World Environmental and Water Resources Congress 2008: Ahupua'a

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1 Soil Erosion and Sediment Yield Modeling with the Hydrologic Modeling System (HEC-HMS) By Jang Pak 1, Matt Fleming 1, William Scharffenberg 1, and Paul Ely 2 1 U.S. Army Corps of Engineers, Institute For Water Resources, Hydrologic Engineering Center, 609 Second Street, Davis, CA 95616; PH (530) ; FAX (530) ; respectively, Jay.H.Pak@usace.army.mil, Matthew.J.Fleming@usace.army.mil, William.A.Scharffenberg@usace.army.mil 2 Consultant, 414 Highland Avenue, Trinidad, CA 95570; PH (707) ; paul@ely.name Abstract The effects of surface erosion and stream sediment loading in watersheds have become increasingly important in water quality best management practices (BMPs), watershed management, and natural resources conservation planning. Many water resources studies must now consider the erosion related effects of watershed activities. Surface erosion models describe the detachment, deposition and transport of soil particles by the erosive forces of raindrops and surface flow of water from their point of origin to the watershed outlet. The current version of the Hydrologic Modeling System (HEC-HMS) contains no capacity to simulate surface erosion processes; however, the need of erosion and sediment yield modeling exists throughout the Corps of Engineers, especially as the Corps moves towards watershed level investigations, including Total Maximum Daily Load (TMDL) studies. Therefore, the Hydrologic Engineering Center (HEC) has added existing, developed new and tested soil erosion and sediment yield methods to include in HEC-HMS. The goal is to develop tools within HEC-HMS that provide output necessary for making informed decision about managing soil erosion within the watershed. This paper discusses the addition of soil detachment, deposition and transport methodologies to the HEC-HMS program These new sediment modeling tools will increase the application of HEC-HMS for sediment modeling studies by directly computing sediment yield. An effort was made to ensure that sediment output from HEC-HMS could be easily used as boundary conditions in HEC-RAS for more detailed river mechanics modeling. Two surface erosion methods were included in the HEC-HMS subbasin element to model sediment erosion/wash-off for both pervious and impervious areas. In addition, an in-channel sediment routing method was included in the HEC-HMS reach element. These methods model the translation and attenuation of the sediment load along with deposition and erosion processes occurring in the channel. 1

2 Introduction The Hydrologic Engineering Center s Hydrologic Modeling System (HEC-HMS) is a computer program designed to model watershed hydrology. Historically, HEC-HMS has focused on modeling rainfall-runoff processes; however, a significant effort is underway to add sediment and water quality modeling capabilities. This paper provides a description of the surface erosion and in-stream sediment modeling capabilities that will be available in future versions of HEC-HMS. The subbasin element is one of seven hydrologic elements that compose a basin model network in an HEC-HMS model. The subbasin element is used to represent a drainage basin where precipitation falls, infiltration occurs, and surface runoff may result. Outflow from the subbasin element is calculated by subtracting precipitation losses due to interception by the canopy, storage on the land surface and infiltration into the soil from the total precipitation. Once losses have been computed, the excess precipitation is treated as surface runoff and transformed to stream flow at the subbasin outlet, and baseflow is added. Initially, two surface erosion methods will be included in the subbasin element: the Modified Universal Soil Loss Equation (MUSLE) and the build-up and wash-off methods. The MUSLE method simulates the sediment yield processes from a pervious land segment and the build-up and wash-off method simulates sediment yield processes from an impervious land segment. Future work will eventually include adding additional erosion methods suitable for both pervious and impervious areas, allowing the engineer to select the best method for a specific watershed study. Before sediment from the land surface is available to the reach element, a sediment enrichment ratio is introduced to determine the relationship between particle size of watershed sediment and fluvial suspended sediments. The enrichment ratio presents a mechanism to translate the sediment distribution from the land surface throughout the basin to a sediment distribution representative to that found at the basin outlet. The reach element is one of seven hydrologic elements that compose a basin model network in an HEC-HMS model. The reach element is used to convey stream flow downstream in the basin model. Inflow into the reach element can come from one or many upstream hydrologic elements. Outflow from the reach is calculated by accounting for translation and attenuation of the inflow hydrograph. Multiple methods for modeling sediment transport and erosion/deposition within the channel will be added to the reach element. Several sediment transport equations can be used to route sediment through the stream network in HEC-HMS. The sediment continuity equation was used in conjunction with a sorting algorithm to solve for the actual volume of deposition or erosion. Additionally, temporal entrainment and deposition functions similar to those employed in HEC-RAS have been adapted for use in HEC- HMS. 2

