United States

Department of

Agriculture

Forest Service

Southern

Research Station

General Technical

Report SRS–57

Forest Service National Visitor

Use Monitoring Process:

Research Method Documentation

Donald B.K. English, Susan M. Kocis,

Stanley J. Zarnoch, and J. Ross Arnold
Jennifer D. Knoepp, Research Soil Scientist, and

James M. Vose, Project Leader, U.S. Department of

Agriculture, Forest Service, Southern Research Station,

Coweeta Hydrologic Laboratory, 3160 Coweeta Lab Road,

Otto, NC 28763.

The Authors

Donald B.K. English, Research Social Scientist, USDA Forest

Service, Southern Research Station, 320 Green Street, Athens, GA

30602; Susan M. Kocis, NVUM Project Coordinator, USDA Forest

Service, 1645 Highway 20 East, Bend, OR 97701; Stanley J.

Zarnoch, Mathematical Statistician, USDA Forest Service,

Southern Research Station, 200 Weaver Blvd., Asheville, NC

28804; and J. Ross Arnold, Resource Economist, USDA Forest

Service, Strategic Planning and Resource Assessment,

Washington, DC 20250.

July 2002

Southern Research Station

P.O.Box 2680

Asheville, NC 28802
1

Forest Service National Visitor Use Monitoring

Process: Research Method Documentation

Donald B.K. English, Susan M. Kocis,

Stanley J. Zarnoch, and J. Ross Arnold

Abstract

In response to the need for improved information on recreational

use of National Forest System lands, the authors have developed a

nationwide, systematic monitoring process. This report documents

the methods they used in estimating recreational use on an annual

basis. The basic unit of measure is exiting volume of visitors from a

recreation site on a given day. Sites are stratified by type. Days are

stratified by expected volume of exiting recreation visitors. A

double sampling strategy is the primary means used to obtain

measures of exiting recreation traffic. Where possible, observable

counts of other measures highly correlated with visitation, such as

fee envelopes, ski lift tickets, or concessionaire reports, are used to

reduce variation in visitation estimates. In addition to showing how

sampling units were defined, the authors also provide calculations

they used in developing estimators for the mean and variance of

visitation.

Keywords: Monitoring, National Visitor Use Monitoring, NVUM,

recreation use, research methods, sampling, wilderness.

Introduction

Overview

Both the U.S. Congress and the General Accounting Office

have questioned the credibility of recreational visitation

estimates reported by the U.S. Department of Agriculture

Forest Service (USDA Forest Service). Accurate

information about the amount of recreation occurring on

National Forest System (NFS) lands is necessary for a

variety of reasons, including forest planning and budget

allocation; however, methods used to estimate recreational

use have been inconsistent across reporting units and often

have yielded results of questionable validity. In response to

the need for improved information, the USDA Forest

Service has begun a new, ongoing process of measuring

recreation visitation on the national forests and grasslands.

The Agency will incorporate this process into its standard

inventory and monitoring efforts.

As a first step, in 1998 the Agency completed a pilot study

to test a statistically valid method for estimating visitor use.

Building on that effort, a team of research scientists and

NFS personnel developed a standard method that could be

used nationwide. Implementation and refinement of the

method are being accomplished through a partnership of

Agency recreation staff, as well as personnel from strategic

planning and resource assessment, research and

development, ecosystem management, inventory

andmonitoring, and the Missoula Technology and

Development Center. The method is called National Visitor

Use Monitoring (NVUM), and it is designed to provide

statistically reliable estimates of recreation visitation on the

national forests, national grasslands, and designated

wilderness areas.

What This Process Provides

The NVUM process is designed to provide an estimate of

recreation visits. Moreover, it will help ensure USDA

Forest Service-wide consistency in data collection and will

establish a minimum standard of statistical accuracy. A

recreation visit is defined as “. . . one person entering and

exiting a national forest, national grassland or designated

wilderness area for the purpose of recreation.” In a single

visit, an individual may participate in any number of

recreation activities. Also, a single visit may last only 15

minutes or 15 or more days; it might be one individual

visiting only one recreation site, or one individual visiting

every recreation site on a given Federal ownership. Counts

or estimates of recreation users exiting individual sites are

referred to as recreation site visits. The NVUM is used to

sample and develop estimates of recreation site visits—an

intermediate step in estimating recreation visits.

Using the NVUM, managers can generate visitation

estimates for individual national forests or grasslands,

USDA Forest Service regions, and for the NFS as a whole.

The primary reporting unit is the national forest or national

grassland. Recreation visitation estimates will be developed

annually for about one-fourth of the reporting units in each

region; once the cycle is established, each unit will be

resurveyed every 5 years. Total visitation estimates will be

made by summing the estimates from each region and the

Nation. In the first 3 years of implementation, regional and

national estimates will be made by extrapolating data from

the surveyed reporting units. In the fourth and subsequent

years, regional and national recreation use will be

calculated as the sum of the most recent estimate for each
2

reporting unit in the region. Statistically, visitation estimates

for every level of reporting will be within 15 percent of

actual visitation, at the 80-percent confidence level.

Collaborative efforts among administrative branches of the

Agency will ensure quality control in data collection,

sampling design, and statistical accuracy. In addition, the

process will incorporate ongoing research results to

improve the accuracy of estimates and reduce costs.

Consistency among reporting units will be key—all will

follow the same national protocol.

In addition to total visitation estimates, to some extent the

annual reports will provide a profile of visitors.

Descriptions will be averages for the sampled population or

percentage distributions across several categories. For

example, sample averages for length of stay, number of

annual visits to the forest, and party size will be available.

Percentage distributions will include proportion of visitors

that engaged in different recreation activities, proportion of

visitors from various distance zones, and proportion of

visitors who used designated wilderness areas. Each

reporting unit will obtain an estimate of the number of

recreation visits to wilderness areas, the percentage that are

overnight visits, and the percentage of visitors who use

outfitter or guide services.

