21 2 Modeling Runoff and Erosion in Phosphorus Models Mary Leigh Wolfe Virginia Polytechnic Institute and State University, Blacksburg, VA CONTENTS 2.1 Introduction 22 2.2 Modeling Runoff 22 2.2.1 Runoff Volume 22 2.2.1.1 Curve Number Method 23 2.2.1.2 Curve Number Method Implementation 25 2.2.1.3 Infiltration-Based Approaches 29 2.2.2 Hydrograph Development 32 2.2.2.1 Kinematic Flow Routing 33 2.2.2.2 SCS Unit Hydrograph 34 2.2.2.3 Hydrograph Development Implementation 35 2.2.3 Streamflow, or Channel, Routing 36 2.2.3.1 Hydrologic, or Storage, Routing 37 2.2.3.2 Muskingum Routing Method 37 2.2.3.3 Streamflow, or Channel, Routing Implementation 39 2.2.4 Peak Rate of Runoff 40 2.2.4.1 Rational Formula 40 2.2.4.2 SCS TR-55 Method 41 2.2.4.3 Peak Runoff Rate Implementation 41 2.3 Modeling Erosion and Sediment Yield 44 2.3.1 USLE-Based Approaches 45 2.3.2 USLE-Based Approach Implementation 48 2.3.3 Process-Based Approaches 49 2.3.4 Process-Based Approach Implementation 52 2.3.5 Channel Erosion 53 2.3.6 Channel Erosion Implementation 54 2.4 Summary 56 References 60 © 2007 by Taylor & Francis Group, LLC 22 Modeling Phosphorus in the Environment 2.1 INTRODUCTION Runoff and erosion are the overland processes that transport phosphorus. The processes and equations describing the processes have been described in many references. The purpose of this chapter is to present the common approaches used for modeling runoff and erosion processes in models that simulate phosphorus transport and to illustrate similarities and differences in implementation among selected phosphorus models. Implementation of the processes varies among the phosphorus models, depending on model characteristics such as spatial representation of the drainage area (e.g., lumped or distributed), spatial scale (e.g., field or watershed), purpose of the model (e.g., event prediction or average annual predictions for management), computational time step (e.g., daily vs. shorter time steps during rainfall or runoff events), and land uses and conditions represented (e.g., agricultural, urban, forested land uses, frozen soils). Examples of implementation from the following models are included in the chapter: Annualized Agricultural Nonpoint Source (AnnAGNPS) (Cronshey and Theurer 1998), Areal Nonpoint Source Watershed Environment Response Simulation 2000 (ANSWERS-2000) (Bouraoui 1994), Erosion Productivity Impact Calculator (EPIC) (Sharpley and Williams 1990), Groundwater Loading Effects of Agricultural Management Systems (GLEAMS) (Knisel 1993; Leonard et al. 1987), Hydrologic Simulation Program-Fortran (HSPF) (Bicknell et al. 2001), and Soil and Water Assessment Tool (SWAT) (Neitsch et al. 2002). Unless otherwise noted, the infor- mation about the models is from the sources cited in this paragraph. Because of the variety of equations and variability in how they are implemented in different models, a mixture of units is used in this chapter. Generally, units are expressed as length, mass, time (L, M, T, respectively) or in both International System of Units (SI) and English units for empirical equations or as used in the cited models. 2.2 MODELING RUNOFF Runoff is a complex, variable process, influenced by many factors such as soil characteristics, land cover, and topography. Runoff calculations typically include estimating runoff volume, peak runoff rate, and hydrographs, or the time distribution of runoff. For some phosphorus models, peak runoff rate is computed only for use in erosion calculations. For example, in GLEAMS the peak rate is used in the erosion component for calculating the characteristic discharge rate, sediment transport capa- city, and shear stress in a concentrated flow. Common approaches used in phosphorus models for estimating runoff volume, hydrographs, and peak discharge are described in the following sections. 2.2.1 R UNOFF V OLUME Runoff volume, often termed rainfall excess, is the total amount of rainfall minus infiltration and interception. Two general approaches are used to model runoff volume in phosphorus transport models: (1) the curve number (CN) method and (2) infiltration methods. The CN method directly calculates runoff volume, whereas the infiltration methods calculate infiltration first and then estimate runoff as the differ- ence between rainfall and infiltration. Some phosphorus models include both CN © 2007 by Taylor & Francis Group, LLC Modeling Runoff and Erosion in Phosphorus Models 23 and infiltration methods. The CN method is usually used when daily rainfall values are available; infiltration methods require hourly — or other intervals shorter than daily — rainfall values. 