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2 -< - CONFERENCE 

February 9 - 12, 1997 

St. Petersburg, Florida, USA 

Conference Proceedings 
Prediction of Long-Term Erosion From Landfill Covers in the Southwest 

Clifford E. Anderson 1 and John C. Stormonf 

Abstract 

Erosion is a primary stressor of landfill covers, especially for climates with high intensity storms and 

low native plant density. Rills and gullies formed by discrete events can damage barrier layers and 

induce failure. Geomorphologic, empirical and physical modeling procedures are available to 

provide estimates of surface erosion, but numerical modeling requires accurate representation of 

the severe rainfall events that generate erosion. The National Weather Service precipitation 

frequency data and estimates of 5, 10, 15, 30 and SO-minute intensity can be statistically combined 

in a numerical model to obtain long-term erosion estimates. Physically based numerical models 

using the KINEROS and AHYMO programs have been utilized to predict the erosion from a 

southwestern landfill or waste containment site with 0.03, 0.05 and 0.08 meter per meter surface 

slopes. Results of AHYMO modeling were within 15 percent of average annual values computed 

with the empirical Universal Soil Loss Equation. However, the estimation of rill and gully formation 

that primarily degrades cover systems requires quantifying single events. For southwestern 

conditions, a single 1 0-year storm can produce erosion quantities equal to three times the average 

annual erosion and a 1 00-year storm can produce five times the average annual erosion. 

Introduction 

As a result of implementing new solid waste regulations for existing facilities, many communities 

now find it advantageous to close their existing landfills and use regional facilities. Consequently, 

many existing facilities are being closed and a smaller number of new landfills are being 

constructed. The regulations for closure of municipal waste landfills in New Mexico follow the 

Federal regulations established by the Resource Conservation and Recovery Act (RCRA, 1976, 

Subtitle D program, 40 CFR 258) and require that the top soil layer have a surface slope of not less 

than 0.02 meter per meter, and not greater than 0.05 meter per meter. This minimum slope is 

required because the surfaces of a landfill are subject to substantial local settlement due to the 

normal process of decomposition of solid waste. Covers for hazardous waste remediation will 

generally have similar slopes. The application of minimum slope criteria provides for a surface that 

is relatively free of local depressions arid pond areas where excess precipitation can accumulate. 

Because surfaces of waste containment sites can have differential settlement depths of one meter 

or more, the use of slopes steeper than 0.02 meter per meter will further minimize the future 

occurrence of pending. It is common for designers and regulators to try to approach the 0.05 meter 

per meter limit. There has even been some discussion about changing the regulations to allow 

slopes of 0.08 or 0.10 meter per meter. 

In many areas of the United States, the vegetative cover will form a protective blanket that 

effectively inhibits erosional processes on the cover system. But for many areas of the southwest 

United States, natural vegetation on covers is sparse, with vegetation covering only 10 to 20 percent 

of the surface. The native plants that have evolved for this environment commonly establish root 

systems that collect moisture from the surrounding areas and store moisture during drought periods. 

While it is possible to provide revegetation with nonnative species to provide a higher plant density, 

such attempts to modify the native plant community are frequently unsuccessful. In order to sustain 

the nonnative species, supplemental watering may be required, but introduction of water is not 

----------------------------------------------------------------------------------------

1 University of New Mexico, Dept. of Civil Engineering, Albuquerque, NM 87131, 

(505) 277-4809, ceanders@unm.edu 

2 University of New Mexico, Dept. Of Civil Engineering, Albuquerque, NM 87131, 

(505) 277-6063, jcstorm@unm.edu 

389 
normally advisable for long-term post-closure operations. The most likely long-term success with 

reseeding will be found by restoring the native plant community and density. Furthermore, some 

native plant species depend upon the naturally occurring depressions as a source of moisture. 

When conditions are created that minimize local depressions, some native plant species cannot be 

sustained. 

If the native plant community is to be utilized for southwestern cover systems, there will likely be no 

opportunity to establish a continuous erosion blanket. Much of the land surface will be exposed to 

the impacts of rainfall and surface runoff, with the resulting transport of soil through erosion. 

Erosion has been shown to be greatly affected by the intensity of rainfall and the steepness of the 

terrain. The impact from raindrops initiates local soil movement, but it is the conveyance across 

slopes that causes the local soil movement to become erosion. A decision to create greater surface 

slopes can have consequences for cover erosion that will become obvious only after severe rainfall 

events. Erosion does not usually occur as a uniform lowering of the surface, but by the formation 

of rills or small gullies. Rills can be defined as the smallest channel, formed by runoff, that can be 

destroyed by minor surface disturbance, such as plowing. Gullies are the somewhat deeper 

channels, formed where no defined channel recently existed. The distinction between the two is 

not precise, and the terms are frequently used interchangeably. Rills and gullies have the potential 

to cut through the top soil (erosion) layer of a cover system and damage the underlying barrier soil 

layer or liner. Such damage could compromise the protection that the cover system was designed 

to provide. 