3 Surface Erosion Modeling sediment from the land surface is important because sediment transports nutrient and toxic materials from urban, agricultural and forested lands. Many methods are available for modeling sediment from watershed surface (Wischmeier and Smith, 1965 and 1978; Renard, 1997; Foster, 2003; Williams, 1975; Leavesley et al. 1983; Bicknell et al. 2001). The first surface erosion method added to HEC-HMS was the Modified Universal Soil Loss Equation (MUSLE) method. William (1975) developed the MUSLE method to predict sheet and rill erosion from a single rainfallrunoff event. The rainfall energy factor (R) in the USLE model was replaced with a runoff energy factor (R m ). The runoff energy factor was designed and validated using data from 18 watersheds ranging in size from three acres to over 4,000 acres. Williams (1975) argued that the modified method s inclusion of a runoff energy factor produced a more accurate estimate of sediment yield because watershed characteristics influence runoff rates and sediment yield in a similar manner. This conclusion was supported by additional research (Kinnell 1998). The runoff energy factor in the MUSLE method is a good match for the methods and philosophy of HEC-HMS. The MUSLE method computes the sediment yield from a pervious land segment based on Eq. 1 for a storm event (Williams, 1995) Sed = 11.8 ( Q q ) K LS C P (1) surf peak where Sed is the sediment yield for a given event (metric tons), Q surf is the surface runoff volume (m 3 ), q peak is the peak runoff rate (m 3 /s), K is the soil erodibility factor, LS is the topographic factor, C is the cover and management factor, and P is the support practice factor. The MUSLE method can be used in HEC-HMS to determine sediment yield for one rainfall-runoff event or from a multi-year simulation. Not all rainfall-runoff events generate sediment; therefore, additional parameters were added to the MUSLE method, as calibration factors in HEC-HMS, to allow the engineer to define which events would be considered sediment generating rainfall-runoff events. A sediment generating rainfall-runoff event is identified using the combination of two criteria, critical time period and threshold peak runoff rate. The threshold peak runoff rate is used to determine whether enough a runoff rate resulted from the event to likely entrain sediment. The critical time period defines the minimum duration based on the physiographic factors (slope, area, and shape etc.) for which a runoff hydrograph will generate sediment. Once sediment is entrained, additional energy is needed to move sediment through the watershed to the outlet without re-deposition. Only storm events that exceed the critical time period are assumed to have this energy. HEC-HMS tracks the amount of time the direct runoff hydrograph is greater than the threshold flow. The direct runoff must exceed the threshold flow for longer than the critical time period, in order for the event to generate sediment. Figure 1 shows an example 3

4 of how the critical time period and threshold flow could be used to define sediment generating events. For this example a threshold flow of 40 cms and a critical time period of 2-hour are used. Given this threshold, there are two events where sediment could be generated; however, only one of these events meets the critical time period criteria. HEC-HMS would only compute sediment runoff for the 3 rd rainfall-runoff event because this event maintains a flow rate greater than the threshold for duration longer than the critical time period. This storm event contained enough energy to move the sediment to the basin outlet. Flow (CM S) Hour Time Period Flow Threshold 2-Hour Time Period Figure 1. Example of using a threshold flow and hydrograph time-window to define a sediment event. Erosion from impervious areas is fundamentally different from pervious areas where the MUSLE approach may apply. A common approach to modeling impervious areas is the build-up and wash-off method, similar to SWMM, Storm Water Management Model (Huber and Dickinson, 1988) and Soil and Water Assessment Tool (SWAT) 2005 (Neitsch et al. 2005). In this approach, sediment accumulates on the watershed between storm events. All of the accumulated sediment or possibly only a portion of it washes off during a storm event. Street cleaning operations may also be incorporated into the modeling process. The build-up and wash-off method tracks the time between storm events to accumulate sediment from an impervious land segment. Build-up of solids is calculated based a Michaelis-Menton formulation as shown in Eq. 2 (Huber and Dickinson, 1988). SEDmx td SED = ( t + td) half (2) where, SED is the solid build up (kg/curb km) td days after the last occurrence of SED = 0 kg/curb km, SED mx is the maximum accumulation of solids possible for the urban land type (kg/curb km), t half is the length of time needed for solid build up to increase from 0 kg/curb km to ½ SED mx (days), and td is a day with surface runoff less than 0.1 mm. The build-up and wash-off method computes a time-series of load. 4