2.2.1.1 Curve Number Method The most common method used to estimate runoff volume in phosphorus models is the U.S. Department of Agriculture (USDA) Soil Conservation Service (SCS) (now Natural Resources Conservation Service, NRCS) runoff approach. The CN method correlates runoff with rainfall, antecedent moisture condition (AMC), soil type, and vegetative cover and cultural practices. Runoff volume is computed using the fol- lowing relationships (SCS 1972): (2.1) , S in mm or , S in in. (2.2) where Q is direct storm runoff volume (mm or in.), P is storm rainfall depth (mm or in.), S is the retention parameter or maximum potential difference between rainfall and runoff at the time the storm begins (mm or in.), and CN is the runoff curve number, which represents runoff potential of a surface based on land use, soil type, management, and hydrologic condition. Rainfall depth, P, must be greater than 0.2S (referred to as the initial abstraction, I a ) for the equation to be applicable. Values of CN have been tabulated (Table 2.1) by hydrologic soil group for AMC II, or average conditions. The CN ranges from 1 to 100, with runoff potential increasing with increasing CN. Required information to determine a CN value from the table includes the hydrologic soil group (defined in Table 2.2), the vegetal and cultural practices of the site, and the AMC (defined in Table 2.3). The CN obtained from Table 2.1 for AMC II can be converted to AMC I (dry) or III (wet) using the values in Table 2.3. Curve numbers can be determined from rainfall-runoff data for a particular site. Investigations have been conducted to determine CN values for conditions not included in Table 2.1 or similar tables. Examples include exposed fractured rock surfaces (Rasmussen and Evans 1993), animal manure application sites (Edwards and Daniel 1993), and dryland wheat–sorghum–fallow crop rotation in the semi-arid western Great Plains (Hauser and Jones 1991). The CN approach is widely used for estimating runoff volume. Because the CN is defined in terms of land use treatments, hydrologic condition, AMC, and soil type, the approach can be applied to ungaged watersheds. Errors in selecting CN values can result from misclassifying land cover, treatment, hydrologic conditions, or soil type (Bondelid et al. 1982). The magnitude of the error depends on both the size of the area misclassified and the type of misclassification. In a sensitivity analysis of runoff estimates to errors in CN estimates, Bondelid et al. (1982) found that effects of variations in CN decrease as design rainfall depth increases and confirmed Hawkins’s (1975) conclusion that errors in CN estimates are especially critical near the threshold of runoff. Q PS PS = − + (.) . 02 08 2 S CN =− 25 400 254 , S CN =− 1000 10 © 2007 by Taylor & Francis Group, LLC 24 Modeling Phosphorus in the Environment TABLE 2.1 Runoff Curve Numbers for Hydrologic Soil-Cover Complexes Land Use Description/Treatment/Hydrologic Condition Hydrologic Soil Group Residential: a ABCD Average lot size (ha) Average % impervious b 0.05 or less 65 77 85 90 92 0.10 38 61 75 83 87 0.13 30 57 72 81 86 0.20 25 54 70 80 85 0.40 20 51 68 79 84 Paved parking lots, roofs, driveways, etc. c 98 98 98 98 Street and roads: Paved with curbs and storm sewers c 98 98 98 98 Gravel 76 858991 Dirt 72 82 87 89 Commercial and business areas (85% impervious) 89 92 94 95 Industrial districts (72% impervious) 81 88 91 93 Open spaces, lawns, parks, golf courses, cemeteries, etc. Good condition: grass cover on 75% or more of the area 39 61 74 80 Fair condition: grass cover on 50 to 75% of the area 49 69 79 84 Fallow Straight row — 77 86 91 94 Row crops Straight row Poor 72 81 88 91 Straight row Good 67 78 85 89 Contoured Poor 70 79 84 88 Contoured Good 65 75 82 86 Contoured and terraced Poor 66 74 80 82 Contoured and terraced Good 62 71 78 81 Small grain Straight row Poor 65 76 84 88 Good 63 75 83 87 Contoured Poor 63 74 82 85 Good 61 73 81 84 Contoured and terraced Poor 61 72 79 82 Good 59 70 78 81 (continued) © 2007 by Taylor & Francis Group, LLC Modeling Runoff and Erosion in Phosphorus Models 25 2.2.1.2 Curve Number Method Implementation The curve number method is used in several phosphorus models to compute runoff volume. The most common implementation (e.g., AnnAGNPS, GLEAMS, EPIC, SWAT) includes a modification of the CN to account for daily changes in soil moisture content (Williams et al. 1990). Typically, the