What This Process Does Not Provide

The data collection and reporting processes will not

estimate recreation visits to particular sites or ranger

districts, nor will they make any description of visitors to a

particular site or district. Results will describe the size and

composition of the overall recreation visitor population for

a national forest or grassland. Descriptive information for

particular subgroups of recreation users, e.g., campers,

dispersed users, local users, generally will not be available.

Within the NVUM process framework, opportunities for

more detailed sampling of particular user groups, or for

special data collection for a national forest or grassland,

will be limited. A major goal of NVUM is to ensure the

consistency of methods used to estimate recreation visits

across reporting units. More intensive sampling of

particular user types could compromise methodological

consistency and increase the difficulty of calculating the

statistical accuracy of visitation estimates.

Opportunities for Special Studies

Special studies that gather in-depth information from or

about selected subgroups of recreation visitors (including

those engaged in particular activities or using individual

recreation sites) will be pursued through other survey

efforts, not as a part of the NVUM process. The effects on

field personnel workload will be reduced by the narrow

focus of sampling required for NVUM. Federal law requires

that such surveys be administered within the guidelines of

information collections approved by the Office of

Management and Budget (OMB). Special surveys must be

fully funded by the requesting unit. Technical assistance in

developing survey instruments and sampling plans that

conform to OMB guidelines is available from the NVUM

research team.

Research Design

The research design for NVUM uses the double sampling

technique developed over 35 years ago to measure

recreation use on national forests (James 1967, James and

Henley 1968, James and Ripley 1963). The first stage of the

process involves selecting a stratified random sample of

times and locations where recreational visitors can be

counted. For each time and location, survey personnel

compile traffic counts for a 24-hour period. Concurrently,

they conduct interviews of a random sample of visitors to

calibrate traffic counts to the number of unique visits. Each

reporting unit will have done some presampling to identify

its population of recreation sites and the days each is open

for public use. Appendix A provides a flow chart that

summarizes the prework steps and data collection

processes.

Defining Recreation Sites

It is helpful to categorize a recreation visit with reference

both to where and when it occurs. Recreation sites and the

days they are open form the population of sampling units.

Five strata are used to categorize location types:

1. Day-use developed sites (DUDS) include sites with

facilities that meet the INFRA1 definition development

scale for moderate, heavy, or high degrees of

modification. Generally, such facilities provide for

visitor comfort, convenience, and education

opportunities. Within the NVUM framework, sites with

facilities that provide only for the safety and health of

1 INFRA (Infrastructure Application) is the USDA Forest Service’s

corporate database that tracks the resources and infrastructure on Agency

lands as well as the outputs that come from them. Additional information

about INFRA data and definitions is available on the web at http://

www.fs.fed.us/eng/infomgmt/infra.htm.
3

visitors are not sufficiently developed to be included in

this category. The DUDS include picnic areas, fish

viewing sites, fishing sites, interpretive sites,

observation sites, playground-park sport sites, ski areas

(alpine and Nordic), some wildlife viewing sites, caves,

visitor centers, museums, and swimming areas. The

DUDS do not include overnight sites. Boat launches,

trailheads, and ranger stations that provide only minimal

information services are also not included.

2. Overnight-use developed sites (OUDS) meet the INFRA

definition for development scales of moderate, heavy, or

high degrees of modification. They include campgrounds

(family and group), fire lookouts and cabins, hotels,

lodges and resorts (both publicly and privately owned),

horse camps, organization sites (both publicly and

privately owned), and any other overnight-developed

sites within USDA Forest Service jurisdiction, whether

managed by the Agency or by a concessionaire.

Organizational camps are not included in this category,

nor are recreational residences; they typically are

sampled as part of the general forest area.

3. Wilderness (WILD) includes lands and waters that are

part of the National Wilderness Preservation System.

Wilderness study areas, research natural areas, or other

roadless areas are not included in this category.

Interviews with WILD visitors may be conducted at

trailheads and other access points.

4. General forest area (GFA) includes all national forest not

included in DUDS, OUDS, or WILD categories.

Generally, sample points will be at trailheads or on NFS

roads where users exit the national forest. These are the

portals though which visitors engaging in dispersed

activities such as hiking, hunting, and dispersed camping

can access undeveloped areas. In some cases, a GFA

entry point will be a river, lake, boat harbor, or airport.

Sample points may be on both high-speed and low-speed

roads, which are managed by the USDA Forest Service

or another jurisdiction.

5. On-forest viewing corridors: viewing scenery on USDA

Forest Service lands from public roads, ferries, scenic

trains, cruise ships, airplanes, trams, or other travel

corridors is a popular recreation activity. In many rural

communities, money spent by sightseeing tourists is a

vital economic force. Managing the viewsheds of travel

corridors is an ongoing element of Agency stewardship.

In measuring use levels, the USDA Forest Service long

has included sightseers, who constitute a significant

proportion of recreation visitation. Nonetheless, little of

this activity fits the strictest definition of a national

forest recreation visit. For example, people traveling on

roads not under USDA Forest Service jurisdiction may

not actually enter a national forest. Still, recognizing the

significance of such use, we have incorporated into the

NVUM process a sampling of this stratum to roughly

estimate its magnitude. Estimates of the number of

people who travel these corridors to view the forest are

not included as national forest recreation visitation, but

are reported separately. Nor have we made an effort to

establish a preassigned level of statistical accuracy for

such counts.

This last stratum allows reporting units to identify important

travel corridors—beyond those listed in GFA—that pass

through or close to NFS lands, but where the speed, layout,

jurisdiction, and/or location of the corridor do not provide

physical access to the forest. Individuals who stay within

these travel corridors are not included in sampling at sites

of the four other types. The stratum includes places from

which visitors may view scenery, wildlife, and other natural

objects while traveling through or near NFS lands. Most

sites of this type are travel corridors (usually a road) owned

or maintained by some other public agency.

