&EPA         Issue   Paper
                        Advances in  Restoration  Science
United States
Environmental Protection
Agency
                        Number 1:
                        Research  Needs in  Riparian  Buffer Restoration

                        Eric E. Jorgensen,Timothy J. Canfield and Paul M. Mayer
 [ADVANCES in
  RESTORATION SCIENCE
                   Riparian buffer restorations are used as management tools to produce favorable water quality impacts;
                   moreover, the basis for riparian buffers as an instrument of water quality restoration rests on a relatively
                   firm foundation.  However,  the extent to which  buffers can restore riparian ecosystems, their
                   functionality and species composition, are essentially unknown.  In light of the foregoing, two broad
                   areas of  research are indicated.  First, data are needed to document the relative effectiveness of
                   riparian buffers that differ according to width, length, and plant species composition. These questions,
                   of managing buffer dimension and species composition for functionality, are of central importance even
                   when attenuation of nutrient and sediment loads alone are considered. Second, where ecosystem
                   restoration is  the goal, effects to  in-stream and terrestrial riparian biota need to be considered.
                   Relatedly, the effects of the restoration on the landscape need to be considered. Particularly, at what
                   rate do the effects  of the riparian buffer on in-stream water quality,  biota, and habitat diminish
                   downstream from restored sites?  Answers to these important questions are needed to further the
                   advance  of riparian restoration from art form to science and to maximize the societal value of future
                   restorations.
                   For further information contact Eric Jorgensen (580) 436-8545, or Timothy Canfield (580) 436-8535,
                   or Paul Mayer (580) 436-8647 at the Subsurface Protection and Remediation Division of the National
                   Risk Management Research Laboratory,  Office of Research and Development, U. S.  Environmental
                   Protection Agency, Ada, Oklahoma.
                   Riparian Restoration through Buffer Management
                   Aquatic ecosystems have been altered through the combined effects of municipal,  industrial, and
                   agricultural activities (National Research Council, 1992). Municipalities spend large amounts of money
                   to remedy non-point pollution problems in their drinking water (Schultz et al., 1995). Nonpoint pollution
                   is the major remaining cause of surface water pollution (U.S. EPA, 1989; Baker, 1992).  Sedimentation
                   and excess nutrients are the two leading nonpoint pollution problems in rivers and estuaries (Baker,
                   1992). Nitrogen and  phosphorus contribute to eutrophication of surface waters and nitrogen is
                   frequently limiting in estuaries (Smith et al., 1987), thereby altering biotic interactions and competitive
                   regimes.  Estuaries are the ultimate sinks for most riverine discharge in the eastern United States.
                   Buffer strips, areas of planted or preserved vegetation between developed land and surface water, are
                   effective at reducing sediment and nutrient loads (Lowranceetal., 1985; Groffmanetal., 1990; Castelle
                   et al., 1994; see also reviews in Castelle et al., 1992). Buffer strips reduce the severity of impacts to
                   riparian areas caused by storm events (Bertulli, 1981) that can incise channels and adversely affect
                   riparian ecosystem function (Henshaw and Booth, 2000). A relatively sound scientific foundation exists
                   to support the use of riparian buffer strips to  manage nutrients  and  sediment and  to support an
                   expectation of their success as an ecosystem management tool. (Bren,  1993; National Association of
                   Conservation Districts, 1994; NRC, 1992; USDA, 1996).  Further, it is also believed that even greater
                   benefits will be realized through incorporation of wetlands as components of buffers (Zak and Grigal,
                   1991; Niswander and Mitsch, 1995);  that is, while  either buffers or wetlands alone are expected to
                   provide benefit,  integration of these together will likely provide unexpectedly high  rates of success
                   (Lowrance et al., 1995).
                   The role  of denitrification, a microbially meditated  process, in processing nutrient inputs to riparian
                   zones is an area of primary importance (Jones and Holmes, 1996; Boulton etal., 1998). Denitrification
                   requires anaerobic conditions and is strongly influenced by ground-water dynamics (Burt et al.,1999;
                   Devito et  al., 2000), typically occurring  in hyporheic zones (Dahm et al., 1998; Baker et al., 1999) where
                   stream geomorphology interacts with ground water and affects sediment deposition, nutrient flux, and
                   stream temperature (Naiman, 1988; Naiman et al.,  1994; Fennessy and Cronk, 1997). Interaction of
                   these factors can produce high quality habitat for biota including fish (Boulton et al., 1998).
                   In the eastern United States, agriculture, forestry, and other economic developments are frequently
                   conducted in areas that closely border rivers, streams, and reservoirs.  Restoration of these border

