Hydrologic Engineering Center's Hydrologic Modeling System (HEC-HMS, Feldman, 2000) was developed by US Army Corps of Engineers. HEC-HMS consists of four different models to represent each component of the runoff process viz. models to compute runoff volume, direct runoff, baseflow, and channel routing. HEC-HMS is capable of performing both event and continuous hydrologic simulations. The Soil Moisture Accounting (SMA) algorithm is a continuous, semi-distributed and empirical loss method available within HEC-HMS. It consists of series of different layers for the movement of water within the land-based components (Bennett, 1998).

One of the most widely adopted methods for estimating soil erosion worldwide is Universal Soil Loss Equation (USLE). Modified Universal Soil Loss Equation (MUSLE) is an advancement over USLE, developed by replacing the rainfall erosivity factor with the runoff energy factor (Williams, 1975). Unlike USLE for annual sediment application, MUSLE is an event-based soil loss model which considers the effect of runoff energy on generating sediment. The mathematical expression for MUSLE is given by: S=95×(Q×qp)0.56×K×LS×C×P Where S is the sediment yield in tons, Q is the runoff volume in acre-ft, qp is the peak discharge (ft3 s-1 or cfs), K is the soil erodibility factor, LS is the topographic factor (ft), C is the cover management factor, and P is the support practice factor.

HEC's River Analysis System (HEC-RAS) version 5.0.3 (Brunner, 2016) was used in the present study. The model enables the simulation of the river using the two-dimensional (2-D) flow equations, also referred to as the shallow water equations. Inflows can be admitted through boundaries at the edge of the solution domain or even through direct rainfall. Use of 2-D solution is particularly adequate to consider effects of river meandering, proposed alternatives for stream modification and changes of velocity magnitude across the Dean-Road bridge cross-section.

Catchment delineation for the study area was performed using HEC's Geospatial Hydrologic Modeling Extension: HEC-GeoHMS (Doan, 2000). A stream definition of 0.4 sq. km was selected by using a trial and error method to match the generated streams with the natural streams. This procedure divided the donor catchment into 15 subcatchments and seven subcatchments for Soapstone Branch watershed.

Unsupervised classification using the Iterative Self-Organizing Data Analysis Technique (ISODATA, Nellis et al., 1998) with 40 classes of the similar spectral signature was applied to 2011 and 2015 National Agriculture Imagery Program (NAIP) dataset using ERDAS IMAGINE 2016 software. Using multispectral NAIP imagery, these 40 classes were categorized into 4 different land use types viz. forest (34.4 % in 2011; 28.7 % in 2015), agricultural land (56.3 % in 2011; 58.1 % in 2015), rangeland (8.7 % in 2011; 12.6 % in 2015), and water (0.6 % in 2011 and 2015). For improving the accuracy of land cover classification, the cluster busting technique was applied (Civco et al., 2002).

Sensitivity analysis is an important tool for decision makers to identify sensitive or important variables (Pannel, 1997). Therefore, a local sensitivity analysis was performed by varying the values of parameters ±10 % from initial estimates and their effect on Nash-Sutcliffe model efficiency (NSE) and percent error in volume (PEV) is shown in Figs. 3 and 4. On the basis of their sensitivities, parameters were ranked and then highly sensitive thus important parameters together with calibration parameters were then transferred to the receiver catchment. Finally, areal average values of highly sensitive and calibration parameters from the donor catchment were then applied to each of the seven subbasins (Fig. 5) of the Soapstone Branch catchment.

HEC-GeoHMS was used for background map development and creating the distributed-basin schematic model file for each of three study catchments. It was also used in checking of errors in catchment model development and connectivity of streams. HEC-HMS model setup for Soapstone branch catchment is shown in Fig. 5 as an example.

K factor was obtained from soil data available from SSURGO using the online USDA soil data viewer (https://www.nrcs.usda.gov/wps/portal/nrcs/detail/soils/home/?cid=nrcs142p2_053620). LS factor was calculated from slope length and slope gradient values obtained from 3.28 m (1 ft.) resolution DEM of the catchment. The C factor was developed from land cover maps provided by NLCD. However, the most recent available NLCD data is for 2011 and unable to account for land cover changes that occurred during the year 2011–2015. NAIP provides multispectral imagery at a spatial resolution of 1 m every 2 years making it suitable for our study. The C factor for the catchment was developed using normalized difference vegetation index (Gitas et al., 2009) for two different years 2011 and 2015 (Fig. 6) to account for the land cover change in the catchment. Since NAIP imagery was collected during the agricultural growing season (August–September) every two years in the continental US, the computed C factor values are conservative due to the absence of specific information on agricultural practices in the catchment, a conservative value of 1 was selected for P factor.