We identified two classes of travel corridor that provide

opportunities for viewing forest scenery. For each, we

developed criteria to define characteristics of the travel

route and of the people who might use them to view the

forest landscape. We selected the criteria to ensure

consistency across reporting units in categorizing travel

ways and travelers.

Class 1—Highways, roads, or other public conveyances

designed for viewing scenery that are within NFS

ownership but not under NFS jurisdiction. These include

interstate, State, or local highways, as well as rivers or other

waterways. All air travel routes are excluded. Corridors

must be: (a) displayed on secondary, series-base maps

(forest visitor maps) as directly traversing continuous

USDA Forest Service ownership; and (b) of sufficient

length to require at least 15 continuous minutes of travel

across USDA Forest Service ownership at normal speed.

Visitors must be: (a) on a recreational trip, or (b) traveling

for another purpose, but specifically state that viewing

forest scenery was the main reason for choosing that

particular travel route.

It is problematic to get an unbiased estimate of the

proportion of people using a scenic corridor for the purpose

of viewing forest landscapes. Rest areas and scenic view
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sites are suitable and safe locations to conduct interviews,

although such locations invite a biased sample because the

interviewer must select vehicles and individuals to be

interviewed. Nonetheless, because stopping people at

random on high-speed or busy roads is unsafe for interviewer

and traveler alike, we chose interview locations that were

safe and would introduce a minimum amount of bias.

Class 2—Routes over which commercial trips or tours are

taken to view national forest scenery, but where individuals

do not enter onto routes defined as class 1. This class

provides the visitor who has made a conscious decision to

pay for commercial services an opportunity to view scenery

on USDA Forest Service lands. Reporting units document

the number of passengers on such trips or tours, but do not

conduct visitor surveys. Trips or tours include scenic boat

rides on waters adjacent to NFS ownership, scenic

overflights, and scenic bus, train, or tram travel.

Site Days

Some developed sites, trailheads, designated wilderness

entry points, forest roads, or other access are open and

available for public recreation use year round; others are

open only seasonally. Recreation use can be measured any

day a site is open. A site day describes the spatial-temporal

combination of one location open for 1 calendar day.

Any recreation visit to any site necessarily involves the

individual entering the site, engaging in one or more

recreation activities, and exiting the site. It is important to

count each visitor only once per site visit. The risk of

double counting is reduced by making counts either when

visitors first enter the site, or at their final exit. If the goal is

simply a visitor count, either will suffice. However, James

(1967) showed that better information may be collected by

surveying visitors as they leave. Exiting visitors are able to

provide information about length of stay, facilities used, and

activities; those just beginning their visit may be less

willing to be interviewed. For these reasons, we count and

interview visitors as they exit recreation sites and areas.

Basic Data Sampling Process

On each randomly selected sample day, the reporting unit

collects two types of data. Personnel first take a 24-hour

count of exiting visitor traffic, usually using a mechanical

counter; however, where available they may use other

routinely collected data, such as ski lift tickets, mandatory

permits, or fee envelopes. During the same 24-hour sample

period, they conduct 6 hours of on-site interviews. On-site

interviews occur during one of two randomly selected 6-

hour interview periods during the sample day.

Interviews are done with a sample of exiting visitors, but

full interviews are administered only to visitors who

recreated at the site and are leaving for the last time that

day. By identifying the proportion of last-exiting recreation

visitors to total exit traffic, the reporting unit can calibrate

the 24-hour count to estimate the number of unique

recreation visits that occurred.

Interview protocol for on-forest viewing corridors is slightly

different. Installing 24-hour traffic counters on some travel

routes, especially major Federal and State highways, may be

unsafe. It may be most practical to make manual traffic

counts using a hand-tally recorder. Interview locations are

moved to an adjacent rest area or similar off-road site. Due

to the difficulty of simultaneously interviewing and

conducting a hand tally, personnel are encouraged to

alternate duties according to a specified schedule. The

person conducting the hand tally counts all traffic on the side

of the roadway with the rest area and records commercial

and private vehicles to obtain a proportional sample.

Proxy (External) Information

Information collected while operating some recreation sites

is closely related to the amount of recreation visitation.

Although such information is often collected for an entire

use season or year, it is possible to have it for only one or a

few days. If the information meets certain criteria, it can

serve as a proxy for the amount of site visitation (Yuan and

others 1995). Site days for which such information exists

are called proxy site days.

Incorporating proxy information should improve the

accuracy of site-visitation estimates and reduce the error of

total visitation estimates at the national forest level.

Ultimately, there is a reduction in the amount of sampling

necessary to reach targeted accuracy levels. Some visitor

sampling is needed to estimate conversion rates from the

observed proxy measure to the desired visitation units.

However, proxy site days can be sampled at a lower rate,

because conversion coefficients are more easily estimated.

Several criteria are used to determine the feasibility of

visitation proxy information. First, the information must

represent all users of the site. Proxy data that pertain only

to a particular segment of users, e.g., number of visitors

using outfitters, but not individuals who do not use

outfitters, is not acceptable. Second, the proxy count must

be an exact tally; it cannot be an estimate. Third, only a

few types of proxy information are acceptable: fee receipts,

fee envelopes, mandatory permits, permanent traffic

counters, and ticket sales. Fee sites or sites where a
5

fee-envelope system is used primarily include

campgrounds, ski areas, fee demo sites, and some other

day-use recreation sites. Some designated wilderness,

backcountry areas, and rivers require permits for all users.

Such areas are acceptable for gathering proxy information.

Voluntary permit and trail register systems are not. Using

these criteria, a reporting unit can determine which proxy

information can be used.

Use-Level Strata

For either proxy or standard sites, it is possible to

enumerate all site days in which recreation could occur.

