations below a stream’s water surface, channel cross sections were surveyed by a USGS field crew in May 2019. A total of 11 cross sections were surveyed along the study reach. The USGS used both differential global navigation satellite system (GNSS) surveys and differential-leveling surveys (“conventional” surveys) for this study. Differential GNSS surveys were done to establish a horizontal and vertical control network at selected locations along the study reach. Conventional surveys were done to obtain stream and hydraulic-structure geometry. All conventional survey data collected met horizontal and vertical third-order accuracy criteria (Federal Geodetic Control Committee, 1984). Differential GNSS surveys were done using level III real-time GNSS surveying techniques (Rydlund and Densmore, 2012). Elevations determined by using a differential GNSS at three nearby benchmarks had a root-mean-square error of 0.10 ft compared to the National Geodetic Survey published elevations.

By using the Hydrologic Engineering Center’s Geospatial River Analysis System (HEC-GeoRAS) computer program (U.S. Army Corps of Engineers, 2011), which is a set of procedures, tools, and utilities for processing geospatial data in ArcGIS, land-surface elevation data were extracted from the DEM for 117 cross sections at desired locations along the study reach. DEM-derived cross-section data were colocated with the 11 in-channel field-surveyed cross sections where possible. In those cases, in-channel data were directly merged with the DEM data. The bathymetric data for the DEM-derived cross sections that did not have surveyed in-channel cross sections were estimated (accounting for channel-bed elevation and bottom-of-channel width) by interpolating between the closest upstream and downstream field-surveyed cross sections. These data subsequently were input to the HEC-RAS model.

Although HEC-GeoRAS was used for much of this study, most of the same geospatial capabilities are now available in HEC-RAS within the RAS Mapper module. After the initial model development, refinements to the geometry of the hydraulic model (such as extending cross sections) were made by using RAS Mapper. One additional feature within RAS Mapper is the ability to have the in-channel bathymetry merged with (sometimes referred to as “burned” or “carved” into) the DEM data, resulting in a combined DEM that contains overbank (floodplain) and in-channel elevations. The combined DEM was used in the development of the flood-inundation maps to improve the accuracy of estimates of water depth within the main channel.

Hydraulic Structures

Various structures (bridges, culverts, and roadway embankments) in and along Fourmile Creek affect or have the potential to affect water-surface elevations along the stream during floods. To properly account for these features in the model, structural dimensions for two bridges, five culverts, and three roadway embankments were obtained from field surveys as described in the “Topographic and Bathymetric Data” section and subsequently input to the HEC-RAS model. The hydraulic structures in and along Fourmile Creek include (from upstream to downstream) a single-span bridge at Uhl Road, a single-span bridge at Messmer Road, a roadway embankment (Tiemeier Lane) with a circular culvert underneath, a roadway embankment (Kentucky Route 8, also known as Highway 8 or Mary Ingles Highway) with two identical box culverts underneath, and a railroad embankment with one box culvert and one arch culvert underneath (fig. 1B; fig. 2). Off-channel culvert locations were confirmed, where possible, by aerial imagery or field inspection; the confirmation of culvert locations was needed to aid in determining whether disconnected flood-inundation areas are actually connected to the river or are just low areas in the topography. No levees or flood-management structures are known to exist in the study reach.

Energy-Loss Factors

Hydraulic analyses require the estimation of energy losses that result from frictional resistance exerted by a channel on the flow. These friction coefficients (Manning’s roughness coefficients or n values) account for energy (friction) loss in the model (Arcement and Schneider, 1989). Initial (precalibration) n values for the channel and floodplain were selected on the basis of field observations, high-resolution aerial photographs, and the most recent FIS. As part of the model-calibration process, the n values were adjusted from initial estimates until the differences between computed and rating-based (rating number 1.1, not theoretical) water-surface elevations at the Grays Crossing streamgage were minimized for the given streamflows. This process also involved roughness-coefficient adjustment factors (flow roughness factors), which are a feature in the model that allows the specified n values to adjust with changes in flow. The final Manning’s n values ranged from 0.023 to 0.052 for the main channel and from 0.050 to 0.055 for the overbank areas.