models require the user to input a value for CN 2 , the curve number for average conditions, or AMC II. Then, TABLE 2.1 (CONTINUED) Runoff Curve Numbers for Hydrologic Soil-Cover Complexes Land Use Description/Treatment/Hydrologic Condition Hydrologic Soil Group Close–seeded Straight row Poor 66 77 85 89 legumes d Straight row Good 58 72 81 85 or Contoured Poor 64 75 83 85 rotation Contoured Good 55 69 78 83 meadow Contoured and terraced Poor 63 73 80 83 Contoured and terraced Good 51 67 76 80 Pasture Poor 68 79 86 89 or range Fair 49 69 79 84 Good 39 61 74 80 Contoured Poor 47 67 81 88 Contoured Fair 25 59 75 83 Contoured Good 6 35 70 79 Meadow Good 30 58 71 78 Woods or Poor 45 66 77 83 forest land Fair 36 60 73 79 Good 25 55 70 77 Farmsteads — 59 74 82 86 Note: Antecedent moisture condition II and I a = 0.2S. a Curve numbers are computed assuming the runoff from the house and driveway is directed toward the street with a minimum of roof water directed to lawns where additional infiltration could occur. b The remaining pervious areas (lawn) are considered to be in good pasture condition for these curve numbers. c In some warmer climates of the country a curve number of 95 may be used. d Close-drilled or broadcast. Source: SCS. 1972. Hydrology, Section 4: National Engineering Handbook, U.S. Soil Conser- vation Service, Washington, D.C., Government Printing Office. With permission. © 2007 by Taylor & Francis Group, LLC 26 Modeling Phosphorus in the Environment curve numbers corresponding to AMC I (dry), CN 1 , and AMC III (wet), CN 3 , are computed as a function of CN 2 . The retention parameter, S, also changes due to fluctuations in soil moisture content. For example, the same relationship is used in EPIC and SWAT, with the soil water content expressed differently: in EPIC or in SWAT (2.3) where S 1 (L) and S max (L) is the value of S associated with CN 1 (computed with Equation 2.2), FFC is the fraction of field capacity, SW is the soil water content (L 3 /L 3 ), and w 1 and w 2 are shape parameters. FFC is computed in EPIC as (2.4) TABLE 2.2 Hydrologic Soil Group Descriptions and Antecedent Rainfall Conditions for Use with SCS Curve Number Method Soil Group Description A Lowest Runoff Potential. Includes deep sands with very little silt and clay, also deep, rapidly permeable loess. B Moderately Low Runoff Potential. Mostly sandy soils less deep than A, and loess less deep or less aggregated than A, but the group as a whole has above-average infiltration after thorough wetting. C Moderately High Runoff Potential. Comprises shallow soils and soils containing considerable clay and colloids, though less than those of group D. The group has below-average infiltration after presaturation. D Highest Runoff Potential. Includes mostly clays of high swelling percent, but the group also includes some shallow soils with nearly impermeable subhorizons near the surface. 5-Day Antecedent Rainfall (mm) Dormant Growing Condition General Description Season Season I Optimum soil condition from about lower plastic limit to wilting point < 6.4 < 35.6 II Average value for annual floods 6.4 to 27.9 35.6 to 53.3 III Heavy rainfall or light rainfall and low temperatures within 5 days prior to the given storm > 27.9 > 53.3 Source: SCS. 1972. Hydrology, Section 4: National Engineering Handbook, U.S. Soil Conservation Service, Washington, D.C., Government Printing Office. With permission. SS FFC FFC e wwFFC =− +       − 1 1 12 [()] SS SW SW e wwSW =− +       − max () 1 12 FFC SW WP FC WP = − − © 2007 by Taylor & Francis Group, LLC Modeling Runoff and Erosion in Phosphorus Models 27 where SW is the soil water content in the root zone, WP is the wilting point water content (corresponds to 1500 kPa matric potential for many soils) (L 3 /L 3 ), and FC is the field capacity water content (corresponds to 33 kPa matric potential for many soils) (L 3 /L 3 ). In EPIC, values for w 1 and w 2 are obtained by simultaneous solution of Equation 2.3 with the assumptions that S = S 2 when FFC = 0.5 and S = S 3 when FFC = 1.0. In SWAT, w 1 and w 2 are determined by solving Equation 2.3 with the following assumptions: S = S 1 when SW = WP, S = S 3 when SW = FC, and the soil has a CN of 99 (S = 2.54) when completely saturated. The soil water content can be taken as being uniformly distributed through the root zone or top meter or some other depth of soil, or a nonuniform distribution of soil water can be considered. If more of the soil water is at the surface than deeper in the profile, the potential