Days on which a site is closed or recreation use is expected

to be zero are classified as closed/zero days. Such days are

not sampled. The remaining site days are stratified to

reduce the variance of estimated annual visitation. Previous

USDA Forest Service research stratified sites by expected

annual use and by weekday versus weekend or holiday day

types (Gregoire and Buyhoff 1999, James and Henley 1968,

James and Rich 1966, Lucas and others 1971, Yuan and

others 1995).

However, analysis of a pilot study indicated that exit

volume for many trailheads and overnight sites was near

zero on some Saturdays, but quite high on Sundays and

Monday holidays. This resulted in high variance in exiting

recreation volume for weekend strata. We felt that more

homogeneous strata could be developed by asking reporting

units to stratify site days by the expected level of exiting

visitor traffic, relative to all site days in that site type.

Stratification of day-use sites results from identifying site

days that have the highest and lowest level of last-exiting

recreation traffic. We stratify site days in each site-type

stratum into four classes—high, medium, low, and zero/

closed exit volume—in order to most efficiently use the

limited number of available sampling days. This divides site

days into classes that minimize exit-volume differences

within a class, and maximize differences across classes.

Sample Allocation

Units involved in the first year of sampling had an average

of 64,000 site days. Based on results from the 1998 pilot

study, an average of about 200 sampling days per reporting

unit (more on those with larger populations of site days, less

on those with smaller populations) are needed to obtain the

target level visitation-estimate accuracy. Each USDA Forest

Service region is allotted 200 sampling days per surveyed

reporting unit. Within regions, sampling days are allocated

to reporting units in a series of stages. The allocation of

days to a reporting unit is a three-step process:

Step 1. Assign to each reporting unit 8 sample days2

 in

on-forest viewing corridors, 3 each for high- and

medium-use days, and 2 for low-use days.

Step 2. Each reporting unit is allotted no more than 50

sample days for proxy site days.

Allocations within a reporting unit are made as follows:

a. Initial allocation of 4 sample days for each proxy

sample cell (defined by a combination of site type and

proxy type).

b. If any of the 50 days remain, allocate a fifth sample

day to each sample cell with more than three different

sites.

c. If any of the 50 days still remain, assign a sixth sample

day to cells with more than five different sites.

d. If any of the 50 days still remain, assign a seventh

sample day to cells with eight or more different sites.

e. If any of the 50 days still remain, assign an eighth

sample day to cells with ten or more different sites.

f. Return any unallocated proxy sample days to the

unobligated regional total.

Step 3. Each reporting unit will have up to 12 sample

cells (combinations of site type and use level) for site

days without proxy information. Sample days are

allocated among cells within a region according to the

following rules:

a. Initial minimum allocation of 8 sample days per

nonproxy sample cell for each reporting unit, to ensure

that visitation variance for each cell is computed on at

least eight observations (unless the cell has fewer than

8 site days).

b. Any sample days still available for the region are

allocated across all nonproxy cells in all survey units.

Allocation proportions are determined by the number

of site days in each cell (provided in appendix A);

weighted by the product of: (1) the cell’s estimated

standard error from the previous year’s survey, and (2)

a factor that reflects the relative importance of each

use-level stratum in visitation estimates. The

2 In NVUM’s first year, each reporting unit was allocated 5 sample

days for this site.
6

importance weight factors are: high-20, medium-10, and

low-1.

That is, high-use site days (regardless of site type) have a

weight 20 times that of low-use site days, and twice that

of medium-use site days. (Note: In NVUM’s first 2 years,

no standard errors estimates will be available, so weights

equal the importance factor alone.)

Selection of Interviewing Days and Times

The set of days for sampling visitation is drawn at random

for each stratum, but with a small adjustment. We

encountered a logistical problem when the same calendar

day was selected for more sites than survey crews could

cover. To avoid that problem, we take the following steps in

developing a sampling calendar:

1. Group by calendar day the site days selected for

sampling.

2. Identify calendar days that have more than 3 site days

scheduled; select 2 at random and retain them in the

sample.

3. Determine the number of site days in each proxy and

nonproxy stratum that need to be replaced.

4. Draw replacements at random from the set of unused site

days on calendar days that have fewer than 2 site days

already selected for sampling.

Previous research (Yuan and others 1995) indicates that the

percent of visitors exiting a site for the last time varies by

time of day. To ensure unbiased estimates of the volume of

last-exiting recreation traffic, we sample over as much of

the day as is practical. For nonproxy sample days, one of

two interview periods is selected at random with equal

probability. The a.m. survey period begins at 08:00 and

concludes at 14:00; the p.m. period runs from 14:00 to

20:00. From late fall to early spring, schedules are adjusted

to ensure that interviews are completed before dark. For

example, if the sun sets between 17:00 and 17:30, an

appropriate afternoon interview period may be 11:00 to

17:00.

For proxy site days, a particular time period is not

identified. The purpose of surveying is to obtain

information to convert proxy counts to site-visit estimates.

Interviews are conducted during the 6-hour daylight period

with the greatest level of exiting recreation traffic.

Closed Sites

Unpredictable weather, precipitation patterns, fires, or other

natural phenomena may change the dates a site is open or

closed, and some changes may continue indefinitely.

Unfortunately, no ex-post adjustment for such changes

really is possible. Reporting units must try to determine a

priori a site’s most likely opening and closing dates. The set

of open site days is defined before the survey year begins,

and it is to that set that the visitation estimate applies. For

all days that a site will be closed due to reconstruction,

restoration, or any other reason, that site should be listed as

closed.

Sites may be closed administratively, in whole or part, for

unforeseen reasons such as fire, flood, heavy snowfall;

construction (including unanticipated repairs); or resource

protection (too little snow, wildlife protection). In all such

cases, the site will be shown as open but with below normal

visitation. If a site is partially closed, interviewing should

continue as scheduled but below normal visitation should be

noted in the daily summary form. If a site has been closed

completely and unexpectedly, the interviewer should record

zero traffic counts on the daily summary form. Conversely,

sites that are open when they were expected to be closed are

treated as closed.