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areas,  in the form of buffer strips, should have a measurable
impact on water quality (Rodgers  and Dunn, 1992). This may be
especially true in lower order streams where nutrient processing
can be especially efficient (Alexander et al., 2000; Peterson et al.,
2001).  Nonetheless, substantial questions remain: how do buffers
function in various landscapes and precisely which ecosystem
services can buffer strips restore (Osborne and Kovacic, 1993;
Schultzetal., 1995)?
Design criteria have  been identified as an area of information
deficiency (van der Valk and Jolly,  1992).  In the ecosystem
context, design criteria refer not only to functional relationships
sufficient to produce a desired water quality result, but also refer
to functional  relationships relative to wildlife,  biodiversity,
sustainability, and aesthetics. Although riparian buffer areas have
been proposed and are being evaluated as a nutrient management
method nationwide, the exact design requirements of these riparian
areas  (including  size of  buffer  zone,  species composition,
interaction  between  surface and ground water,  stream flow
regulation, provision of in-stream habitat, function for terrestrial
wildlife, sediment transport reduction, and maintenance of biotic
integrity) are incompletely understood and must be evaluated
along with nutrient management.
Research Environment

We will now describe the scope and content of research projects
that are needed to help elucidate, define, and quantify the function
of riparian  buffers as  instruments for riparian restoration.
Frequently, function  and design  criteria for reducing  nutrient
inputs  are of central  interest to  buffer designers.   Therefore,
function and design criteria for riparian buffers for reducing nutrient
inputs  are  of central interest.   However, ecosystem and/or
watershed restoration  are by definition concerned with more than
water  quality.   The ecological  functions and  landscape
characteristics of riparian buffers as expressed by soil, flora, and
fauna are also of primary interest and do interact with nutrients to
a large degree.
The efficacy of riparian buffers as tools of ecosystem  restoration
can be established by measuring and comparing effects among
three types of riparian  buffers: TYPE 1 areas are stream reaches
that have received plantings and undergo associated management
with the purpose of restoring the riparian buffer; TYPE 2 areas are
stream reaches that are initially similar to those in TYPE 1  but that
do not  receive plantings or undergo associated management to
restore the riparian buffer; and, TYPE 3 areas are stream reaches
that are effectively undisturbed or mature, and that represent
stream reaches that TYPE 1  areas are supposed to resemble 30+
years after initiation of the restoration.  Comparing these three
basic types  of stream reach will allow  researchers to quantify
restoration  endpoints  (TYPE 3  areas), and  measure  success
(TYPE 2 areas contrasted with  TYPE 1 and TYPE 3  areas).
These measures of endpoints and success are critical components
of restoration and  are frequently the subject of administration,
management, landowner, and researcher initiated questions for
which there is too often little or no data. This is a void that research
can fill.
Research Questions
There are five general questions driving riparian buffer research:
1)  What are the characteristics of existing riparian buffer zones
    and surrounding landscape areas?
2)  How do riparian areas function?
3)  Where should riparian buffers be placed  on the landscape?
4)  What aspects of riparian ecosystems  can be restored with
    riparian buffers?
5)  How effective is the restoration?
These general questions guide development of focused research
needs. In the enumeration of tasks that follows, it will be apparent
that some tasks are closely related and may be accomplished
together. The tasks are not meant to describe discrete research
efforts; rather, they  are meant to describe discrete data needs
that, although in some cases are related, stand on their own as
being important areas where information relative to determining
the ecological function  of riparian buffers  is  needed, including
restoration  of water quality, in-stream and  terrestrial  riparian
habitat for flora  and fauna, and  landscape function relative to
adjacent land use, upstream activities, and downstream benefits.
Water Quality Effects
Task 1:  In-Stream Water Quality as a Function of Riparian
    Buffer Condition.
    Where waterquality, especially regarding reduction of nutrients
    and suspended sediments, is  an important  motivation for
    developing restored  riparian buffers, data concerning the
    ability of restorations to provide these services, compared to
    unrestored and  mature communities, are needed.
Task 2:  In-Stream Water Quality as a Function of Riparian
    Buffer Width.
    The width of riparian buffer can affect water quality at the
    stream.   It is unclear whether these improvements to water
    quality accumulate linearly with increasing buffer width, or
    whether the rate of improvement declines with increasing
    buffer width.
Task 3:  In-Stream Water Quality as a Function of Riparian
    Buffer Length.
    It is reasonable  to expect that the length (of stream reach) of
    restored riparian buffer will affect water quality to at least the
    extent of buffer width. The effect of buffer length needs to be
    quantified.
Task 4:  In-Stream Water Quality as a Function of Riparian
    Buffer Plant Community Composition.
    It is hypothesized thatthe composition of the plant communities
    that make up restored riparian buffers will have an impact on
    the resulting in-stream water quality (i.e.,  nutrients and
    sediment). The  effects of plant community composition and
    interactions with buffer condition, width, and length  need to
    be determined.
Task 5:   Measure the Relative Contributions of First, Second,
    and Third Order Streams to Watershed Loads of Nutrients
    and Sediment.
    Although there is  substantial speculation, the  relative
    contributions of first, second,  and third order streams to
    watershed loads of nutrients and sediment need  to be more
    clearly quantified. This information can  be used to target
    restoration activities to locations where the greatest amounts
    of nutrients and sediment are entering  the system.
Task 6:   Measure the Relative Contributions of Mixed Riparian
    and Wetland Complexes to Watershed Loads of Nutrients
    and Sediment.
    There is substantial reason to expectthatwetland restorations,
    integrated and designed as part of riparian restoration, can
    enhance the ability  of these riparian areas to remove and
    reduce nutrients and sediment from non-point source runoff.
    It is thought that the dynamic nature of the wetland system,
    coupled with the long-term stability of the riparian area, will
    have a synergistic effect and function better than either type
    system (riparian or wetland) alone.  The effect of integrating