5 An equivalent time-series of concentration can be computed by dividing the load by the flow volume for each time interval. Wash-off is represented by an exponential curve, Eq. 3, that is a function of the accumulated sediment at the beginning of the storm, and the peak flow rate of the storm (Huber and Dickinson, 1988). Therefore, it is necessary to know the peak flow that immediately follows the initiation of direct runoff. Y sed = SED (1 e 0 urbcoef q peak t ) (3) where Y sed is the cumulative amount of solids washed off at time t (kg/curb km), SED 0 is the amount of solids built up on the impervious area at the beginning of the precipitation event (kg/curb km), urb coef is the wash off coefficient (mm -1 ) ( mm -1 ), and Q peak is the peak runoff rate (mm/hr). Street cleaning operation is performed to control build-up of solids in urban areas. The sweep process (Huber and Dickinson, 1988) is simulated based on Eq. 4. SED = SED 0 (1 fr av reff ) where SED is the amount of solids remaining after sweeping (kg/curb km), SED 0 is the amount of solids present prior to sweeping (kg/curb km), fr av is the fraction of the curb length available for sweeping, and Reff is the removal efficiency of the sweeping equipment. The available factor and removal efficiency are specified by the user. Whether the simulation run includes one storm event, several events, or many events, it is necessary to distribute the total sediment yield as a time-series. As a result, HEC-HMS computes both a concentration time-series and a load time-series. The MUSLE and build-up and wash-off methods compute only the sediment yield per event. A procedure was needed to translate this yield to a time distribution of sediment yield. The concentration time-series is computed using a power function of water discharge (Haan et al. 1994). An equivalent time-series of loading can be computed by multiplying the concentration for each time step by the flow rate for that same time step. Enrichment Ratio (4) Significant errors may result if the transportability of sediment is inferred from dispersed particle size distributions rather than actual or effective sediment sizes (Slattery, 1996). Knowledge of the changes in the particle size distribution from source material at the point of erosion to the catchment discharge point is important to understand the comprehensive sediment transport process at work in the watershed. The physical relationship between particle size characteristics of eroded material and source material is complex but simple ratios can be used to update the erosion and sediment delivery processes operating throughout the watershed (Slattery, 1996). An 5

6 enrichment ratio option is provided in the sediment routing features of HEC-HMS that converts the watershed particle size distribution into an outlet particle-size distribution that reflects in-stream gradations. The enrichment ratios (ER) for each particle size are determined from Eq. 5. % sediemnt in a given size class in outlet ER = % sediement in a given size class in watershed (5) An ER value greater than 1 represents an enrichment condition: a given size class forms a greater percentage of the transported load at the outlet than at the source. An ER value less than 1 represents a depletion condition: a given size class forms a greater percentage at the source than in the transported load at outlet. In-Stream Sediment Routing Multiple in-stream sediment modeling methods were selected and tested for HEC- HMS. The hypothetical sediment reservoir method was selected among them as the first method because it provides a better representation of the physical processes as described below. In-stream sediment routing consists of calculating transport capacity, modification of the hypothetical channel bottom to reflect deposition or erosion, and routing of the sediment load from upstream to downstream. For each flow in the runoff time-series, a water surface profile and the resulting hydraulic parameters were calculated based on fixed channel geometry. The model calculates sediment transport capacity by a number of available methodologies. The sediment continuity equation is solved in conjunction with sorting algorithms to solve for the actual volume of deposition or erosion. Additionally, temporal entrainment and deposition functions similar to those employed in HEC-RAS (Gibson et al. 2006; Bruner and Gibson, 2005) have been adapted to control how much deposition and erosion can occur during one time-step. Finally, a sediment routing method was used to route sediment from upstream to downstream. Transport Calculations Seven different transport functions will be available in HEC-HMS and include the Ackers and White (1973), Englund-Hansen (1967), Laursen (1958), Myer-Peter-Muller (1948), Toffaleti (1968), Yang (1972), and Wilcock (2003) functions. The engineer will have the option to divide the sediment gradation curve into discrete size classes. The program will compute the sediment transport potential independently using one of seven transport functions for each grain size class in the bed. The transport potential is multiplied by the fraction of each size class present in the bed a model time step to yield the transport capacity for that size class (USACE 1993). Based on the sediment transport capacity, the sediment continuity equation is solved for the reach segment to update the depth of the active layer. Physical Constraints to Erosion and Deposition: Without physical constraints, surplus or deficit sediment computed by the sediment continuity equation would go 6