Hydraulic Model

The hydraulic analysis for this study was done by using HEC-RAS (version 5.0.7) with one-dimensional steady-state flow calculations. Inputs for steady-state flow calculations consisted of flow regime, boundary conditions, and streamflow estimates that produced modeled water-surface elevations at the Grays Crossing streamgage cross section that closely matched target water-surface elevations. The target water-surface elevations coincided with 0.5-ft or 1-ft increments of stage, referenced to the local gage datum. A mixed flow regime was used for the simulations, but the flow was subcritical (tranquil) nearly all of the time. A baseline water-surface elevation of 460 ft (NAVD 88) was used as the reach’s downstream boundary condition for the hydraulic model and is representative of a normal pool level on the Ohio River at Silver Grove (U.S. Geological Survey, 2021c). For the combined flooding scenarios on Fourmile Creek and the Ohio River, the downstream boundary condition was varied from 478 ft to 492 ft (NAVD 88) in 2-ft increments to represent a variety of backwater-flooding conditions. The 478-ft elevation is approximately 6 ft below the NWS flood stage at the Cincinnati streamgage (considering the elevation offset on the Ohio River between Cincinnati and Silver Grove). The purpose for starting the range below the flood stage on the Ohio River is to account for possible coincident flooding on Fourmile Creek. The 492-ft elevation is approximately 4 ft above the NWS moderate flood stage at the Cincinnati streamgage (again, considering the elevation offset on the Ohio River between Cincinnati and Silver Grove). Thus, this range of downstream boundary conditions represents a range of minor and moderate flood events on the Ohio River that on their own are not too impactful on the city of Silver Grove but could be damaging if there is coincident flooding on Fourmile Creek. The upstream boundary condition was a series of input flow rates (streamflow estimates), as discussed in the “Hydrologic Data” section.

The hydraulic model was calibrated to the current stage-discharge relation at the Grays Crossing streamgage by using the vertical datum of the streamgage to convert the stage information to NAVD 88 elevations. The stage-discharge relation used for the Grays Crossing streamgage was rating number 1.1, which allows for computation of streamflow for stages as high as 8.54 ft. The model was calibrated by adjusting Manning’s n values and flow roughness factors until the results of the hydraulic computations minimized the differences between the rating-based (target) water-surface elevations and the simulated peak streamflows. Differences between target and computed water-surface elevations for a range of simulated flows (corresponding to stages from 4.0 to 8.5 ft) at the Grays Crossing streamgage were all within ±0.30 ft (table 4). The model calibration occurred before the theoretical rating extension was developed, and the relatively large differences above a stage of 6.5 ft support the use of the theoretical rating. The results demonstrate that the model is capable of simulating reasonable water levels over a range of flows (within the range covered by rating number 1.1) at the streamgage. Because this study needed simulated flows greater than the upper end of the calibrated range (8.5 ft), the results for those flows should be used with caution.

Development of Water-Surface Profiles

The calibrated hydraulic model was used to generate water-surface profiles corresponding to 83 combinations of flood stages on the Ohio River and Fourmile Creek at incremental stages ranging from 4 ft to 16 ft, as referenced to the Grays Crossing streamgage, and with Ohio River backwater conditions ranging from normal pool (460 ft, NAVD 88) to various flooding conditions (478–492 ft, NAVD 88). See appendix 2 for a table of modeled stage combinations. Water-surface profiles for selected stages modeled, including the lowest (4 ft) and the highest (16 ft) stages, with the Ohio River at a normal pool level are shown in figure 2.

Backwater flood profiles (from the Ohio River) did not require a hydraulic model and instead were computed for the Fourmile Creek reach by means of spatial analysis within GIS software. A total of 50 water-surface profiles were produced for flood elevations at 1-ft intervals referenced to the Highway 8 streamgage and ranging from approximately normal pool (460 ft, NAVD 88) to approximately a 0.2-percent AEP flood (509 ft, NAVD 88) on the Ohio River. For each water-surface profile, a flat (level) backwater profile from the Ohio River and negligible flow coming down Fourmile Creek were assumed.