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    wetland and riparian restoration needsto be betterunderstood
    and evaluated.

In-Stream Flora and Fauna Effects
Task 1:    In-Stream  Flora  Response to Riparian Buffer
    Restoration.
    Ultimately, a primary reason for restoring riparian buffers is
    restoration of riverine flora. The re-establishment and growth
    of native aquatic plants is an important water quality and
    habitat result that is expected to follow  riparian  buffer
    restoration.  The effects of restoration condition and buffer
    width  and length on the ability of riverine vegetation to re-
    establish and prosper needs to be documented.
Task 2:    In-Stream  Fauna Response  to  Riparian Buffer
    Restoration.
    Ultimately, a primary reason for restoring riparian buffers is
    restoration of riverine fauna. The re-establishment of native
    aquatic fauna is an important water quality and habitat output
    that is expected to follow riparian  buffer restoration.   The
    effects of restoration condition  and buffer width and length on
    the ability of riverine fauna to re-establish and prosper needs
    to be documented.
Task 3:    Document the Characteristics of Plant and Animal
    Communities Associated with In-Stream Riparian Habitat.
    Determine  population and community  characteristics and
    habitat associations of extant in-stream  flora and fauna.
    What  changes could be expected if buffer restorations are
    implemented?
Terrestrial Riparian Flora and Fauna Effects
Task 1:    Riparian Buffer Terrestrial Flora Response to Riparian
    Buffer Restoration.
    An important reason for restoring riparian buffers is restoration
    of associated terrestrial riparian-habitat dependent flora. The
    re-establishment and growth of native terrestrial plants is an
    important restoration and conservation resultthat is expected
    to follow riparian buffer restoration. The effects of restoration
    condition and buffer width and length on the ability of terrestrial
    vegetation  to  re-establish  and  prosper needs to  be
    documented.
Task 2:    Riparian Buffer Terrestrial Fauna Response to Riparian
    Buffer Restoration.
    An important reason for restoring riparian buffers is restoration
    of associated terrestrial riparian-habitat dependent fauna.
    The re-establishment of native terrestrial fauna is an important
    restoration and conservation resultthat is expected to follow
    riparian buffer restoration. The effects of restoration condition
    and buffer width and length on the ability of terrestrial fauna
    to re-establish and prosper needs to be documented.
Task 3:    Riparian Buffer Terrestrial Microbe Response to
    Riparian  Buffer Restoration.
    Microbial communities play a substantial role in the nitrogen
    cycle and are especially important relative to the production
    and retention of nitrate.  The role  of microbial denitrifying
    activity relative to buffer condition and buffer width needs to
    be documented. It is not expected that buffer length will affect
    microbial denitrifying activity to any great extent.
Task 4:    Document the Characteristics of Plant and Animal
    Communities Associated with Terrestrial Riparian Habitat.
    Determine  population and community  characteristics and
    habitat associations of extant terrestrial -  riparian habitat
    dependent - flora and fauna.  How do these conditions differ
