## NOTE

Brent Sohngen's draft case study appears co urtesy of the Northeast-Midwest Institute and the National Oceanic and Atmospheric Administration. The final case study will appear in a guidebo ok on Great Lakes environmental benefits valuation which is being develope d by the Institute and NOAA and will be publis hed in the winter of 1998-99.1

SOIL EROSION IN THE MAUMEE RIVER BASIN: A CASE STUDY USING MARKET METHODS TO VALUE ENVIRONMENTAL EXTERNALITIES

DRAFT: June 5, 1998

Brent Sohngen Department of Agricultural Economics The Ohio State University 2120 Fyffe Rd., Columbus, Ohio, 43210-1067 Phone: 614-688-4640 ; Fax: 614-292-0078 Email: sohngen.1@osu.edu
Jon Rausch Department of Agricultural Economics The Ohio State University 2120 Fyffe Rd., Columbus, Ohio, 43210-1067 Phone: 614-292-6421 ; Fax: 614-292-0078 Email: rausch.7@osu.edu2

BACKGROUND
Although many environmental externalities result in non-market impacts to recreation or ecosystems, externalities can also affect the value of goods and services traded in markets. Industrial pollution, for example, may degrade building exteriors more quickly than otherwise, therefore increasing maintenance costs. Because materials and labor are purchased on the open market, we can value these impacts using material prices and wages set in the marketplace. In this case study, we examine an example where the externalities arising from soil erosion are measured using standard market techniques. The case is the Maumee river basin in northwestern Ohio, where soil erosion from upstream land use leads to damages in the harbor where the river drains into Lake Erie (Figure 1). The Toledo harbor serves as a shipping port for many regional commodities, including grain from Midwestern farms and coal from Ohio mines. The Maumee river basin drains 4.2 million acres in northwestern Ohio, southern Michigan, and northeastern Indiana. Approximately 75% of the land is used for farming, 5% for forests, and the remaining land for urban and other uses. In the basin, 10.2 million tons of soil erodes each year, or 2.39 tons per acre. Of this, about 1.3 million tons of sediment flows to the Toledo harbor (USDA Soil Conservation Service, 1993). Because the Toledo harbor is a federal navigation channel, the Army Corps of Engineers spends an average of $2.2 million dollars each year dredging the harbor and the approach channel in Lake Erie. The possibility that sediments are contaminated by toxic chemicals leaching from local landfills causes the Army Corps of Engineers to confine sediments dredged from the harbor itself in a disposal facility (see Figure 1).3

Approximately one half of sediments dredged each year are confined. Although material dredged from further out in Lake Erie currently is disposed with open lake dumping, the Environmental Protection Agency has issued an order that all sediments eventually must be confined. The Army Corps of Engineers and the Natural Resource Conservation Service have asked the question: would reducing soil erosion on agricultural land in the basin reduce the costs of dredging sediments? They have undertaken a project that attempts to establish conservation tillage across 75% of the corn and soybean fields in the basin. Conservation tillage is a farming practice that reduces soil erosion by leaving a larger proportion of the soil covered during winter and spring months. This is accomplished by leaving 30% of the soil surface covered with crop residues (i.e. corn or soybean stalks). The USDA Soil Conservation Service (1993) predicts that additional residue cover can reduce the quantity of sediment dredged downstream by up to 15%. In this case study, we describe how to estimate the benefits of reduced dredging costs arising from lower soil erosion upstream. Although it is not done in this case study, these savings, or benefits, should be compared to the costs of reducing soil erosion in order to determine if a 15% reduction in dredging is economically efficient. While both market (i.e. dredging) and environmental goods (i.e. water quality) are affected by sediment deposition, this case study focuses on market impacts. Dredging is considered a market impact because the Army Corps of Engineers must expend resources by hiring private contractors to dredge the harbor. The benefits of reducing soil erosion are measured by the decrease in dredging expenditures associated with a 15% reduction in sediments entering the harbor.4

Figure 1: The Maumee river basin and Toledo harbor.5

There are other economic impacts of soil erosion. Market impacts include increased water treatment costs and increased drainage ditch cleaning costs, while non-market impacts include impaired fish spawning habitat or altered aquatic ecosystems. Furthermore, the move to confine all dredged materials may require building additional confinement space. Depending on where the facility is built, other non-market values may be affected, such as loss of wetlands or recreation space. Given the low levels of remaining coastal wetlands along Lake Erie shores, the impacts of sedimentation on these resources in the Maumee Bay may be substantial. These other market and non market impacts of soil erosion are important, but they are ignored here in order to focus our attention on the techniques necessary to value dredging impacts. It is interesting to note that the economic value of avoided dredging costs alone may be sufficient to justify the costs of reducing soil erosion.