Selecting Interviewees

Interviewers will conduct as many surveys as possible, but

normally fewer than 60 interviews per day. It is important,

nonetheless, to spread out interviews over an entire

sampling day. For example, at a busy developed site where

many interviews could be conducted quickly, interviewers

should time them to cover the whole sampling period. To

determine the individual in a vehicle or group to survey, use

a random selection process, e.g., the person over age 15

with the most recent birthday.

Survey Forms

Each interviewee is asked basic questions from a survey

form. One or two additional questions are asked at proxy

sites to convert proxy counts to site-visit estimates. Onefourth of the sample is asked a set of questions about

economic benefits and trip-related spending. Another onefourth is asked questions about satisfaction with recreation

services and facilities.
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Data Analysis

Part I—Daily Site Visits at Nonproxy Site Days

Although traffic counters tally either exiting vehicles or

exiting persons, the method for estimating daily site visits is

essentially the same for both. Most site-visit estimators

follow standard formulae for stratified random samples

(Cochran 1977). For a given stratum h (h = 1, 2, 3, . . . , H)

and sampled site day i ( i =1, 2, 3, . . . , nh ), within stratum

h let:

Chi = total car (or person) count (obtained from traffic

counter) during the 24-hour sampling period for day i in

stratum h,

Vhij = number of persons in the j

th ( j = 1, 2, 3, . . . J)

sampled vehicle on site-day i [obtained from the onsite

questionnaire (note that when traffic counts are of exiting

visitors, Vhij = 1 is a constant)],

LRhij = indicator variable in the onsite questionnaire, coded

as:

= 1 if the j

th vehicle sampled on site-day i is a lastexiting recreation vehicle,

= 0 otherwise.

The proportion of vehicles on site day i that were last

exiting (Phi) is:

,

J hij

hi

j=1

LR

P = ∑ J

The mean persons per recreation vehicle for last-exiting

recreation vehicles (Vhi ) is:

.

J

hij hij

j=1

hi J

hij j=1

LR V

V = 

LR

∑

∑

Therefore, the estimate for total exiting site visits ( ) hi SV on

site day i is:

. SV C P V hi hi hi hi =

An estimate of mean daily site visits for stratum h is simply:

,

nh

hi

h

i=1 h

SV

SV = n ∑

with estimated variance

. h 2 n hi h

h

i=1 h h

( - SV SV ) V( ) = SV ∑ n n ( - 1)

This formula implies a simplifying assumption. The

sampling frame for nonproxy days is actually a two-stage

design. The first stage is a random sample of site days, and

the second is a random sample of visitors within each firststage sampling unit. However, the first-stage sampling rates

are relatively small. Preliminary information from the

presampling work for reporting units surveyed in the first

year indicates that across all sampled forests, the average

first-stage sampling rate was about 0.25 percent. Hence, the

second term in the sample variance equation for a two-stage

sample (Cochran 1977, p. 278) will be negligible and could

be eliminated, yielding the above formula.

Expansion to the stratum total (SVh ) is:

, SV N SV h hh =

with estimated variance

( ) ( ) 2 , V SV N V SV hh h =

where

Nh = total number of site days in stratum h.

Part II—Proxy Site-Visit Estimates

Estimation of recreation site visits for the proxy component

differs from that of the nonproxy in several ways. First,

strata are defined differently. For a given site type, there

may be several different types of proxy information. Each

unique combination of site type and proxy type constitutes a

stratum. Second, a component of the proxy site-visit

estimation equation is not based on a sampling survey but is

obtained by direct census (a count known without error) of

the proxy count, which yields a reduction in estimator

variance. Here, the purpose of sampling is to obtain the

information needed to convert proxy counts to site visits.

Let Phk be the annual total proxy count for site k in stratum

h, and let CRhk be the known compliance rate of visitors

with respect to the proxy count at that site. For example, not

all campground users may pay the required fee, or not all

designated wilderness users may obtain mandatory permits.

Then, the compliance adjusted proxy count for site k

(PChk ) is the proxy count that would have been observed

with 100 percent compliance, and
8

where

nh = number of days sampled in stratum h, and which has a

variance of

2 , 2 2 2

hi hi h h hi hi h 2

hi h ii i h h

i

1

V( A SG SR SG SR ) = [ ( )] A A

( )( -1)( n n SR n )

+ - / ∑∑ ∑ ∑

Then the estimator for mean daily site visits in stratum h is

. h hh SV A PC =

with a variance of

An exception is if the proxy count is a permanent traffic

counter that may count nonrecreation use as well as

recreation users, such as along a scenic roadway or at a dayuse site where people may enter just to use the bathroom. In

these cases, the mean daily proxy count is adjusted by the

proportion of all of the individuals surveyed on site days in

that stratum who were recreating at the site . Here, the

mean daily site-visit estimate is given by

h h h h SV PC = A RP

and its variance by

. 2 2 22 2 V( ) = V( ) + V( ) - V( ) V( ) SV PC PC PC hh h h RP RP RP h hh AA A hh h

Expansion to total site visits for stratum h is

, h h h SV N = SV

where

Nh = total number of site days in stratum h. The estimated

variance for total site visits is

, 2 V( ) = V( ) SV N h h SV h

Part III—Expansion to Forest Population Mean

and Total

To estimate mean daily site visits for the entire population

of site days over all strata, combining both proxy and

nonproxy, let strata weights be defined as

, h

h H

h

h=1

N W = 

∑N

( ) RPh

. hk

hk

hk

P PC

CR =

For a given stratum h the mean daily proxy count is

,

K

hk

k=1

h K

hk

k=1

PC

PC = 

N

∑

∑

where

Nhk = number of site days whose use is represented by

proxy count for site k in stratum h.