for runoff is greater. Some of the phosphorus models keep track of soil moisture by layer, so they have the potential to include the soil water distribution in their runoff calculations. For example, because EPIC estimates water content of each soil layer daily, the effect of depth distribution on runoff is expressed by using a depth-weighted FFC value in Equation 2.3: (2.5) TABLE 2.3 Conversion Factors for Converting Runoff Curve Numbers Curve Number for Factor to Convert Curve Number for Condition II to Condition II Condition I Condition III 10 0.40 2.22 20 0.45 1.85 30 0.50 1.67 40 0.55 1.50 50 0.62 1.40 60 0.67 1.30 70 0.73 1.21 80 0.79 1.14 90 0.87 1.07 100 1.00 1.00 Note: AMC II to AMC I and III (I a = 0.2S). Source: SCS. 1972. Hydrology, Section 4: National Engineer- ing Handbook, U.S. Soil Conservation Service, Washington, D.C., Government Printing Office. With permission. FFC FFC Z i M i ZZ Z i M ZZ Z i ii i ii i * ,= ∑ ( ) ∑ ≤ = − = − − − 1 1 1 1 110. m © 2007 by Taylor & Francis Group, LLC 28 Modeling Phosphorus in the Environment where FFC * is the depth-weighted FFC value for use in Equation 2.3, Z is the depth (m) to the bottom of soil layer i, and M is the number of soil layers. Equation 2.5 reduces the influence of lower layers because FFC i is divided by Z i and gives proper weight to thick layers relative to thin layers because FFC is multiplied by the layer thickness. GLEAMS also computes a depth-weighted retention parameter: (2.6) where W i is the weighting factor, SM i is the water content in soil layer i (L), and UL i is the upper limit of water storage in layer i (L). The weighting factors decrease with depth according to the equation: (2.7) where D i is the depth to the bottom of layer i (L) and RD is the root zone depth (L). The sum of the weighting factors equals one. Assuming that the CN 2 value in Table 2.1 (SCS 1972) is appropriate for a 5% slope, Williams et al. (1990) developed an equation to adjust that value for other slopes: (2.8) where CN 2s is the handbook CN 2 value adjusted for slope and s is the average slope of the watershed (L/L). This adjustment is included in EPIC but not in SWAT. EPIC also accounts for uncertainty in the retention parameter, or CN, by gen- erating the final curve number estimate from a triangular distribution. The mean of the distribution is the best estimate of CN based on using Equations 2.2 through 2.5, and 2.8 and an equation to adjust S for frozen ground. The extremes of the distribution are ±5 curve numbers from the mean. Another example of a modification in implementation of the CN method is seen in GLEAMS. In the U.S., soils are grouped by series name, and a hydrologic soil group is assigned to each series. However, a series name can include different soil textures, which would have different runoff potentials but would still be in the same hydrologic soil group. The developers of GLEAMS expanded Table 2.1 to give a range of curve numbers for each combination in the table to allow users to distinguish between similar soils within a series (Table 2.4). For example, CN 2 for row crops with straight rows in good hydrologic condition could be 78 for a Cecil sandy loam and 82 for a Cecil clay loam. Care must be taken in utilization of the CN method in different scale models. The CN method was developed based on data from small watersheds, so it should SS W SM UL i i i i N =−               = ∑ 1 1 10. We e i D RD D RD ii =− −       −       − 1 016 416 416 1 .         CN CN CN e CN s s 232 13 86 2 1 3 12=−− + − ()[] . © 2007 by Taylor & Francis Group, LLC Modeling Runoff and Erosion in Phosphorus Models 29 not be applied to a whole watershed larger than that. A larger watershed is subject to spatial variability in rainfall amounts and increased transmission losses due to increased flow path lengths, changing the CN value from that of a smaller watershed. For example, Simanton et al. (1996) found that the optimum curve number — to match measured runoff values — decreased with increasing drainage area for 18 semi-arid watersheds in southeastern Arizona. Some phosphorus models divide large watersheds into subwatersheds or other smaller hydrologic response units. It is reasonable to apply the CN to the smaller response units and then to determine how the runoff from the individual units contributes to streamflow, through routing or other methods, as described in the following sections (2.2.3). 