Quincy Library Group
P.O. Box 1749 Quincy, CA 95971

March 4, 1999

Steve Clausen
EIS Team Leader, USDA Forest Service
Sierra Nevada Framework Project, Room 419
801 “I” Street
Sacramento, CA 95814

Dear Mr. Clausen,

Several comment letters from environmental organizations have suggested that riparian buffers should be implemented according to the formula proposed in SNEP by Erman, Erman, Costick, and Beckwitt. We believe the use of the methods proposed in that paper for the computation of riparian buffer widths would not be appropriate, for the reasons explained below.

Riparian Buffer Width Proposed by Erman, et al.

The main issues are not about the special nature of riparian areas but rather how much area belongs in this category and what activities are acceptable. The ecological function and process should be guides to use and protection.

The functions and processes take place in three areas at varying distances from the aquatic system: a community area, an energy area, and a land-use influence area. The size of these areas will change depending on the characteristics that define them.
(Erman, et al. Management and Land Use Buffers, SNEP Vol III, Ch 5, Appendix 3)

After a three-paragraph introduction of the above concept, the remainder of the paper is divided into three sections: The Community Area, The Energy Area, and Riparian Buffer Area.

The Community Area. The authors say,

From a knowledge of the habitat requirements and life connections of the dependent species, we should be able to define the general dimensions of this community area in the various regions and elevations zones of the Sierra. However, the exact requirements and hence the dimensions for many species are unknown.

Examples are mentioned that might define a riparian “community area” from a few meters to about a hundred meters wide on each side of the watercourse.

The Energy Area. The authors say,

Riparian areas contribute a year-round supply of organic material that ranges from nearly the total supply of food at the base of the food chain ... to critical quality food... The surrounding riparian area also blocks energy from the sun and reradiation from the water (thus reducing temperature changes). And the role of large organic matter ... is of major importance to the structure of stream channels and complexity, to the routing of sediment, to the retention of nutrient supplies, and to the diversity of aquatic habitats. The dimensions of this region vary by season, ... by the hydrologic conditions, ... by the contributing area, ... and by the species mix. A useful summary index of this area is the slope distance around the aquatic system equivalent to the height of the site potential tree.

The Riparian Buffer Area (the land use influence area). The authors say,

The likelihood of disturbance to a stream from most land uses increases as a function of proximity to a stream, the steepness of surrounding hillsides and the erodability of soils. These relationships, as in many risk factors, are probably multiplicative and therefore a doubling of slope has more than twice the risk of disturbance to the stream (i.e., an exponential change).

They specify that “proximity to a stream” and “steepness” should be computed for five 100-foot segments, starting from the stream outward, with the slope of each segment contributing to a “weighted average” of the total slope, so that the slope of a segment close to the stream is more significant than the slope of a segment farther away from the stream. They compute the weighted average by multiplying the slope of the closest segment by five, the second closest by four, the third by three, the fourth by two, and the fifth by one. Add up these products and divide by five, which they say will be the weighted average slope.

They specify that “erodability of soils” is measured by the “K~factor” described by one of the authors (Costick) in SNEP Vol III, Ch 3. The K~factor is said to vary from 0.1 to 0.46 on the Eldorado NF, or from about 0.2 to 0.69 according to other references. Low K~factor is equivalent to low erodability.

The authors then give a formula for buffer width:

Buffer Width = (the larger of Community or Energy area width) times (e) to the power of (1 + weighted average slope + K~factor - slope times k~factor).

Example: If the larger of Community or Energy area width = 150 ft,

S = weighted Slope, and K = K~factor, then:

Buffer Width = 150 * e ^{(1 + S + K - S*K)}

Note: “e” = 1 + 1 + 1/2! + 1/3! + 1/4! ... which is 2.71828...

Discussion.