7 directly into deposition or erosion within one time step. HEC-HMS implements methodologies similar to those in HEC-RAS for applying temporal erosion and deposition modifiers to enhance the sediment continuity calculations. Deposition can be limited using Toffaleti s concentration relationships (Vanoni, 1975). Using fall velocity and the expected center of mass of the material in the water column, the deposition rate can be calculated for each grain size using Eq. 6. Deposition Rate = V s ( i) () i D e t (6) where V s (i) is the settling velocity for particle size i, D e (i) is the effective depth for sediment size i (e.g. the midpoint of the depth zone in which transport is expected for the grain class), and t is the duration of the computational time step (USACE (1993) and Thomas (1994)). The temporal modifier for erosion uses the characteristic length approach found in HEC-6. This approach follows the assumption that erosion takes a distance of approximately 30 times the effective depth to fully develop. Therefore, in cases where capacity exceeds supply, the amount of discrepancy is multiplied by an entrainment coefficient which limits the amount of erosion. L D Entrainment Coefficient = e 30 (7) where L is the length of the control volume and D is the effective depth (USACE, 1993) and (Thomas, 1994). Sorting: The other major constraint in the computation of sediment continuity is the potential supply limitation based on the amount of materials in the active layer as a result of bed mixing processes. Currently HEC-HMS is expected to employ a twolayer algorithm similar to that used by HEC-RAS (Gibson and Piper, 2007) to compute bed sorting mechanisms as shown in Figure 2. The active layer approach divides the hypothetical sediment bed into two layers (active and inactive). Initially, sediment is removed from or added to the active layer. During each time step, the composition of this active layer is evaluated based on the deposition/erosion and updated according to the d 90 of the active layer with sediment from the inactive layer. The amount of material available to satisfy excess capacity can be limited by the amount of material in the active layer for each time step. Figure 2. Schematic of 2-layers used in the Active Layer Sorting Method 7

8 Transporting: A sediment routing method is included to route sediment from upstream to downstream. The amount of sediment transported from the reach is calculated from Eq. 8 (Neitsch et al. 2005). sed out V out = sed ch (8) Vch where sed out is the amount of sediment transported from the reach, sed ch is the amount of suspended sediment in the reach, V out is the volume of outflow during the time step, and V ch is the volume of water in the reach segment. Summary and Conclusions This paper presents a brief description of the new sediment modeling methods that will be available in future versions of HEC-HMS. The new features will make it possible to use HEC-HMS to estimate background and anthropogenic nonpoint source sediment loads that can be used in the TMDL studies for watersheds containing significant nonpoint sources of pollution. These new sediment capabilities of HEC-HMS focus on runoff volume, and sediment loading to streams, rivers and lakes. HEC-HMS will be able to model the amount of sediment from pervious and impervious areas in a watershed and route it to the stream. In addition, HEC-HMS utilizes hydraulic parameters calculated based on the fixed channel geometry and one of seven transport capacity equations to solve the sediment continuity equation in the stream for sediment processes. Future versions of the program will include a convenient user interface to specify the necessary data for a sediment analysis and a wide range of available outputs for analyzing results. References Ackers, P., and White, W. R. (1973) Sediment Transport: New Approach and Analysis, Journal of Hydraulics Division, American Society of Civil Engineers, Vol. 99, No. HY11, pp Bicknell, B, Imhoff, J, Kittle, J, Jobes, T, and Donigian, A (2001) Hydrological Simulation Program Fortran Version 12, User s Manual AQUA TREEA Consultants, Mountain View, CA. Bruner, G., and Gibson, S. (2005) Sediment Transport Modeling in HEC-RAS Procedings World Water and Environmental Resources Congress 2005, Editor: Raymond Walton, May 15 19, 2005, Anchorage, Alaska, American Society of Civil Engineers. Englund, F. and Hansen, E. (1967) A Monograph on Sediment Transport in Alluvial Streams Teknisk Vorlang, Copenhagen. 8