    from the desired state and what changes are expected if
    buffers are restored?
Task 5:   Measure the Benefits to Terrestrial Diversity from the
    Placement of Riparian Buffers, and Document Interactions
    between Such Diversity and Buffer Function, Sustainability,
    and Succession.
    Buffer placement on the landscape  can be expected to play
    a substantial role in determining its final functionality. This is
    especially true regarding effects on  diversity, where the size
    and shape of the restored buffers will interact with proximity
    to other restorations and undisturbed native sites to determine
    the ultimate benefit. The interaction of these various conditions
    relative  to use of riparian buffers as tools to conserve
    biodiversity needs to be documented.
Task 6:   Determine the Extent  to Which Riparian Buffers
    Function as Habitat for Terrestrial Species and the Extent to
    Which They Function as Corridors and Refugia.
    Riparian buffers have the capacity to act as dispersal corridors,
    refugia, orhabitatformanyterrestrialfauna. Thesetendencies
    need to  be documented  and management  prescriptions
    regarding buffer size and placement need to be formulated to
    assure that restored riparian buffers function as intended.
Landscape Scale Considerations
Task 1:   Mapping of Stream Reaches  and Watersheds that are
    Highly Suitable for Riparian Buffer Restoration Based Upon
    Proximity of Denitrifying Subsurface Strata.
    Research indicates that an important factor that limits nitrate
    concentration in surface waters is the proximity of denitrifying
    strata to the surface.  In areas where this denitrifying stratum
    is  below the root zone of plants, little water quality impact
    relative to reduction of nitrate concentration in surface waters
    can be expected.  It is necessary to map the extent of these
    denitrifying strata and determine the miles of stream reach
    where water quality restoration relative to nitrate loading is so
    limited.
Task 2:   Determine  Whether Relationships  Exist Between
    Watershed Size and Proportionate Land Use and the Design
    Requirements of Riparian Buffer Restorations.
    The type and extent of  land  uses that  are  found  within
    individual  watersheds may  play an  important role  in
    determining the types and extents of buffer restorations that
    are appropriate. In some cases, large extensive restorations
    may be necessary to provide desired improvements to water
    quality and habitat; in  other  watersheds, several  small
    restorations may  provide  equivalent  improvements.   The
    ecological, social, and economic characteristics of individual
    watersheds that may affect the types and extent of necessary
    restorations need to be documented.
Task 3:   Determine  the Landscape  Conditions  and Spatial
    Extent Over Which Substantive Ecosystem Benefits Cannot
    be Expected to be Achieved with Restored Riparian Buffers
    Alone.
    Riparian  buffers cannot address all resource management
    questions.  The subset of questions  that buffers can be used
    to impact needsto be distinguished from the subset that they
    cannot.   Particularly, spatial and temporal scale concerns
    need to  be addressed relative to this question.
Task 4:   Measure the Distribution of Riparian Buffer Widths
    Associated with Each Stream Order and Document Their
    Distribution.
    Determine the extant coverage and frequency distributions of