2.2.1.3 Infiltration-Based Approaches Infiltration is defined as the entry of water from the surface into the soil profile. From a ponded surface or a rainfall situation, infiltration rate decreases over time and asymptotically approaches a final infiltration rate. The final infiltration rate is approximately equal to the saturated hydraulic conductivity, K s , of the soil. The amount and rate of infiltration depend on infiltration capacity of the soil and the availability of water to infiltrate. Infiltration capacity is influenced by soil properties, soil texture, initial soil moisture content, surface conditions, and availability of water to be infiltrated, i.e., precipitation or ponded water. Rainfall intensity affects infil- tration rate. If the infiltration capacity of the soil is exceeded by the rainfall intensity (L/T), then water will pond on the soil surface, and the infiltration rate will equal the infiltration capacity. If the rainfall rate is less than the saturated hydraulic TABLE 2.4 Excerpt of Expanded Curve Number Table for GLEAMS Model Land Use Treatment or Practice Hydrologic Condition Hydrologic Soil Group ABCD Row Crops SR Poor 65 72 77 78 81 85 86 87 88 90 91 92 SR Good 60 67 73 74 78 82 83 85 87 88 89 90 SR + CT Poor 66 71 75 76 79 83 84 86 87 88 89 90 SR + CT Good 57 64 70 71 75 79 80 82 83 84 85 86 CNT Poor 64 70 75 76 79 81 82 84 86 87 88 89 CNT Good 59 65 70 71 75 79 80 82 84 85 86 87 Note: SR = straight row; CT = conservation tillage; CNT = contoured. Source: Knisel, W.G., GLEAMS: Groundwater Loading Effects of Agricultural Management Sys- tems, Version 2.10, University of Georgia, Coastal Plain Experiment Station, Biological and Agri- cultural Engineering Department, Publication 5, p. 130, 1993. With permission. © 2007 by Taylor & Francis Group, LLC 30 Modeling Phosphorus in the Environment conductivity of the soil, the infiltration rate will equal the rainfall rate, and ponding will not occur. A number of infiltration equations have been developed, ranging from solving the Richards (1931) equation to empirical equations. The Richards equation, the generalized equation for flow in porous media, is a partial differential equation derived from conser- vation of mass and Darcy’s equation describing flux. To simulate infiltration, the Richards equation is solved subject to appropriate boundary and initial conditions. Empirical infiltration equations typically include coefficients or exponents to represent soil prop- erties and to generate the relationship of decreasing infiltration rate with time. Some infiltration equations that have been used in phosphorus models include the Holtan (1961) equation, which was used in the original ANSWERS event-based model (Beasley et al. 1982); the Philip (1957) equation, which is the basis of the infiltration calculations in HSPF; and the Green and Ampt (1911) equation. 2.2.1.3.1 Green and Ampt Approach Description In phosphorus models that include infiltration simulation (e.g., ANSWERS-2000, SWAT), the Green and Ampt (1911) equation as modified by Mein and Larson (1973) is the most common approach used to estimate infiltration. This approach is phys- ically based, and its parameters can be determined from readily available soil and vegetal cover information. The approach has been tested for a variety of conditions and has successfully simulated the effects of different management practices on infiltration. The original Green and Ampt (1911) equation was derived using Darcy’s law for infiltration from a ponded surface into a deep, homogeneous soil profile with uniform initial water content. Water is assumed to enter the soil as slug flow resulting in a sharply defined wetting front that separates a zone that has been wetted from an unwetted zone. Infiltration rate is expressed as (2.9) where f is infiltration rate (L/T), K s is saturated hydraulic conductivity (L/T), M is the difference between final and initial moisture content (the difference in moisture content across the wetting front) (L 3 /L 3 ), S av is average wetting front suction (L), and F is cumulative infiltration (L). Substituting into Equation 2.9 and integrating with F = 0 at time (t) = 0 yields (2.10) Mein and Larson (1973) extended the Green and Ampt equation to rainfall conditions by first determining cumulative infiltration at the time of surface ponding: (2.11) fK MS F s av =+       1 fdFdt= Kt F S M F MS sav av =− +       ln 1 F SM R K p av s = −1 © 2007 by Taylor & Francis Group, LLC [...]