Flood-Inundation-Map Delivery

The flood-inundation maps from this study depict estimates of the areal extent and depth of flooding corresponding to selected water levels (stages) at Fourmile Creek at Grays Crossing at Silver Grove, Ky. (USGS streamgage 03238785), and Fourmile Creek at Highway 8 at Silver Grove, Ky. (USGS streamgage 03238798). A Flood Inundation Mapping Science website (U.S. Geological Survey, 2021e) has been established to make information from USGS flood-inundation studies available to the public; that site links to a mapping application (https://fim.wim.usgs.gov/fim/) that presents map libraries and provides detailed information on flood-inundation extents and depths for selected sites. The mapping application enables the production of customized flood-inundation maps from the map libraries for Fourmile Creek at Silver Grove, Ky. A link on each map library connects to the USGS National Water Information System (U.S. Geological Survey, 2021b, c), which presents the current stage and streamflow at the Grays Crossing streamgage and the current stage at the Highway 8 streamgage to which the flood-inundation maps are referenced. Another link within the mapping application connects to the NWS AHPS site (National Weather Service, 2021a) so that the user can obtain applicable information on forecasted peak stage for the Cincinnati streamgage on the Ohio River.

The estimated flood-inundation maps are displayed in sufficient detail for informed decisions to be made about potential flooding for the purposes of flood preparation and emergency response. Depending on the flood magnitude, roadways and bridges are shown as shaded (inundated and likely impassable) or not shaded (dry and passable) to facilitate emergency planning and use. A shaded building should not be interpreted to mean that the structure is completely submerged but, rather, that the land surfaces near the building are inundated. In these instances, the water depth (as indicated in the mapping application by clicking the cursor over an inundated area) near the building would be an estimate of the water depth inside the structure (at ground level), unless flood-proofing measures had been implemented.

Disclaimer for Flood-Inundation Maps

The flood-inundation maps should not be used for navigation, regulatory, permitting, or other legal purposes. The USGS provides these maps “as-is” for a quick reference, emergency planning tool but assumes no legal liability or responsibility resulting from the use of this information.

Uncertainties and Limitations Regarding Use of Flood-Inundation Maps

Although the flood-inundation maps represent the boundaries of inundated areas with a distinct line, some uncertainty is associated with these maps (Bales and Wagner, 2009). The flood boundaries shown were estimated on the basis of water stages and streamflows at selected USGS streamgages. Water-surface elevations along the stream reach were estimated by steady-state hydraulic modeling, assuming unobstructed flow, and using streamflows and hydrologic conditions anticipated at the USGS streamgages. The hydraulic model reflects the land-cover characteristics and any bridge, culvert, or other hydraulic structures existing as of May 2019. Meteorological factors (timing and distribution of precipitation) can cause actual streamflows along the modeled reach to vary from those assumed during a flood, which could lead to deviations from the water-surface elevations and inundation boundaries shown. Additional areas could be flooded because of unanticipated conditions such as changes in the streambed elevation or roughness, backwater into major tributaries along a main-stem river, or backwater from localized debris or ice jams. The accuracy of the flood-inundation extent portrayed on these maps will vary with the accuracy of the DEM used to simulate the land surface. Additional uncertainties and limitations pertinent to this study could be described elsewhere in this report.

If this series of flood-inundation maps will be used in conjunction with NWS river forecasts, the user should be aware of additional uncertainties that could be inherent or factored into NWS forecast procedures. The NWS uses forecast models to estimate the quantity and timing of water flowing through selected stream reaches in the United States. These forecast models (1) estimate the amount of runoff generated by precipitation and snowmelt, (2) simulate the movement of floodwater as it proceeds downstream, and (3) predict the flow and stage (and water-surface elevation) for the stream at a given location (AHPS forecast point) throughout the forecast period (every 6 hours and 3–5 days out in many locations). More information on AHPS forecasts is available at https://water.weather.gov/ahps/about/about.php.

Although the flood-inundation maps created in this study cover a wide range of combined flooding scenarios on Fourmile Creek and the Ohio River, not every possible flooding scenario could be represented because of the incremental nature of the flood-inundation maps and flood-peak timing. The hydraulic modeling and flood-inundation mapping assumed coincident flood peaks for the two streams studied, and actual flood-peak timing within the study area is important to understand. The drainage areas for the two streams studied are orders of magnitude different from one another (9.8 mi² for Fourmile Creek at Grays Crossing, as opposed to 76,580 mi² for the Ohio River at Cincinnati; table 1), which affects the time scale at which each stream responds to precipitation events. Fourmile Creek is a flashy stream, which means runoff from rainfall within its relatively small drainage basin causes a rapid rise and fall in the gage height. Flooding on the Ohio River typically occurs with more widespread rainfall (sometimes accompanied by snowmelt), resulting in water levels that rise and fall at slower rates than on small tributary streams. In general, the time scale for a flood on Fourmile Creek is on the order of several hours to a day, whereas the time scale for a flood on the Ohio River is on the order of several days to weeks. Some examples can help illustrate these situations.

