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. 1611 WATERSHED MANAGEMENT ESTIMATING EROSION 169 where S = sediment yield (t/mi2/yr) Q = annual runoff (in.l A= watershed area (mil). Because of widely varying .local factors the au:thors may not have intend- ed for this equation to be used for 'a specific location. However,_ the equation does express a rational relationship for sediment yield that I think is realistic for conditions encountered in the. southwest. To estim~te the average annual runoff for a watershed, I used the relationship developed 'by Renard (10) for the Walnut Gulch Experimental Watershed: . southwestern United States, and it uses a deterministic sediment trans- port relationship (8). Sediment yield is then computed by simulatin9 individual hydrographs and computing the ~ediment transport for the sim- ulated hydraulic conditions. Annual yield is the sum of the yield of individual runoff events. Thus sediment yield is a function of runoff, hydrograph peale. Manning's roughness. slope. hydraulic radius and the size distribution of the sediment in the streambed. The method was applied and calibrated with sample data for several of the larger water- sheds on Walnut Gulch in. southeastern Arizona. With the roodel. a sim- pI Hied relationshi_p was developed which relates the annual sediment yield to watershed drainage area in the form Q = 0.4501 A-0.1449 (2) Y = 0.001846 Aa-.1187 (5) where the terms are as defined above. SUbstituting Eq. 2 into Eq. 1 gives where Y =-average annual sediment yi~ld in ac-ft/ac/yr Aa = drainage area in acres S = 887 A-.0667 (1.43 - 0.26 log A) (3) Thus. because of transmission losses (abstractions from runoff by the alluvial channels) in the watershed. water yield decreases with in- creasi n9 drai nage area and this same trend is reflected ,in the sediment yield reJationship. Conversions are required to produce the units com- parable to the other methods. To convert the annual sediment yield to ac-ft/mi2/yr, I assumed the sediment deposited weighed 90 lbs/ft3, Fl axman Method: where log tY + 100) = 6.21301 - 2.19113 log (XI + 100) + 0.06034 log (X2 + 100) - 0.01644 log (X3 + 100} + 0.04250 log (X4 + 100) (4) Y = antilog of [log (Y + 100)) - 100. Y = average annual sediri1ent yield (ac-ft/mi2/yr) Xl = ratio of average annual precipitatio~ (in) to ave~age an- l1Ja 1 temperature X2 . average watershed slope (~) X3 x soil particles greater than 1.0 mm (~) X4 = soil aggregation Index WATERSHEOS CONSIDERED The Walnut Gulch Experimental Watershed is a 58 mil drainage in southeastern Arizona operated by -the Science and Education Admi nistra- tion of USDA- to evaluate the effect of land use and conservation prac,- tices on water and sediment yield of arid and semiarid r.angelands. The watershed in the Southeastern Arizona Basin and Range land resource area (1.) is typical of the intermountai n alluvial areas of the southwest. Elevations in the watershed range from 4200 to 6000 feet above nean sea level. ,Cover in the watershed is a mixture of brush and grasses with vegetation basal areas less than 10%. Soi Is are typically calcareous with large amounts of gravel and larger material. A gravel pavement develOps with erosion on the land surface. and in some areas it repre- sents nearly a 100% cover. Precipitation in the area. 'fCtlich averages about 14 in/yr. is domi- nated by sunmer rainfall (about two-thirds of the annual) consisting of high-i ntensity. short-duration thunderstorms of limited areal extent. 'Wi nter storms are generally of greater areal extent and of low intensity so that runoff is rot corrmon. The sumner ai r-mass thunderstorms result in high peak flows that generally have high sediment loads. Withi n the watershed, a number of small earthen. dams (stock pondS) provide water .for the grazing animals. Periodic topographic. surveys of the pond storage area have been made to determine sediment accUlllIla- tions. The. nine ponds for which such infonnation was available are shown in Table 2 along with data on the characteristics of the watershed area. The ponds generally have enough storage space that discharge through the emergency spillway is infrequent. .Pond 223 spilled more of- ten than the others. Flaxman (4) developed a regression equation for reservoir design on rangeland watersheds in the western U.S. relatinq sediment yield to four parameters. His expression is The parameters are eKpressions of cHmate and also reflect vegetative growth (Xl ), topography (X2) and soil properties (X3 and X4). The equa- tion explained about 911 of the variance in average anra1 sediment yield from 27 watersheds ranging in size from 12 to 54 mi in 10 west- ern states. Renard Method: A method for estimating sediment yield was developed by Renard (12) and Renard and Laursen (11). This method uses a stochastic runoff model (3), which generates hydrographs for semiarid watersheds in the 2~lO .