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    buffer widths  by stream order.  Assess how these values
    compare  among watersheds, particularly contrasting
    watersheds with good versus poor water quality.
Task 5:   Measure the Effects of Improvements Attributable to
    Riparian Buffer Restoration in Parts of the Watershed not
    Directly Restored.   Particularly,  to What Extent are
    Downstream Areas Cumulatively Impacted?
    Determine the extent to which the water quality and in-stream
    biota of areas downstream of riparian buffer restorations can
    be positively affected.   In particular,  is  it realistic to expect
    water quality and habitat to improve in estuaries because of
    riparian buffer restorations?
Task 6:   Measure and Document Interactions Among Upstream
    Land Use and Downstream Aquatic and Terrestrial Effects.
    To an extent,  restoration of riparian buffers can only be
    expected to produce a limited suite of outputs. The effects of
    upstream activities also play a large role in determining the
    final function of the buffers on the landscape. The extent to
    which upstream activities limit the range of outcomes that can
    be seen downstream needs to be documented.
Monitoring and Indicators
Task 1:   Determine  Which  Variables to  Monitor  to Assess
    Restoration Success  Over Short,  Intermediate,  and Long
    Time Periods.
    Identify  indicators that can  be  used to assess  short,
    intermediate,  and long-term  performance  and function  of
    restored riparian buffers. Identifythevariabilityofthe indicators
    - determine  the conditions  under which they can be
    appropriately used - and assess error rate.
Task 2:   Identify Biotic and Abiotic Indicators, and Sampling
    Schedules  for Such  Indicators, that will  Help  Determine
    Restoration Effectiveness and Measure Senescence - Such
    that the Need to Renovate or Otherwise Maintain Restored
    Riparian Buffers can be Determined.
    Identify indicators  and concurrent monitoring schedules that
    can track restoration  senescence and  predict the need to
    conduct renovation - including expected renovation benefits
    and costs.
Physical Sciences
Task 1:   MeasuretheExtentto Which Restored Riparian Buffers
    Influence Hydrology.
    Riparian buffers are hydrologically connected to streams and
    stream processes. Thus, to what extent are water quality and
    habitat limited by the characteristics of hydrology that may be
    amenable to engineered  manipulations?  For  example,
    denitrification, a microbially mediated process in which nitrate
    nitrogen is converted  to  gaseous nitrogen,  is strongly
    influenced by ground-waterdynamics in riparianzones. When
    the watertable is close to the soil surface, nitrate in the ground
    water interacts with carbon-rich  soils in  an  anaerobic
    environment creating high potential for denitrification. Natural
    or  anthropogenic factors that  lower water tables greatly
    reduce  riparian denitrification  potential and  other
    biogeochemical processes.
Task 2:   Measure the Extentto Which Riparian Buffers Influence
    Flood Plain Processes.
    Riparian zones represent a distinct component  of stream
    flood plains.  Riparian zones and  associated buffers  may
    influence annual  overbank flows  and/or  in-stream  flow
    dynamics, consequently affecting biogeochemical processes.
    For example,  beavers (Castor canadensis) are natural
    engineers that manipulate stream flow dynamics through
    construction of impoundments.  Such impoundments may
    have watershed-wide  influences on sediment deposition,
    nutrient flux, and stream temperature.
Task 3:   Measure the Extentto Which Riparian Buffers Influence
    Hyporheic Zone Processes.
    Riparian buffers may influence the way in which ground water
    and surface water interact in stream ecosystems.  Such
    hyporheic zones are regions of  high microbial activity that
    greatly influence rates and fluxes of nutrients and  oxygen
    through assimilation and respiration. Consequently, hyporheic
    zones  represent productive, high quality habitats for both
    invertebrates and vertebrates including fish.
Task 4:   Document Differences  in  Restoration Potential  for
    Riparian Zones in Urbanized Areas versus Streams in Less
    Affected Ecosystems.
    In urban areas, high volume diversions of storm water runoff
    into stream channels cause stream incision that disconnects
    floodplainsfromgroundwaterprocesses. Similarly, infiltration
    of  runoff is reduced under zones  of pavement or other
    impervious surfaces, thereby reducing riparian water tables
    in urban watersheds. The extent to which effects attributable
    to  these  and related  alterations limit stream restoration
    potential needs to be well  understood.

Socio-Economic Perspectives
Task 1:   Measure  Economic Impacts  of Riparian  Buffer
    Restorations, Especially Relative to Reduced Crop Yields
    Attributable  to Buffer Shading and Competition, But Also
    Accounting for Economic  Gains Attributable to  Improved
    Nutrient Management.
    Where the establishment of restored riparian buffers depends
    to a large  extent on the cooperation of private landowners,
    especially agriculturists, the economic impacts  of buffer
    placement relative to crop shading and potential competition
    need to be documented in concert with potential  economic
    benefits that may accrue due to improved efficiency in use of
    fertilizer and to improved fin- and shell-fish fisheries.