THE COST OF DREDGING
Several concepts of soil erosion and sedimentation must be defined initially. Soil erosion is calculated as the quantity of soil that moves on the land during a given year. On agricultural land, soil is dislodged as water moves over unprotected soil during rainstorms. In the Maumee river basin total soil erosion is estimated to be 10.2 million tons per year. Approximately 6.4 million tons arises from land where crops are produced. Table 1 presents estimates of all sources of soil erosion in the basin. Only a portion of the 10.2 million tons of soil erosion actually enters streams, however. Some soil moves only from the top of the field to the middle or edge of it. Of6

all the soil that moves during rainstorms, only a portion will leave the field. Furthermore, when soil enters the waterway, only part of it ends up in the Toledo harbor. Some will be deposited in fields downstream (inducing net benefits for that farmer), at the bottom or sides of the river, or in drainage ditches. The second panel of Table 1 presents estimates of the sinks (areas where soil is deposited) for sediments. Most soil erosion is deposited in the field where it arose; it just moves a small distance before settling again. Some sediments are suspended well enough in water to be carried offsite. Approximately 1.3 million tons per year on average make their way to the harbor. The delivery ratio is calculated as the proportion of total soil erosion that ends up in the Toledo harbor. In the Maumee river basin, this is calculated as (1.3/10.2), or 12.7%. Table 1 shows (1) that only a portion of all soil erosion leaves the field; (2) that some sediments are deposited in drainage ditches; and (3) that only a portion of the sediments entering the harbor are deposited in the shipping channel (the rest end up elsewhere in the Lake). The Army Corps of Engineers dredges only the quantity that ends up in the shipping channel, 468,000 tons per year. Because dredging and storing costs are based on the volume of sediment removed, we must translate this number into cubic yards. This is accomplished by using estimates of the average density of soils in the basin. These estimates suggest that each ton of sediment equals 1.82 cubic yards, so that 468,000 tons of sediment equal 850,000 cubic yards. There are three components of dredging costs, the costs of dredging material from the lake bottom and putting it in a boat, the costs of transporting the material to a confined disposal facility, and the costs of confining the material. The first two costs, dredging7

and transportation, are annual costs related directly to the total quantity of sediments dredged. Confining costs, however, are capital costs . As capital costs, they depend on additional variables, such as interest rates, and they must be treated differently.
Table 1: Sources and sinks for soil erosion from the Maumee river basin. Circa (1992) Sources tons/year Percent Agriculture 7,418,900 72% Streambank 100,000 1% Geologic (riverbed) 20,000 0% Gully and Urban 2,761,100 27% Total 10,300,000 Sinks Fields or River Bank 8,515,128 83% Drainage Ditches 484,872 5% Ship Channel 468,000 5% Lake 832,000 8% Total 10,300,000 This data is from USDA Soil Conservation Service, 1993 except for drainage ditch estimates, Which are from Forster and Abrahim, 1985.8

Dredging and Transportation Costs
The annual costs of dredging and transporting material to a disposal point have both variable and fixed components. Variable costs depend directly on the quantity of material dredged and transported each year. They include expenditures such as fuel or labor used to operate dredging machinery. Variable costs increase as more material is dredged and transported to the disposal point. Fixed costs, on the other hand, are the capital costs associated with owning and maintaining dredging equipment. They do not vary with the quantity of sediments dredged each year. No matter how much sediment is dredged, contractors must pay for the machinery to do the dredging. Total costs are the sum of variable and fixed costs. Dredging activity in the Toledo harbor area actually occurs in two different areas