Conversion coefficients are needed to obtain site-visit

estimates from proxy counts. Coefficients for each site typeproxy type stratum are obtained by sampling individuals on

randomly selected site days within the stratum. Two

different variables are needed to make the conversion.

Consider a campground that collects fee envelopes from

campers. Payment is required for each night a campsite is

occupied. However, a person, group, or family camping for

a week can pay in one envelope (one proxy) or as many as

one envelope per day (seven proxies). The first conversion

variable (R) measures the proxy count per group recreation

visit. The second conversion variable (G) measures the

number of people per group recreation visit. For example,

up to five people are allowed to use the same campsite. Let

Rhij = number of proxies per group recreation site visit

for the j

th group surveyed in sample day i in stratum h,

(Rhij ≥ 1.0),

Ghij = group size for the j

th surveyed group on the ith sample

day in stratum h.

Because individual surveys are clustered within sample

days, the conversion coefficient for each stratum is

calculated using a ratio of means approach. Let the sum of

Rhij and Ghij over all surveys on the i

th day be hi SR and

SGhi , respectively. Then the estimate of the proxy

conversion coefficient (Ah ) for stratum h is

,

h

h

n

hi

i=1

h n

hi

i=1

SG

A = 

SR

∑

∑

. 2 V( ) = V( ) SV PC h h Ah
9

then the mean daily site-visit estimator is

,

H

h h

h=1

SV = ∑W SV

with estimated variance

.

H

2

h h

h=1

V( SV ) = V ∑W () SV

Site-visit estimate for the total population is

SV = N SV ,

where

N = total number of site days in the reporting unit’s

population, and the estimated variance is

. 2 V(SV) = V( SV ) N

Part IV—Estimating National Forest Visits

We based the first NVUM survey for a national forest on a

stratified random sampling design of site days, with strata

defined by site type and daily exit volume, i.e., DUDS low.

Our objective was to estimate mean daily site visits and

total annual site visits from a sample of site days randomly

selected in each stratum. Site-visit estimates were obtained

for each sample day, averaged by strata, and then expanded

according to classical stratified random sampling

methodology.

However, a primary reporting goal of NVUM is number of

national forest visits (NFV). Because any single national

forest visitation may include a variety of site visits, we

recognized that recreation visitors might move from one to

another sampling unit when visiting multiple sites. A person

who goes to two sites in a single NFV might be contacted

and correctly included in the last-exiting sample for either or

both, even if the sites are of different site types and/or exitvolume levels. Conversely, a person visiting just one site

might be interviewed only when last exiting that site. Thus,

those who visit more sites per national forest will be

overrepresented in the sample, leading to an upward bias in

the estimator for mean number of site visits per NFV, and a

downward bias in number of NFVs. This type of problem is

uncommon in most classical sampling situations, but a

related issue has been identified in some onsite visitor

samples (Shaw 1988).

We used the following approach to reduce problems

associated with estimating NFVs. Consider that each

national forest visitor has a coupon that was distributed

proportionately to each site visited on that trip. For

instance, if three sites are visited on an NFV trip, then each

site gets one-third of the coupon. The true NFV number is

the total number of coupons on all site days in the forest.

For a given site day, the estimator of NFV is defined

mathematically as

ˆ , iii i NFV = * * P CARS CBAR

where

Pi = proportion of vehicles that were last-exiting

recreationists on site day i,

CARSi = number of vehicles obtained from the car counter

adjusted for axles and one- or two-way traffic on site day i,

and

CBARi = average number of coupons per last-exiting

recreating vehicle on site day i (remembering to use

proportions of a coupon if multiple sites were visited).

To further clarify the meaning of CBAR, let

n = number of last-exiting recreating vehicles interviewed,

PEOPLEj = number of people in last-exiting recreating

vehicle j, and

j SVPNFV = number of sites visited on this NFV for the

people in vehicle j

then CBAR is defined as

.

n j

j=1 j

1 PEOPLE CBAR = n SVPNFV ∑

Note that the NFV estimator is identical to the SV estimator,

except that CBAR is used instead of average people per

vehicle. Justification for this approach for estimating NFV is

verified by a couple of examples. If all visitors only go to

one site on their NFV, then SVPNFV = 1 and CBAR reduces

to the average people per car and NFV = SV as is expected.

Alternatively, if all people go to two sites on their NFV, then

SVPNFV = 2 and CBAR equals one-half the average people

per car and NFV = 0.5 SV as expected. Logical extensions to

other scenarios where the number of sites visited per visitor

varies are more complicated but should be obvious.

Because the NFV estimator is identical to the SV estimator

except for CBAR, all the statistical methodology previously

explained for the SV estimator is appropriate for the NFV

estimator. In particular, the NFVi’s are used to calculate

strata means and variances that are then expanded to forest

level estimates.
10

This approach can be extended to the proxy portion of the NFV

estimator by a simple modification of the proxy conversion

coefficient Ah for stratum h defined previously as

.

h

h

n

hi

i=1

h n

hi

i=1

SG

A = 

SR

∑

∑

For the NFV estimator, SGhi must be replaced with hi SC

which is defined as

.

m hij

hi

j=1 hij

GRPSIZE

SC = ( )

SVPNFV ∑

All other statistical methodologies follow as outlined

previously for the proxy situation.

Part V—Expansion to Regional and National Estimates

All estimates at the reporting unit level, whether totals or

means, have been based on a stratified random sampling

design. To calculate regional-level estimates, these

estimates are folded into a two-stage sampling design from

which the appropriate estimators and their variances are

obtained. National totals and their variances are simply the

sum of all of the regional totals and their variances.

An unbiased estimator for regional totals of a variable of

interest, such as total number of site days, is based on

Cochran (1977, equation 11.21) and is defined as

ˆ ,

n

u i i

i=1

N

Y = M y n ∑

where

N = total number of reporting units in the region,

n = number of reporting units sampled in the region,

Mi = total number of site days in reporting unit i, and

i y = mean estimate per site day for reporting unit i based on

stratified random sampling.