... LW is the length-to-width ratio of the watershed The hydraulic slope of a field is defined as the slope of the longest flow path The longest flow path is the flow line from the most remote point on the © 20 07 by Taylor & Francis Group, LLC 44 Modeling Phosphorus in the Environment field (drainage) boundary to the outlet of the field This length and difference in elevation from the most remote point to the outlet... established, the values of c0, c1, and c2 can be computed The routing operation then consists of solving Equation 2. 30 with the O2 of one routing period becoming the O1 of the succeeding period To maintain numerical stability and to avoid the computation of negative outflows, the following condition must be met: 2 KX < ∆t < 2 K (1 − X ) (2. 31) 2. 2.3.3 Streamflow, or Channel, Routing Implementation The SWAT... Substituting the relationship for travel time into the continuity equation (Equation 2. 26) and simplifying yields the expression for outflow from the reach segment:  2 ∆t   I1 + I 2  O2 =    2 + S1   2T T + ∆t    (2. 32) where T T is travel time In the implementation of the Muskingum routing procedure in SWAT, the value for the weighting factor, X, is input by the user As just noted, for most streams... Substituting Equation 2. 29 for S in Equation 2. 26 and collecting like terms yields O2 = c0I2 + c1I1 + c2O1 (2. 30) KX − 0.5 ∆t K − KX + 0.5 ∆t (2. 30a) where c0 = − c1 = KX + 0.5 ∆t K − KX + 0.5 ∆t (2. 30b) c2 = K − KX − 0.5 ∆t K − KX + 0.5 ∆t (2. 30c) c0 + c1 + c2 = 1 © 20 07 by Taylor & Francis Group, LLC (2. 30d) Modeling Runoff and Erosion in Phosphorus Models 39 The routing period ∆t is in the same... that the amount of rain falling during the time of concentration, Rtc, was proportional to the amount of rain falling during the 24 -h period, or Rtc = α tc R24 , where αtc is the fraction of daily rainfall that occurs during the time of concentration For short-duration storms, all or most of the rain will fall during the time of concentration, causing αtc to approach its upper limit of 1.0 The minimum.. .Modeling Runoff and Erosion in Phosphorus Models 31 where Fp is cumulative in ltration at time of ponding (L) and R is rainfall rate (L/T) Before ponding occurs, the in ltration rate is equal to the rainfall rate After ponding occurs, the in ltration rate is a function of the in ltration capacity of the soil The Green-Ampt-Mein-Larson (GAML) model for in ltration rate is a two-stage model... patterns in rainfall data, the published rainfall erosion index values were generally based on station rainfall records exceeding 20 years © 20 07 by Taylor & Francis Group, LLC 46 Modeling Phosphorus in the Environment The soil loss equation and factor evaluation charts were initially developed in terms of English units commonly used in the U.S., with A being computed in tons/ac/yr; R in 100 ft-tons/acre... computing the storage in a reach is to multiply the length of the reach by the average cross-sectional area of the reach at a given flow rate Flow routed down the channel as the outflow from one reach becomes the in ow to the next reach Additional in ows from overland flow, tributaries, and ground water can be added to the in ow or outflow of each reach as well 2. 2.3 .2 Muskingum Routing Method The Muskingum... over the drainage area The peak rate of runoff can be reflected by the rainfall intensity averaged over a time period equal to the time of concentration for the drainage area The frequency of runoff is the same as the frequency of the rainfall used in the equation The runoff coefficient, C, is the most difficult factor to accurately determine since it represents the impact of many factors — such as interception,... given rainstorm is defined as the product of total storm energy (E) and the maximum 30-min intensity (I30), where E is in hundreds of ft-tons per acre and I30 is in in./h The sum of the storm EI values for a given period is a numerical measure of the erosive potential of the rainfall within that period The average annual total of the storm EI values in a particular locality is the rainfall erosion index . Runoff 22 2. 2.1 Runoff Volume 22 2. 2.1.1 Curve Number Method 23 2. 2.1 .2 Curve Number Method Implementation 25 2. 2.1.3 In ltration-Based Approaches 29 2. 2 .2 Hydrograph Development 32 2 .2. 2.1 Kinematic. Routing 33 2. 2 .2. 2 SCS Unit Hydrograph 34 2. 2 .2. 3 Hydrograph Development Implementation 35 2. 2.3 Streamflow, or Channel, Routing 36 2. 2.3.1 Hydrologic, or Storage, Routing 37 2. 2.3 .2 Muskingum. 21 2 Modeling Runoff and Erosion in Phosphorus Models Mary Leigh Wolfe Virginia Polytechnic Institute and State University, Blacksburg, VA CONTENTS 2. 1 Introduction 22 2. 2 Modeling Runoff