Figure 5A shows an example of separate Fourmile Creek flooding and Ohio River backwater-flooding peaks recorded at the Grays Crossing streamgage. The first peak was from flooding coming down Fourmile Creek and is characterized by a rapid rise and fall with a sharp peak, and the second peak was from a flood on the Ohio River that caused backwater flooding up Fourmile Creek and is characterized by a slower rise and fall along a broader curve (fig. 5A). The duration of the Fourmile Creek flood was about 15 hours, and the duration of the Ohio River flood was about 4 days (U.S. Geological Survey, 2021b).

On the other hand, figure 5B shows an example of a more complex flooding scenario involving combined Fourmile Creek and Ohio River backwater-flooding peaks recorded at the Grays Crossing streamgage. The first two peaks are independent flooding events coming down Fourmile Creek. Then a flood on the Ohio River caused backwater flooding up Fourmile Creek. The flood on the Ohio River was receding when a series of additional precipitation events caused more flooding down Fourmile Creek and the Ohio River to rise again, which caused more backwater flooding (fig. 5B). This example illustrates that combined Fourmile Creek and Ohio River flooding scenarios can be complex and that flooding extents and depths differ by location within the study area.

An additional limitation is that the flood-inundation maps produced in this study are referenced to a streamgage that is not designated as an NWS AHPS forecast point. For the Grays Crossing streamgage, the Fourmile Creek drainage area is too small to be included in the current model configuration used by the NWS for flow forecasts (Brian Astifan, National Weather Service, written commun., July 27, 2021). For the Highway 8 streamgage, the water-surface elevations are strongly influenced by backwater from the Ohio River. Consequently, it was decided to relate the NWS AHPS forecast for the Ohio River at the Cincinnati streamgage (as discussed in the “Hydrologic Data” section) to the Highway 8 streamgage by adding an elevation offset calculated from observed data. When there is a flood on the Ohio River, the Highway 8 streamgage is often effectively the same as the water-surface elevation of the Ohio River at the mouth of Fourmile Creek (river mile 461.2). The Cincinnati streamgage is approximately 9.3 river miles downstream from the mouth of Fourmile Creek (fig. 1A). Using an elevation offset to forecast water levels at the Highway 8 streamgage based on the forecast at the Cincinnati streamgage is possible in this reach because of open river conditions, a mild slope, and a relatively small distance between the two streamgages; however, there are two tributaries (Little Miami River and Licking River) that join the Ohio River within this reach that add uncertainty to the elevation offset.

The elevation offset between the Cincinnati streamgage and the Highway 8 streamgage was calculated by analyzing each flood event with a peak greater than 40 ft (action stage) at the Cincinnati streamgage for the period of record of the Highway 8 streamgage (U.S. Geological Survey, 2021c, d). For each qualified flood event, the peak stage and time of peak at both the Cincinnati streamgage and the Highway 8 streamgage were extracted and screened for anomalies, and the stages were converted to a water-surface elevation in NAVD 88. A total of 33 peaks were used in this analysis, and the difference between the water-surface elevation and the time of peak was calculated for each peak. On average, the peak water-surface elevation at the Highway 8 streamgage was 4 ft greater (standard deviation of 0.5 ft) and occurred 1 hour earlier (standard deviation of 1 hour) than the peak water-surface elevation at the Cincinnati streamgage. A more complex relation for the elevation offset between the Cincinnati streamgage and the Highway 8 streamgage could be calculated, but that is beyond the scope of this report and would likely only offer marginal improvement. Moreover, if a new AHPS forecast point on the Ohio River at Silver Grove were created in the future, then that forecast could be used directly at the Highway 8 streamgage. The elevation offset between the Cincinnati streamgage and the Highway 8 streamgage can be used in conjunction with the NWS AHPS forecast peak-stage information to select the appropriate flood-inundation map for Ohio River backwater flooding in Silver Grove.