Due to stratified random sampling, an estimate of the

variance is obtained as a slight modification of Cochran

(1977, equation 11.24), defined as

ˆ

ˆ ,

n 2

2 i u n

i=1 2 2

u i 2i

i=1

( - Y Y )

N (1- f) N V( ) = + Y M s n n-1 n

∑

∑

where

 = estimate of the total for reporting unit i,

Yu = average total estimate for a reporting unit,

f = ( ) 1 / − n N = finite population correction for reporting

units, and

2

2i s = variance of the mean estimate based on stratified

random sampling.

Note that, for simplicity, the finite population correction at

the second-stage level is ignored, because the number of

site days sampled within a reporting unit is negligible

compared to the total number of site days in the unit.

The unbiased ratio-to-size estimator from Cochran (1977,

equation 11.25) is used to estimate regional means after

slight modification and is defined as

,

n

i i

i=1

R n

i

i=1

M y

Y = 

M

∑

∑

with estimated variance after modification from Cochran

(1977, equation 11.30) as

,

2 2 n n

2 2 i R 2

R i i 2i 2

0 i=1 i=1

1 (1- f) N N ( - y Y ) V( ) = ( + ) Y M M s

M n n-1 n ∑ ∑

where

.

n

i

0

i=1

M M = N n ∑

Again, for simplicity, the finite population correction at the

second-stage level is ignored.

Part VI—Estimators for Visitor Characteristics

The NVUM survey and reporting process also provides

three types of estimates for various visitor characteristics

that are important to managers. They are: (1) total

estimates, such as total number of NFVs by children under

16; (2) mean estimates, such as mean trip or site-visit

duration time; and (3) proportion estimates, such as

proportion of visitors who camp. In addition, each of these

types could be defined on one of three scales: (a) site visit,

(b) NFV, or (c) annual basis. For example, an estimator may

be developed for the proportion of visitors camping

sometime during their NFV, or for how often the average

ˆY i
11

Deborah Chavez (U.S. Department of Agriculture Forest

Service), Tim Green (U.S. Department of Agriculture Forest

Service), Troy Hall (Virginia Polytechnic Institute and State

University), Scott Jackson (U.S. Army Corps of Engineers),

Dennis Propst (Michigan State University), Chris Siderelis

(North Carolina State University), and Jo Tynon (Oregon

State University). In addition, there were a number of U.S.

Department of Agriculture Forest Service personnel who

provided significant contributions to our method, including

(also alphabetically) Jim Bedwell, Rich Calnan, Ken Cordell,

Dave Hackett, Margaret Lincoln, Mike Noland, Stan Specht,

Jerry Stokes, Greg Super, Francisco Valenzuela, and Larry

Warren.

Literature Cited

Cochran, W.G. 1977. Sampling techniques. 3rd ed. New York: John

Wiley.

Gregoire, T.G.; Buyhoff, G. J. 1999. Sampling and estimating

recreation use. GTR-PNW-456. Portland, OR: U.S. Department of

Agriculture, Forest Service, Pacific Northwest Research Station. 39 p.

James, G.A. 1967. Recreation use estimation on Forest Service lands in

the United States. Res. Note SE-79. Asheville, NC: U.S. Department

of Agriculture, Forest Service, Southeastern Forest Experiment

Station. 8 p.

James, G.A.; Henley, R.K. 1968. Sampling procedures for estimating

mass and dispersed recreation use on large areas. Res. Pap. SE-31.

Asheville, NC: U.S. Department of Agriculture, Forest Service,

Southeastern Forest Experiment Station. 15 p.

James, G.A.; Rich, J.L. 1966. Estimating recreation use on a complex

of developed sites. Res. Note SE-64. Asheville, NC: U.S. Department

of Agriculture, Forest Service, Southeastern Forest Experiment

Station. 8 p.

James, G.A.; Ripley, T.H. 1963. Instructions for using traffic counters

to estimate recreation visits and use. Res. Pap. SE-3. Asheville, NC:

U.S. Department of Agriculture, Forest Service, Southeastern Forest

Experiment Station. 12 p.

Lucas, R.C.; Schreuder, H.T.; James, G.A. 1971. Wilderness use

estimation: a pilot test of sampling procedures in the Mission

Mountains Primitive Area. Res. Pap. 109. Ogden, UT: U.S.

Department of Agriculture, Forest Service, Intermountain Forest and

Range Experiment Station. 44 p.

Mood, A.M.; Graybill, F.A.; Boes, D.C. 1974. Introduction to the

theory of statistics. 3rd ed. New York: McGraw-Hill.

Shaw, Daigee. 1988. On-site samples’ regression: problems of nonnegative integers, truncation, and endogenous stratification. Journal

of Econometrics. 37: 211-223.

Yuan, S.; Maiorano, B.; Yuan, M. [and others]. 1995.

Techniques and equipment for gathering visitor use data on

recreation sites. Publ. 9523-2838-MTDC. U.S. Department of

Agriculture, Forest Service, Technology and Development

Program. 78 p.

visitor visits the national forest per year. Thus, with three

estimator types and three scale levels, there are nine

different estimators for a specific visitor characteristic. The

most meaningful estimator will depend on the question

asked and estimator desired.

All total estimates follow the previously defined

methodology for SV and NFV estimates except when

making appropriate, minor changes to reflect the variable of

interest. All mean and proportion estimates are developed

as ratios of two total estimates. The total estimates are

defined on a site-day basis as

ˆ , i i i i TOTAL X = * * P CARS

where

Pi = proportion of vehicles that were last exiting on site-day i,

CARSi = number of vehicles tallied by a counter, adjusted

for axles and one- or two-way traffic on site-day i,

Xij = a variable dependent on the scale and level of the

estimator for group j in site-day i

= Z ZZ 1 23 /( ), and

 = average of the Xij over all groups.