This paper will assess the potential for erosion on a typical southwestern waste containment site 

and quantify the relative impact of slopes on erosion, and on rill or gully formation. For this project 

a typical cover environment near Artesia, New Mexico was selected. This example does not reflect 

the exact conditions of any existing or proposed solid waste facility, but was selected to provide a 

measurable example of physical phenomena. The estimation of erosion can be accomplished 

using three basic procedures described as (1) a geomorphologic evaluation, (2) an empirical 

equation or procedure and (3) mathematical modeling of the physical processes. These three 

procedures will be applied to the Artesia example case. 

A Geomorphologic Procedure 

A geomorphologic evaluation involves the consideration of the geology, hydrology and specific land 

forms of a site, and comparing the results with similar conditions so that the analysis can be used 

to predict what will happen over time. It is the simplest in terms of mathematical procedure, but 

perhaps the most complex in terms of factors that must be considered and the level of expertise 

required to implement an evaluation. An example of a geomorphologic approach is provided by the 

US Bureau of Land Management publication Gully Erosion (Harvey, et al, 1985). This document 

may be applied to cover erosion to evaluate "(1) Threshold conditions for gully initiation (2) The 

stages of gully evolution (3) Current stability of a gully system (4) Long-term gully erosion rates and 

subsequent yields."(Harvey, et al, 1985, p.3) 

The Gully Erosion report also describes the physical processes that are present in gully or rill 

formation. Of particular note for a cover system is the erosion initiated at points where there is an 

abrupt increase or convex change in the longitudinal profile, called a nickpoint. Erosion is initiated 

at nickpoints, and the nickpoints migrate upstream. The upstream migration can continue until 

intercepted by a physical barrier or until the drainage basin is so small that runoff can no longer 

initiate erosion of the steepened section. At waste containment sites, the interface between the top 

surface and the steeper side slopes is a likely location for the initiation of nickpoint erosion. 

Among the geomorphologic thresholds that may be used to identify the potential for erosional 

processes, of particular note for this study is the shear stress threshold indicator that defines a line 

below which gully incision does not occur. The equation for the gully shear stress indicator is: 

390 
S = 0.008 A.o·

26 (Harvey, et al, 1985, p.73) Where: 

and 

A = area in square miles 

(1 square mile= 259 hectare) 

S = slope in meter per meter 

This equation is based on work by J.C. Brice in the Medicine Creek Drainage Basin, Nebraska, 

1966. Only six watersheds from this study were below 250 ha (the smallest with 40 ha) and 

application to small waste containment sites may not be directly transferrable. Nevertheless, Table 

1 shows the results when the gully indicator equation is applied to very small drainage basins. 

Table 1. Application of the gully indicator equation 

Basin Area (ha or hm2

) Threshold slope (meter/meter) 

0.5 (1.24 acre) 0.041 

2.0 (4.94 acre) 0.028 

A figure showing a similar relationship between basin area and slope for gully erosion is included 

in Engineering Analysis of Fluvial Systems (Simons, Li and Associates, 1982, p. 5.38). This figure 

was based on 1975 data from the Piceance Creek area in western Colorado. The data indicates 

that for drainage basins smaller than 1300 ha, the zone between gullied and ungullied is not 

precisely defined and both gullied and ungullied conditions are found for slopes between 0.025 and 

0.065 meter per meter. Thus, a geomorphologic evaluation of conditions similar to those found at 

waste containment surfaces raises concerns about gully erosion potential, and the formation of 

definitive conclusions requires a site specific geomorphologic investigation. 

An Empirical Procedure: the Universal Soil Loss Equation 

An example of an empirical procedure applicable to cover system erosion evaluation is the 

Universal Soil Loss Equation (USLE). This equation is described in detail in Predicting Rainfall 

Erosion Losses (Wischmeier and Smith, 1978). The USLE has been used throughout the United 

States and is particularly directed to the prediction of erosion from agricultural lands, but the 

procedure does include methodology for use in pasture, range and idle land, and for areas disturbed 

by construction. The USLE equation is: 

A=RKLSCP 

where A is the computed soil loss per unit area, R is a rainfall runoff factor, K is a soil erodibility 

factor, L is a slope length factor (a ratio of field length to a 22.1 m test plot), S is a slope steepness 

factor (a ratio of field slope to a 0.09 meter per meter slope), C is a vegetative or mulch cover and 

management factor, and P is a conservation practice factor. The USLE is limited to the 

determination of average annual erosion rates and cannot establish erosion from specific events 

and peak erosional years. The aerial extent and surfacing of many waste containment sites provide 

similar conditions to those described in the procedures for USLE. However, there is no direct 

method within the USLE procedure to determine the depth or magnitude of the gully or rill erosion 

that may be an integral part of the erosion process. 