—the River/Harbor area and the Lake. Dredging costs will differ in the two regions because it generally takes more effort and time, and even different equipment, to extract sediments in the River/Harbor area. Furthermore, these two areas are different distances from the disposal area, so that different transportation costs will apply to each region. Separate dredging and transportation cost functions can be estimated from historical Army Corps dredging contracts (1978 to 1995) to determine specific cost functions for the two regions:
(1) River/Harbor: Total Cost = 331,879 + 2.10*Q R/H
(2) Lake: Total Cost = 215,815 + 1.78*Q L9

The first component of each equation is the fixed cost of a contract to remove sediment. The second part is the variable cost. Variable costs are the cost per cubic yard multiplied by the cubic yards, Q R/Hor Q L . Due to differences in the type of machinery that may be used for dredging, and differences in the channel that must be dredged, the fixed and variable costs differ depending on where the sediments are dredged. When the annual quantity of sediments dredged is 850,000 total cubic yards 1 , this equation suggests that annual dredging and transportation costs in the Toledo harbor amount to $2,188,534 per year. Under the sediment reduction plan, sediments are reduced 15% in the harbor, and dredging costs decline to $1,942,408. While it is possible that dredging may decline more in one particular region (i.e. River/Harbor or Lake), this case study assumes a proportional reduction in each region. This points out an area of uncertainty based on the underlying science. Reductions may not occur proportionally each region, but this could only be determined with more thorough sediment transportation modeling. Economic analysis with such uncertainty should contain relevant discussions pertaining to such difficulties.
Confined Disposal Facility Costs
Confined disposal facilities are “ landfills ” that remove contaminated sediments from the environment. Due to the presence of heavy metals in the Toledo harbor and Lake Erie, sediments dredged in the harbor must be confined in this facility. Currently, the

1 399,500 cubic yards in the River/Harbor and 450,500 cubic yards in the Lake.10

facility is located on the eastern shore of the entrance to the harbor (Figure 1). At historical rates of storage (approximately 400,000 cubic yards per year), the existing facility would last another 20 years. However, since it is likely that all sediments dredged after 1997 must be stored in the facility, this will reduce the effective life of the facility to just 9 years. As the existing facility fills, it is assumed that a new 20-year facility will be built to replace it. This study examines two costs associated with building a confinement facility. The first involves the cost of renting land. Clearly, these costs will depend on the location of the facility. For example, purchasing part of the lake floor to extend the current facility would be costless for the Army Corps of Engineers; however purchasing additional harbor front property would cost up $25,000 per acre near the existing facility. 2In this case, we assume that a new facility will be built farther out into the lake next to the existing one, using no new lake frontage. At the moment, there are few market uses of the additional lake in this area, although there may be substantial non market uses. 3 The second is the capital cost of building the facility. Construction costs for the existing extension of the Toledo facility were $1 per cubic yard in 1994 and construction costs for a recently constructed facility in Cleveland, Ohio were approximately $7 per cubic yard (Personal communication with Weiner Cadet, US Army Corps of Engineers). Current estimates of construction and construction management costs for a new facility in

2Real estate values were approximated in December of 1997. 3 While there are not many other marketable uses of the lake and lake at this time, there may be substantial non market uses, such as habitat for fish, recreation area, and the loss of aesthetic beauty. We recognize these damages as important, but they are ignored here to focus the analysis on market damages. Techniques for measuring these non market uses are described elsewhere in this book, and such estimates could be used within the context of this study.11

Toledo are nearly $10 per cubic yard. 4For this analysis, a cost of $7.5 per cubic yard is used to accommodate recent expenditures and potential future increases. For 20 years of capacity at existing dredging rates, this amounts to $95.6 million 5

.
Determining the Annual Cost of Confinement
This case study focuses on whether or not a 15% reduction in the quantity of sediments dredged each year will reduce the size and cost of the new CDF. Reducing sediment dredging will have two effects. First, it will reduce the size of any new facility. Second it will extend the life of the existing facility. Given the size of the new capital investment required for storing all sediments dredged, extending the life of the existing facility by only 1 year can affect the interest cost of borrowing money. Table 2 presents information for two scenarios

— (1) No Sediment Reduction; and (II) a 15% Sediment Reduction Plan. The first row indicates that the original facility will last for 9 more years in under plan I, but 11 years under plan II. Row (2) presents the date of construction for the new confinement facility; recall that reducing dredging by 15% pushes construction back by 2 years. In addition to extending the life of the existing CDF, construction costs for the new facility are reduced because the new CDF is smaller (rows 3 and 4).