The introduction of the paper and its discussion of the Community and Energy areas are reasonable and useful summaries of those issues, and the general comments on a need to consider land-use influences beyond the Community and Energy areas are appropriate. Unfortunately, the section on riparian area buffers then begins to state unsupported conclusions and specifies the computation of a riparian buffer width by methods that are not based on data and employ very questionable mathematical processes. The buffer width formula may appear “scientific,” but at bottom it is arbitrary and cannot be supported by either mathematical logic or scientific fact. Specific flaws regarding the riparian buffer width computation include:

1. The authors say the risk factors are “multiplicative” and therefore the relationship is “exponential.” This is at best very careless math. For example, if there were two risk factors “p” and “q,” a multiplicative relationship would be p times q, which is not exponential. However, if one wishes to exaggerate the relationship, then there is an intermediate step toward “exponential.” The first stop on the way is a formula like “(p+q) to the Nth power,” where N is some meaningful number. This will give a relationship of the type the authors say they want, where doubling (p+q) would increase the result more than twice. But the authors take it a big step farther by specifying a formula where the formula is of the type “N raised to the power of (p+q).” These differences in mathematical treatments have significant effects. For example, assume that p = 3, q = 4, and N = 2. The three types of formula give quite different results:

a. Multiplicative relationship: p x q = 3 x 4 = 12.

b. Intermediate possibility: (p+q) to the power 2 = (3+4) ^ 2 = 49.

c. The authors' choice: 2 to the power of (p+q) = 2 ^ (3+4) = 128.

Their choice of mathematical method goes beyond what they say it would take to do the job. It is an arbitrary and unsupported exaggeration of the risk factor effect.

2. The authors say the slope used in the formula is a “weighted average” of the segment slopes. Here again their use of mathematics is unusual. Weighting an average is conventionally done by counting some values more often than others. For example, if you want to average values A and B, but give twice as much weight to A as to B, then the weighted average is (A + A + B) divided by 3. The “weighted average” will still be an “average” in the sense that it falls someplace between A and B, though it is “weighted” in the sense that is will be closer to A than to B. The authors compute a “weighted average” by multiplying each segment by a “weight” ranging from 5 down to 1, but then they divide by 5 instead of the actual number of values being averaged, which is 15. For example, if the slopes from closest to farthest were 0.5, 0.4, 0.3, 0.2, and 0.1, they would arrive at a weighted average of 1.1, which is well outside the whole range of input values, whereas the conventional definition of weighted average would give a result of 0.367, closer to 0.5 than to 0.1, but still within the original range of values. The net effect of their unusual method of weighting is to exaggerate the effect of “slope” by a factor of three, but they provide no data or rationale to support that manipulation.

3. One could accept the unusual math if the results made sense, but they don't. There are no data and there is no logic to support the particular content or form of their computation.

a. The authors say “The size of these areas will [depend on] the characteristics that define them.” But they do not actually consider the full range of significant characteristics, nor do they consider the effect of these characteristics over the entire buffer area being defined. Instead, they consider only slope and K~factor within 500 feet as significant characteristics. However, in another paper one of the authors specifies other characteristics that are at least as important as K~factor in determining the erodability of soils (Costick, SNEP Vol II, Chapter 3). He cites work which shows that “the rate of soil loss decreased exponentially with increase in ground cover by mulch.” He also says, “In the field, K is not only a function of texture, structure, and permeability, but is highly influenced by S (slope gradient) and L (slope length).” The formula being promoted in the Erman paper entirely neglects the truly exponential effect of mulch or other cover, and it arbitrarily sets slope length at 500 feet, whether drainage toward the stream comes from that far, or a shorter or longer distance.

b. There is no foundation or logic to the inclusion of “e” in the formula. Its only effect is to make the formula “look scientific” when in fact it isn't based on demonstrated scientific data or logic. Substituting 2.5 or 2.7 or 2.9 for “e” would not make the outcome any more or less valid, because the validity of any particular value as the base for the exponential computation is not established at all.

c. The formula produces a buffer width that varies directly as the Community or Energy zone width, whichever is greater. But there is no science-based finding that, if “community” or “energy” area width were doubled, it would require doubling the buffer width as well. One could just as well argue that, if the “energy zone” itself already provided a wide protection area, the required additional buffer would likely be smaller, not larger.