Mathematical Modeling with AHYMO and KINEROS 

There is no known procedure that presents an accurate measure of the physical processes 

concerning erosion on a cover. However, there are several procedures that combine modeling of 

some physical processes along with application of empirical equations. One applicable 

methodology includes the determination of storm water runoff hydrographs using hydrologic 

modeling, the estimation of sediment wash loads (fine silts and clays that can be suspended in 

runoff) using the storm based Modified Universal Soil Loss Equation (Williams, 1975), and 

estimation of channelized sediment transport rates using regression equations developed from 

more complex sediment transport procedures. This computational methodology has been included 

in the AHYMO Computer Program (Anderson, 1994). The sediment volume for any storm event can 

391 
be computed from the above procedure. All of the runoff events for a period can be accumula.ted 

to obtain an average annual volume. An average annual sediment yield can also be computed by 

using a statistically weighted function of the 2, 5, 10, 25, 50 and 100-year sediment yields. 

As an alternative, the KINEROS, Kinematic Runoff and Erosion Model (Woolhiser, et al, 1990) 

provides a computerized procedure to compute rainfall hydrographs and erosion quantities. 

"KINEROS is a distributed, event-oriented, physically based model describing the processes of 

surface runoff and erosion from small agricultural and urban watersheds.u (Woolhiser, et al, 1990, 

p.3) The KINEROS model derives its name from the kinematic wave equations that are used to 

solve for overland flow and flow through channels, and from the capability to compute the quantity 

of erosion. Successful use of the model to simulate runoff and erosion at the Walnut Gulch 

Experimental Watershed in southern Arizona is described in the KINEROS documentation. Of the 

six sediment transport relations available with KINEROS, the tractive force relation (Meyer and 

Wischmeier, 1969) and the Bagnold/Kilinc relation (Kilinc and Richardson, 1973) were selected for 

this case study. 

Estimates of Gullv and Rill Erosion 

None of the procedures described above provide a method to compute the extent of rill or gully 

erosion, but the study by Kilinc and Richardson (1973) presents the results of erosion simulation 

tests made on a 1.52 m by 4.88 m watershed test bed. Artificially simulated rainfall using a sprinkler 

system was run using rainfall intensities that varied from 3.175 to 11.68 em per hour, using uniform 

bed slopes from 5. 7 to 40 meter per meter, with 24 one-hour test runs. Of special interest for cover 

systems are the regression equations that quantify rill area, rill volume and rill depth as functions 

of slope and rate of runoff. Because the regression equations were established based on a 

constant rainfall and runoff rate for a one-hour simulation, it is not possible to directly apply the 

equations to a hydrograph computation. However, incremental hydrograph quantities can be 

combined with the regression equations in a spreadsheet to estimate the volume of rill erosion for 

the peak one hour of runoff. Because the regression equations are based on a single 7.4 m2 test 

bed, there is no mechanism to accommodate dimensional scale effects with the computations. 

Rainfall 

Rainfall is the driving condition for most moisture and erosion that can impact a cover system. 

While snow melt may also produce moisture, it is of lesser consequence for erosion throughout 

much of the southwest US. For the Artesia site, rainfall conditions for a one-hundred (100) year 

period were simulated with the US Army Corps of Engineers, Hydrologic Evaluation of Landfl/1 

Performance (HELP) Model (HELP3) (Schroeder, et al., 1994). This model uses probabilistic 

methods to identify the daily rainfall, or lack thereof, for every day in the 100-year period. The 

HELP3 simulation for the Artesia area used synthetic precipitation data for the nearby city of 

Roswell, New Mexico. For the 1 00-year simulation, a total of 156 days had precipitation greater 

than 2.2 em; this is the precipitation threshold expected to produce measurable runoff. The values 

computed by HELP3 were compared with the 24-hour precipitation amounts in the Precipitation 

Frequency Atlas of the Western United States, Volume IV-New Mexico (NOAA Atlas) (National 

Weather Service, 1973). It was found that the values computed by HELP3 were substantially less 

than the NOAA Atlas values as shown on Table 2. 