4These costs are notably higher for two reasons. First, the last site was cheaper because it was not difficult to establish. Second, waste handling costs may be higher due to new environmental regulations. 5 This number is calculated as follows: 850,000 cubic yards per year x 20 years x $7.50 per cubic yard x 0.75. This last multiplier (0.75) involves the assumption that volume of sediments will subside 25% over the life of the facility as water evaporates or is drained from the sediments.12

Row (5) introduces the concept of discounting. Discounting is important when the costs and benefits of environmental programs occur at different times. Here, for example, the Army Corps of Engineers must expend resources now to reduce soil erosion, but these activities do not provide benefits until later when they defer the costs of installing a new confinement facility. Without a sediment reduction plan, the new facility must be built in the year 2006, but with sediment reduction, it can be built in 2008. Although a large share of benefits under the sediment reduction plan arise because the Army Corps of Engineers can build a smaller facility, additional benefits accrue because the Army Corps of Engineers can put the building costs off for two more years. Putting off large capital expenditures is some benefit because it allows the Army Corps of Engineers to pursue alternative activities in the meantime.13

Table 2: Comparison of CDF data for two strategies.

Plan I: No Sediment Reduction Plan II: Sediment Reduction 1) Original Facility Life 9 years 11 years 2) New CDF Opens 2006 2008 3) New CDF Capacity 12.75 million cubic yards 10.86 million cubic yards 4) Total Cost of New CDF $95.6 million $81.5 million 5) PV of total cost $61.6 million $47.7 million 6) Annual Cost $4.1 million $3.1 million Note : Because the calculations presented above involve several additional decimal places, you may obtain slightly different results if you calculate these values on your own.14

Figure 2 shows the present value of building costs under the two alternatives. Under plan I, future costs are $95.6 million and they occur in 2006; under plan II they are $81.5 million and they occur in year 2008. These values are discounted to 1997 to determine the present value of future costs, $61.6 and $47.7 million under the two plans respectively. Present values are calculated with the following formula:
(3) PV of Cost in Year (1997 + n) = Future Value*(1+r) -n , Where r is the interest rate (in this case 5%), and n is the number of years into the future when construction occurs. For example, under plan I, equation (4) is
(4) PV of Cost in 2008 = $95.6*(1.05) -9= $61.6
The overall benefits of building a smaller facility and pushing that two years into the future is $13.9 million ($61.6 - $47.7). The values in row (5) of Table 2 are the present value of construction costs for different size CDF ’ s. These costs, however, are not comparable to our estimates of dredging and transportation costs because those are annual costs, and these are the costs of a facility that can be used for multiple years. Discounting techniques can be used again to determine a set of equal annual payments that just equal the present values shown in row (5). These annual equal payments are shown in row (6). For a description of how to obtain the values in row (6), please see the appendix to this chapter15

Figure 2: Calculating present value of alternative future confinement (CDF) capital costs.

1997 1998 2006 2005
Present Values $95.6 $81.5 $61.6 Future Values Plan I: Build CDF Plan II: Build CDF $47.7
Benefits: $13.9 2008
...................................................... .16

Comparison of Costs
With costs for each underlying component expressed annually, we are prepared to compare the costs of two alternatives (no sediment reduction and sediment reduction). The benefits of the sediment reduction plan in terms of avoided downstream costs are the difference between the total annual costs of the two proposals. The total costs for each plan are shown in Table 3. Plan II, or the plan including a 15% reduction in sediment dredging, benefits the Army Corps of Engineers $1.3 million dollars per year. The benefits of each additional cubic yard of dredging avoided can be calculated as reduction in total costs divided by the reduction in quantity dredged. This is $1.3 million divided by 127,500 cubic yards, or $10.19 per cubic yard. 6These benefits can also be translated into the benefits of a reduction in soil erosion on land upstream. To do this, one must account for three factors: (1) the delivery ratio (13%); (2) the ratio of cubic yards to tons of sediments (1.82 cubic yards per ton); and (3) the ratio of sediments dredged to the total quantity of sediments that enters the Toledo Harbor (65%). Accounting for these, soil erosion in the basin would have to be reduced by approximately 1.5 million tons in order to avoid 127,500 cubic yards of dredging. The benefits per ton of soil erosion in the basin could therefore be calculated as $1.3 million divided by 1.5 million tons, which equals $0.87 per ton of soil erosion.