d. The authors say that “Current information and computer aided analytic methods are sufficient for layout of such a buffer system for many regions of the Sierra.” The method they (and Costick) describe is based on computer analysis of slopes derived from the 30-meter Digital Elevation Model (DEM) and GIS layers indicating soil characteristics. However, in his article cited above, Costick clearly indicated that results based on computations of slope from the DEM were suitable only for large-scale screening, not for project-specific applications. He cautioned, “While this model is relatively easy to apply, and cost effective, it is a screening tool and is proposed for use in the allocation of human resources.” That warning is well-founded, because (1) there is no assurance that a given data point of the DEM will actually be in the stream, and (2) even if accurate slopes and distances from the stream could be computed, the method itself does not provide buffers that would accurately reflect site-specific or project-specific conditions. A similar warning was also given about project-specific use of the SNEP LS/OG maps (and also ignored by many of the same organizations who now promote the Erman formula). That warning should apply with even more force to use of the Erman formula.

Examples. Page 1 of the attachments shows five examples of riparian area profile, assumed K~factor, and the resulting buffer width calculated by the above formula. All of these examples are based on a “Community or Energy zone width” of 150 feet. In each case a profile of the first 500 feet is shown, and the baseline is extended to show the minimum and maximum calculated buffer widths. These few examples illustrate the logical inconsistency of buffer widths computed from the Erman formula. Major discrepancies include:

a. Even a very shallow slope (profile 1) extends the buffer width outside the area where slope and erodability are considered, and for steeper slopes (profiles 3 to 5) the buffer could easily extend to twice the distance where slope is measured and soil characteristics are considered.

b. The logic of the actual profile plays no part in the computation. Two examples:

(1) Based on the measured profile within 500 feet, example 3 seems more likely than example 4 to give problems arising in the buffer area beyond 500 feet, but the computed buffer width is greater for 4 than for 3.

(2) Example 5 has the same near-stream profile as example 4, but in #5 the slope levels off at 300 feet and starts to drop away from the stream at 400 feet. However, this huge change in the logic of the situation causes only about 9 percent reduction in buffer width, which is still almost three times the distance where the crucial change of slope takes effect.

c. Erodability (the K~factor) does not affect the computation in a logical way. This can be seen in both page 1 of example profiles and in Table 2 on page 2 of the attachments. On the first page, for example, with very shallow slopes (profile 1) the difference between a K~factor of 0.1 (heavy gravel or other very stable soil) and 0.4 (very erodible soil, such as fine silt) would cause an increase of 29 percent in buffer width, but on a very steep slope (example 4) that large difference in erodability would make only a 4 percent difference in buffer width. Common sense would seem to say that erodability should be more crucial on steep slopes than on shallow ones, and no data are given that would over-ride common sense. Table 2 on the second page shows the buffer widths for a wider range of weighted average slopes and K~factors. At shallow slopes, the buffer is wider if the soil is more erodable (higher K~factor), which would seem to confirm common sense. However, as the slope gets steeper, the effect of the K~factor decreases, until at a “real” slope of 33 percent (“weighted average” of 100 percent) the same buffer width appears right across the page, and at any steeper slope their computation says that narrower buffers are required for more erodable soils! Can the effect of erodability be one thing at the top of the table and the exact opposite at the bottom of the table?

In Summary. This buffer width formula is at bottom an arbitrary construction, intended to look like science, but the authors fail to establish that the buffer width they compute is actually related by scientific data or science-based logic to the risk factors they claim to be addressing.

The only relationship proved by the paper is this: the authors wanted “wide buffers,” so they put together a formula that would yield wide buffers.

Sincerely,

/s/                   /s/
Linda L. Blum         Edward C. Murphy
Corresponding Secretaries

Attachments (Not Yet included on web): Page 1 of five examples based on various slope profiles and K~factors.
           Page 2 of weighted average and buffer width computations by the Erman methods.

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