The DEM for Dale County, AL served as a base for the needed elevations for the HEC-RAS 5 model. Mesh sizes were selected so that the typical 2-D cell was around 1.5 to 2 m wide and there would be at least five cells across the bridge cross section. Recorded stage levels were used for model calibration and assessment. Through modification of DEMs using an algorithm implemented in Excel VBA, various alternatives of stream bed elevation near the bridge were considered, emulating the possible strategies for stream modification

A calibration period of three years from October 2009–September 2012 and a validation period of three years from October 2012–September 2015 were adopted for the donor catchment. NSE values of 0.73 during calibration and 0.63 during validation period were obtained which are rated as good and satisfactory performance by a continuous hydrologic model (Moriasi et al., 2007), respectively. The receiver catchment (Double Bridges Creek) is a gauged catchment, however to test the efficiency of the model parameter transfer process, it was assumed as an ungauged catchment for the model parameter transfer. The discharge was then simulated for the receiver catchment during a transfer validation period of three years from October 2009–September 2012. NSE value of 0.64 was obtained, which is rated as satisfactory performance for the continuous hydrological model (Moriasi et al., 2007). In 2010, some parts of Alabama experienced severe to extreme drought. Cumulative annual rainfall during this year varied from 508–1778 mm (20–70 in.). throughout Alabama (Tamang, 2017). Due to the fewer number of rainfall stations in both donor and receiver catchment and the discrepancy during this year introduced by the coarser spatial resolution of precipitation data have reduced the NSE values. The semi-distributed HEC-HMS model for Soapstone Branch catchment was then run from October 2009–September 2016 (Fig. 7) after transferring parameters from the donor catchment. During the study period, the annual average precipitation was 1361.4 mm (53.6 in.) with a standard deviation of 365.8 mm (14.4 in.) and range of 922 mm (36.3 in.). An initial warmup period of 9 months was selected to minimize the effects of initial estimated moisture value on the simulation. As seen from Fig. 7, streamflow was low and had fewer storm events in 2010 and 2011 whereas, the remaining years experienced higher streamflow and frequent storm events. The highest streamflow of 43.9 cumecs (1550 cfs) during the study period occurred on 14 December 2009 due to a storm event of 134.1 mm (5.28 in.).

Two alternative cross-sections modifications near the Dean Road bridge site were simulated thus far using HEC-RAS 5. The geometric characteristics of the stream modification are presented in Fig. 8. The small trapezoidal alternative creates more significant blockage to the flow, which reflects on the higher velocities across the bridge, as shown in Fig. 9.

The small trapezoidal stream modification alternative also creates an increase in backwater effect, and both these have an impact on the resulting shear stress under the bridge. The large trapezoidal peak shear stress is in the range of 0.49 kg m-2 (0.10 lb ft-2), which is 70 % smaller than the corresponding value for the small trapezoidal solution (Fig. 10). Also, as it may be noticed, the region with larger shear stresses downstream from the bridge site are much wider in the small trapezoidal alternative (Fig. 11).

In order to apply event-based MUSLE to continuous streamflow simulation, a threshold of 0.28 cumecs (10 cfs) was selected for sediment generation. SMA model discharge was applied to MUSLE equation to calculate event sediment yield and each event output for a year were summed up to obtain annual sediment yield from 2010–2015 (Fig. 12). In the calculation of sediment yield by MUSLE, 2011 C factor value of 0.347 was determined and applied from 2011–2012 whereas, 2015 C factor value of 0.648 was applied from 2013–2015. During the study period, 2013 had the highest number of storm events i.e. 24 generating sediment whereas 2011 had the lowest number of storm events that generated sediment i.e. 4. The event on 22 February 2013 produced the maximum sediment yield of ∼ 9400 tons. It was also found that the maximum annual sediment yield of 69 439 tons in the catchment was in 2013 which is consistent with the first identification of the aggradation problem. Also, the recent land-cover changes in the catchment have accounted for 34 % increase in sediment yield. The uncertainty of the proposed model for sediment yield computation is dependent on two different parameter sets viz. parameters from hydrologic model and parameters forming the remaining MUSLE equation. Since the discharge is computed for the Soapstone branch only after validating the parameter transfer to an assumed ungauged receiver catchment, the uncertainty associated with the discharge parameters is low and can be considered within the range of satisfactory performance. Also, the attempts were made to reduce the uncertainty of remaining MUSLE parameters by obtaining the data of highest spatial and temporal resolution available, and conservative values viz. 1 m resolution DEM for LS factor, conservative values of C and P factor.