6It is important to note that the additional benefit of each additional cubic yard of dredging avoided is constant for the first 15% of dredging avoided.17

CONCLUSION
As noted in the text, these estimates capture only one impact of soil erosion. There may be many other impacts, including recreational boating, sport and commercial fishing, housing, aquatic life and ecosystem integrity, to name a few. While these would be expected to increase the economic value of impacts, it may not be important to estimate any or all of them. If the benefits calculated in this case study are favorable compared to the costs of reducing sediments, it may be enough to justify efforts at lowering soil erosion. There are several uncertainties surrounding these estimates. First, weather is uncertain from year to year, and actual costs may differ dramatically from these average conditions. Second, some assumptions above are based on hydrological modeling that is itself uncertain. Finally, the economic estimates themselves contain uncertainty. While this case study does not attempt to provide estimates of the possible error, readers should be aware that these errors may exist, and in studies they conduct or evaluate.18

Table 3: Annual costs of dredging, transporting, and confining sediments in the Maumee river basin, in millions (1995)

Plan I: No Sediment Reduction Plan II: Sediment Reduction Dredge and Transport Costs $2.2 $1.9 Confinement Facility Land Rent $0.0 $0.0 Building $4.1 $3.1 TOTAL COSTS $6.3 $5.019

REFERENCES
Cadet, Weiner, US Army Corps of Engineers, 1776 Niagara Street, Buffalo, NY 14207.
Forster D. Lynn and Girmai Abrahim. 1985. Sediment deposits in drainage ditches: A cropland externality. Journal of Soil and Water Conservation.

USDA Soil Conservation Service. 1993. Erosion and Sediment Dynamics of the Maumee River Basin and Their Impact on Toledo Harbor.20

APPENDIX: ANNUAL CAPITAL COSTS OF CONFINEMENT
Estimating the annual c apital costs of confinement require us to determine the annual costs of capital expenditures. This is important because the Army Corps of Engineers must pay for the confinement facility in the year it is built, but they use it for many years. Discounting allows us to spread the costs over many years, taking the time value of money into account. The time value of money recognizes that the Army Corps of Engineers would rather pay for the confinement facility each year, but they have to pay for it in the year it is built. Figure (A.1) describes this situation graphically for plan I in our example. Although the confinement facility costs $95.6 million to build, this expense occurs in year 9. As shown above, we discount this value back to time period 1 to obtain current capital costs of $61.6 million. Because the new facility has a 20 year life, the entire project lasts 29 years (9 years until the facility is built, and 20 years of useful life). We thus must spread these capital costs over 29 years, as shown in Figure (A.1). To spread capital costs over many years, we use a levelized cost factor. The levelized cost factor is the same as that used to calculated periodic payments on a loan for a house or an automobile. It is
(A.1) levelized cost factor =

1 ) 1 ( ) 1 (

− + +
n n r r r21

where r is the interest rate for each period, and n is the number of periods. Under plan I, r is 0.05 per year, and n is 29, and the levelized cost factor is 0.0661. The annual costs are then calculated as
(A.2) Annual Cost = Present Value * levelized cost factor
This is ($61.4) x (0.0661), or $4.1 million per year.
Figure A.1: Timeline for plan I.

These same methods must be used to calculate the annual costs under plan II. In this case, the costs are spread over 31 years because the Army Corps of Engineers can use the existing facility for 2 more years with lower dredging quantities (Figure A.2). They then build a 20 year facility that will last until 2026. With equations (A.1) and (A.2), where r is 0.05 and n is 31, the levelized cost factor is 0.0641, and the annual costs are $3.1 million. 1997
Present Value:
Annual Values: 2026

1998 1999 2000 ...................................................... .

$61.6 $4.1 $4.1 $4.1 $4.1 ...................................................... .22

Figure A.2: Timeline for plan II.

1997
Present Value:
Annual Values: 2028

1998 1999 2000 ...................................................... .

$47.7 $3.1 $3.1 $3.1 $3.1 ...................................................... .