Table 2. Precipitation frequency values for 24-hour storm 

Return period From NOAA Atlas maps Computed by HELP3 

2-year 

10-year 

100-year 

4.95cm 

8.13 em 

12.70 em 

392 

3.35cm 

4.85cm 

6.96cm 
For erosion event computation, extreme rainfall events must be accurately represented. Therefore, 

revised synthetic precipitation data was created using the Extreme Value Type I distribution and 

procedures described in Applied Hydrology (Chow, et al, 1988). This resulted in 137 daily events 

greater than 2.2 em for a 1 00-year simulation, and extreme event values in agreement with the 

NOAA Atlas. 

The simulation of runoff and erosion required that the depth of cumulative precipitation be simulated 

throughout a 24-hour period, with special concern about the rainfall intensity during the peak hour. 

Review of the NOAA Atlas showed that the six-hour precipitation was approximately 80 percent of 

the 24-hour precipitation for the Artesia, NM site. Similarly, the peak 1-hour precipitation was 60 

percent of the 24-hour precipitation. The NOAA Atlas contains a table of adjustment factors to 

obtain 5, 10, 15 and 30-minute precipitation estimates as a ratio of the peak hourly precipitation. 

All of these factors can be combined to obtain a distribution of a typical rainfall event based on the 

24-hour value. Table 3 shows the ratios that were developed. The data from Table 3 was applied 

to each of the 137 daily rainfall quantities to form 137 rainfall distribution tables. 

Table 3. Rainfall distribution factors 

Time 24-hr 6-hr 

Percent of 24-hour 100.0 80.0 

Percent of 1-hour 166.67 125.0 

1-hr 

60.0 

100.0 

30-min 

47.4 

79.0 

Establishing Input Parameters for Erosion Simulations 

15-min 

34.2 

57.0 

10-min 

27.0 

45.0 

5-min 

17.4 

29.0 

In order to simulate runoff from a typical cover system using numerical methods, it was necessary 

to establish some physical parameters that would be used in the models. For this study the 

following values were selected: cover system area at 2.02 ha (5.0 acres), surface dimensions at 

142.2 m by 142.2 m, a coarse sandy loam or loamy fine sand surface soil, median bed material 

gradation (050} of 0.50 mm, and a ground cover with 1Q-percent-native grass cover. Surface slopes 

of 0.02, 0.05 and 0.08 meter per meter were used to simulate three potential surface configurations. 

Results from the Universal Soil Loss Equation Analysis 

The average annual sediment yield from the USLE is tabulated in Table 4. These values are based 

on a rainfall-runoff factor (R) of 80; a length-slope factor (LS) of 0.318 at a 0.02 meter per meter 

slope, 1.15 at a 0.05 meter per meter slope, and 2.14 at an 0.08 meter per meter slope; a soil 

erodibility factor (I<) for coarse sandy loam or loamy fine sand of 0.20; a cover factor for 1 0-percent 

native grass of 0.35; and a conservation practice factor of 1.0. Table 4 summarizes the results from 

the USLE. 

Table 4. Average annual sediment yields based on the USLE 

Slope = 0.02 m/m Slope = 0.05 m/m Slope = 0.08 m/m 

4017 kg/ha/year 14437 kglha/year 26864 kg/ha/year 

8128 kg/year for 2.02 ha 29211 kg/year for 2.02 ha 54359 kg/year for 2.02 ha 

Results from the AHYMO and KINEROS Modeling 

When the 137 largest rainfall events of the 100-year period were evaluated with the AHYMO 

computer progr:am, only 115 events showed measurable runoff. A summary of the AHYMO 

sediment yields is contained in Table 5. The average annual sediment yields computed by the 

AHYMO program are within 15 percent of the values computed with the USLE. 

The KINEROS model was also used to compute storm water runoff and sediment yields for the 137 

largest rainfall events in the 1 OQ-year period. Because the KIN EROS model uses more physically 

based parameters to compute runoff, different runoff rates are computed for the 0.02, 0.05 and 0.08 

393 
meter per meter slopes. Table 6 presents the sediment yields from the KINEROS model for the 

tractive force (Meyer and Wisch meier, 1969) and the Bagnold/Kilinc (Kilinc and Richardson, 1973) 

transport equations. The sediment yields computed by the KINEROS program are substantially 

larger than the values computed with the USLE. 