9 Foster et al. (2003). Draft User s Guide RUSLE2 Version2. USDA ARS, Washington D.C. < (Dec 4, 2007) Gibson, S. and Piper, S. (2007) Sensitivity and Applicability of Bed Mixing Algorithms World Environmental and Water Resources Congress 2007, Restoring Our Natural Habitat, American Society of Civil Engineers, Tampa, Florida. Gibson, S., Brunner, G., Piper, S., and Jensen, M. (2006) Sediment Transport Computations in HEC-RAS. PROCEEDINGS of the Eighth Federal Interagency Sedimentation Conference (8thFISC), April2-6, 2006, Reno, NV, Haan, C.T., Barfirld, B.J., and Hayes, J.C. (1994). Design Hydrology and Sedimentology for Small Catchments. Academic Press, Inc. San Diego, 588p. Huber, W.C., and Dickinson, R.E. (1988). Storm water management model, version4; user s manual. U.S, Environmental Protection Agency, Athens, GA. Kinnell, P.I.A., and Risse, L.M. (1998). USLE-M: Empirical modeling rainfall erosion through runoff and sediment concentration. Soil Sci. Soc. Amer. J. 62, Laursen, E. M. (1958) Total Sediment Load of Streams, Journal of Hydraulics Division, American Society of Civil Engineers, Vol. 84, No. HY 1, pp. 1530:1-1530:36. Leavesley, G., Lichty, R., Troutman, B., and Saindon, L. (1983). Precipitation- Runoff Modeling System: User s Manual U. S. Geological Survey, Denver, CO Meyer-Peter, B. and Muller, T. (1948) Formulas for Bed Load Transport, Report on Second Meeting of International Association for Hydraulics Research, Stockholm Sweden, pp Neitsch, S.L., Arnold, J.G., Kiniry, J.R., and Williams, J.R. (2005). Soil and Water Assessment Tool Theoretical Documentation, Version Temple Tex.: USDA- ARS Glassland, Soil and Water Research Laboratory. < (Nov 25, 2007) Renard, K.G., Foster, G.R., Weesies, G.A., McCool, D.A., and Yoder, D.C. (1997) Predicting soil erosion by water: A guide to conservation planning with the Revised Universal Soil Loss Equation (RUSLE). In: Agric. Handb US Government Pront Office, Washington, DC. 9

10 Slattery, M.C., and Burt, T.P. (1997). Particles size characteristics of suspended sediment in hillslope runoff and stream flow. Earth Surf. Processes. Landforms, 22, 7 Thomas, W. A. (1994) Sedimentation in Stream Networks, HEC-6T User s Manual, Mobile Boundary Hydraulics Software, Inc., Clinton, MS Toffaleti, F. B. (1968) Technical Report No. 5. A Procedure for Computation of Total River Sand Discharge and Detailed Distribution, Bed to Surface. Committee on Channel Stabilization, U.S. Army Corps of Engineers. Toro-Escobar, C. M., Parker, G., Paola, C. (1996) Transfer Function for the Deposition of Poorly Sorted Gravel in Response to Streambed Aggradation, Journal of Hydraulic Research, 34:1, U. S. Army Corps of Engineers (1993) Scour and Deposition in Rivers and Reservoirs: HEC-6 User s Manual. Hydrologic Engineering center, Davis, CA. Vanoni, V.A, (1975) Sedimentation Engineering, ASCE Manuals and Reports on Engineering Practice-No. 54, 745 p. Wilcock, P. R. and Crowe, J. C. (2003) Surfaced-based Transport Model for Mixed- Size Sediment, Journal of Hydraulic Engineering, Vol. 129, No. 2, pgs Williams, J.R. (1975). Sediment-yield prediction with universal equation using runoff energy factor. In Present and prospective technology for predicting sediment yield and sources: Proceedings of the sediment-yield workshop, USDA Sediment Lab., Oxford, MS, November ARS-S-40, Wischmeier, W.H., and Smith, D.D. (1965) Predicting rainfall erosion losses from cropland east of the Rocky Mountains. In: Agric. Handb US Government Print Office, Washington, D.C. Wischmeier, W.H., and Smith, D.D. (1978) Predicting rainfall erosion losses A guide to conservation planning. In: Agric. Handb US Government Print Office, Washington, D.C. Wilcock, P.R., and Crowe, J.C. (2003) Surface-based Transport Model for Mixed- Size Sediment. Journal of Hydraulic Engineering, Vol. 129, No. 2, pp , Yang, C. T. (1972) Unit Stream Power and Sediment Transport, Journal of Hydraulics Division, American Society of Civil Engineers, Vol. 98, No. HY10, pp