Integrated Research
Task 1:   Determine Whether Riparian Buffer Function Varies
    Quantitatively or Qualitatively in Relationship to  Varying
    Types of Adjacent Land Use.  This Includes the Functions of
    Nutrient and Sediment Attenuation and Provision ofln-Stream
    and Terrestrial Riparian Habitat for Plants and Animals.
    The questions of whether and how adjacent land use affects
    riparian buffer function - for water quality improvement and
    for  provision of plant and animal habitat  - need to  be
    investigated. For instance, do  buffers adjacent to  industrial,
    residential, and farming operations provide the same quality
    and quantity of benefit, or does the adjacent land use limit the
    effectiveness of the buffer in some regard?
Task 2:   Measure Differences in  Riparian Buffer  Function,
    Especially Relative to Nutrient and Sediment Attenuation -
    but also  Including Provision of In-Stream  and  Terrestrial
    Riparian Plant and Animal Habitat - Among First, Second,
    and Third Order Streams.
    Just as adjacent land  use can be expected to have  an
    influence on buffer, stream order may also  have  an effect.
    Wherein a buffer in a first order stream may intercept 70% of
    the water that enters the stream and may therefore have a
    large effect on water quality and habitat - so may  a buffer in
    a third order stream only intercept 10% of the water entering

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    the stream, and thereby have a small effect on water quality
    and habitat.
Task 3:   Measure the Rate at Which  Benefits Attributed to
    Restored  Riparian Buffers are Attenuated Downstream,
    Especially Relative to Nutrients and Sediment.
    Realistically, riparian buffer restorations can only be conducted
    along a relatively modest number of stream reaches.  It is
    thought that these will be mostly first, second, and third order
    streams. The ability of supposed water quality improvements
    occurring within  these  stream reaches to  propagate
    downstream and be maintained is unknown.
Task 4:   Determine Types of Engineering Controls that can be
    Used to Complement Restored Riparian Buffers to Provide or
    Enhance  Benefits Relative  to  Nutrient  and Sediment
    Attenuation, and  Provision of In-Stream  and Terrestrial
    Riparian Plant and Animal Habitat.
    Under what conditions can engineering controls be used to
    complement riparian buffer restorations? Which engineered
    solutions have the greatest promise of working? What are the
    complementary benefits to terrestrial and aquatic riparian
    ecosystems that are expected from engineered solutions?
Task 5:   Measure the Effects ofAbove-GroundBiomass, Plant
    Communities,  and Animal Communities on Surface Water
    Runoff and Surface  Water/Ground Water Interactions,
    Especially Relative to Nutrient and Sediment Transport.
    Animal  communities  affect plant communities and  plant
    communities affect subsurface  chemistry,  and  ultimately
    interact with the chemical characteristics (particularly regarding
    nutrients)ofin-streamwaterandin-streamhabitat. Therefore,
    interactions between terrestrial riparian flora and fauna and
    the chemical characteristics of riparian ecosystems need to
    be understood to help design buffers that will  remove or
    otherwise  retain nutrients and  sediment.

Conclusion
This issue paper identifies subject areas where there are critical
data gaps concerning the function of riparian buffers as ecosystem
and watershed restoration tools. We acknowledge that whereas
there is a reasonable foundation of data to support an expectation
that restored riparian buffers can provide some water improvement
relative to reduced  loads of nutrients, there are insufficient data
concerning  other benefits to aquatic and terrestrial riparian biota
and  habitat to  allow the  generalization  that restored  riparian
buffers can function astools forecosystem restoration. Therefore,
we identify research that focuses on water quality measured at the
stream while concurrently measuring other biotic and abiotic
responses.
Restoration of the  Nation's waters will require  manipulation of
upstream watersheds, including buffer management. The relative
contributions of activities in these watersheds and the ability to
manage the effects of these activities with riparian buffers  are
important questions that bear upon research needs described in
this paper. Care must be taken to ensure that the contributions of
all watersheds are considered and statistically represented in any
proposed management solutions that rely upon buffers.   The
effects of small headwater, first, and second order watersheds
relative to the larger ones  need to be clearly understood.

Notice
The U.S. Environmental Protection Agency through its Office of
Research and Development funded and managed the preparation
of this Issue Paper.  It has been subjected to the Agency's peer
and administrative review and has been approved for publication
as an EPA document. The authors acknowledge help provided by
Frederick W. Kutz on an earlier draft of the paper.
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