Table 5. Sediment yield using AHYMO 

Event 24-hr Sediment (kg) at 

frequency rainfall (em) 0.02 m/m slope 

100-year 12.70 54848 

1 0-year 8.13 23387 

2-year 4.95 6214 

Average 9320 

annual 

Table 6. Sediment yield using KINER OS 

Event 24-hr 

frequency rainfall (em) 

Tractive force equation: 

1 00-year 12.70 

1 0-year 8.13 

2-year 4.95 

Average 

annual 

Bagnold/Kilinc equation: 

100-year 12.70 

1 0-year 8.13 

2-year 4.95 

Average 

annual 

Results of Rill Erosion Evaluation 

Sediment (kg) at 

0.02 m/m slope 

69691 

15961 

1371 

5515 

49735 

14293 

1711 

4939 

Sediment (kg) at 

0.05 m/m slope 

184349 

79415 

21509 

31841 

Sediment (kg) at 

0.05 m/m slope 

293695 

76335 

8131 

26310 

247084 

77420 

11673 

27568 

Sediment (kg) at 

0.08 m/m slope 

326523 

141648 

38818 

57018 

Sediment (kg) at 

0.08 m/m slope 

439358 

155589 

19220 

52429 

456987 

171734 

29271 

61564 

The regression equations computed by Kilinc and Richardson (1973) were combined in a 

spreadsheet to estimate rill erosion. Two rainfall events were used for this analysis: (1) a 1 00-year 

storm, and (2) a 1 0-year storm. The rainfall was simulated on the 1.52 m by 4.88 m area used with 

the original test setup. Table 7 is a summary of the spreadsheet computations. These values for 

rill depth, area and volume demonstrate the variability with changes in surface slopes. They can 

not be directly scaled to predict rill erosion for a specific site. 

Table 7. Estimates of Rill Erosion for a 1.52 m by 4.88 m test area. 

Surface Ave. rill depth Ratio: rill area to Ratio: volume rills to Volume 

slope surface area total sediment volume rills 

100-year storm (24-hour precipitation=12.70 em) 

0.02 m/m 0.033 em 0.093 0.088 230 cm3 

0.05 m/m 0.182 em 0.108 0.122 1459 em3 

0.08 m/m 0.433 em 0.1 '17 0.144 3764 em3 

10-year storm (24-hour preeipitation=8.13 em) 

0.02 m/m 0.011 em 0.072 0.049 59cm3 

0.05 m/m 0.060 em 0.084 0.068 376 cm3 

0.08 m/m 0.144 em 0.091 0.080 970 cm3 

394 
Conclusions 

The function of any specific top slope can be greatly impacted by construction measures designed 

to control erosion. While mitigative measures such as revegetation, application of mulches, 

construction of terraces, placement of gravely soils, construction of nickpoint barriers, and use of 

convex slopes may reduce erosion, it is the combination of slope, runoff and transportable soil that 

generates surface erosion. Some of the techniques presented in this study may serve as an outline 

for further erosion investigations at existing or proposed landfill and waste remediation sites. 

The case study presented herein demonstrates that the slope of a final cover can have a profound 

impact on the amount of erosion and on the size of rills or gullies. Geomorphologic considerations 

indicate that gully formation may be initiated when slopes reach maximum regulatory levels. The 

average annual estimates of erosion using the USLE change substantially when slopes. are 

increased above 0.02 meter per meter. In arid climates, a significant percentage of erosion and 

formation of rills may come from single events that are represented by 1 0-year to 1 00-year storms. 

A single 1 0-year storm can to produce erosion quantities equal to three times the average annual 

erosion and a 1 00-year storm can produce five times the average annual erosion. A cover not 

experiencing problems for many years, may suddenly be compromised by a single catastrophic 

event. In order to predict the long-term performance of a cover, it is necessary to consider the 

major precipitation events that are likely to occur over the design life of the cover system. 

References 

Anderson, C.E. (1994) AHYMO Computer Program Users Manual. Albuquerque, NM. 

Chow, V.T., D.R. Maidment and L.W. Mays. (1988) Applied Hydrology. Mc-Graw-Hill, New York, N.Y. 

Harvey, M.D., C.C. Watson and S.A. Schumm. (1985) Gully Erosion. U.S. Department of Interior, Bureau of 

Land Management, Denver, CO. 

Kilinc, M. and E. V. Richardson. (1973) Mechanics of Soil Erosion from Overland Flow Generated by Simulated 

Rainfall. Colorado State University, Hydrology Papers No. 63, Fort Collins, CO. 

Meyer, L.D. and W.H. Wischmeier. (1969) Mathematical simulation of the process of soil erosion by water. In 

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Simons, Li and Associates. (1982) Engineering Analysis of Fluvial Systems. Fort Collins, CO. 

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395