The Xij is straightforwardly defined. The Z1 is the variable

of interest. The Z2 and Z3 variables are defined so as to

adjust Z1 to the appropriate scale. Appendix B lists some

examples of common estimators that clarify how the

estimators are computed for different scales and types.

Given that:

SVPNFV = number of site visits per NFV for vehicle j, and

NFVPY = number of NFVs per year for vehicle j,

then, for

SV scale estimators Z2 = 1 Z3 = 1 ,

NFV scale estimators Z2 = SVPNFV Z3 = 1 ,

annual scale estimators Z2 = SVPNFV Z3 = NFVPY .

Defining a total estimator in this manner on a site-day basis

allows application of the same statistical methodology as

previously described for the SV and NFV estimators.

Acknowledgments

We thank those who provided review comments on earlier

versions of this report. In alphabetical order, they are:

X i
12
13

Appendix A—NVUM process flowchart Phase I—Prework

Define forest’s recreation sites

Classify into site types (DUDS, OUDS, Wilderness, GFA)

[Forest, regional coordinator]1

!

Identify dates each site is expected to be

Open Closed " Site visits = 0

[Forest] 1

!

Determine if proxy information is available for each open site day

[Forest] 1

 ! !

No Yes

(Nonproxy site days) (Proxy site days)

Stratify days in each site type by expected exit volume: Stratify days in each site type by expected exit volume:

High High

Medium Medium

Low Low

[Forest] 1 [Forest] 1

Complete spreadsheet: Complete spreadsheet:

Site ID, site type, date, use class Site ID, site type, date, use class, proxy type, proxy units

[Forest] 1 [Forest] 1

Determine sampling schedule Determine sampling schedule

[National team] 1 [National team] 1

Train, schedule, interview staff

[Forest, regional coordinator] 1

Phase II—Survey Process (For Forest Staff)

Nonproxy site days

One day prior to scheduled sampling, determine if the site will be open

on the sampling day or closed due to unusual circumstances, e.g. late snow

 ! !

Yes No " Record 0 visits and do not attempt interviews

 !

Set up traffic counter to obtain daily count

On scheduled sampling day:

Conduct as many exit interviews as is practical for the assigned time (one interview per group)

Retrieve traffic counter at day’s end

Record traffic count on sampling spreadsheet

One day after scheduled sampling:

Check interview forms for completeness

Mail completed forms to regional coordinator

Proxy Site Days

For each day during the interview year, record the proxy count for sites

One day prior to scheduled sampling, determine if the site will be open

on the sampling day or closed due to unusual circumstances, e.g. late snow

Yes No " Record 0 visits and do not attempt interviews

On scheduled sampling days:

Obtain compliance check for the proxy count to determine what percent of users are measured by the proxy

Conduct exit interviews for the assigned time frame

One Day after scheduled sampling:

Check interview forms for completeness

Mail completed forms to regional coordinator

1 Brackets indicate who is primarily responsible for accomplishing the task.
14

Appendix B—Example of the formulation of several estimators based on the original site visit estimator SV1

Y Estimator description Estimator formulation2 Type Scale

Y1 Total number of annual site visits X = PEOPLE Total SV

Y2 Total number of annual NFVs X = PEOPLE/SVPNFV Total NFV

Y3 Total number of different visitors to the

national forest on an annual basis X = PEOPLE/(SVPNFV*NFVPY) Total Annual

Y4 Average number of NFVs per visitor

per year 2 3 Y Y/ Average Annual

Y5 Total number of annual NFVs by

children under 16 X = NKIDS/SVPNFV Total NFV

Y6 Proportion of NFVs by children

under 16 5 2 Y Y/ Proportion NFV

Y7 Total number of NFVs where

camping was an activity X = (PEOPLE*CAMP)/SVPNFV Total NFV

Y8 Proportion of NFVs where camping

was an activity 7 2 Y Y/ Proportion NFV

Y9 Total number of group trips to the

national forest on an annual basis X = 1/SVPNFV Total NFV

Y10 Sum of the ages of one person per

group for each group trip to the

national forest X = (1*AGE)/SVPNFV Total NFV

Y11 Average age of a NFV 11 9 Y Y/ Average NFV

PEOPLE = the average number of people in a last-exiting recreating car; SVPNFV = number of site visits per national forest

visit; NFVPY = number of national forest visits per year; NKIDS = number of people under the age of 16 years in a last-exiting

recreating car; CAMP = an indicator variable that is equal to 1 if camping was an activity on the national forest trip and 0 if it

was not; AGE = age of one person selected at random from a last-exiting recreating car.

1

 All estimators are based on the original site visit (SV) estimator defined as SV = P*CARS*X, where P = proportion of vehicles

that were last-exiting recreating vehicles, CARS = number of cars exiting the site during the 24-hour period, and X = average

number of people in a last-exiting recreating vehicle.

2

 The estimator is formulated from either the original SV estimator by substituting the specified X into the original SV estimator

or as the ratio of the two previously defined estimators.
15
16
English, Donald B.K.; Kocis, Susan M.; Zarnoch, Stanley J.; Arnold, J. Ross. 2002. Forest

Service National Visitor Use Monitoring Process: Research Method Documentation. Resch.

Pap. SRS–57. Asheville, NC: U.S. Department of Agriculture, Forest Service, Southern

Research Station. 14 p.

In response to the need for improved information on recreational use of National Forest

System lands, the authors have developed a nationwide, systematic monitoring process. This

report documents the methods they used in estimating recreational use on an annual basis. The

basic unit of measure is exiting volume of visitors from a recreation site on a given day. Sites

are stratified by type. Days are stratified by expected volume of exiting recreation visitors. A

double sampling strategy is the primary means used to obtain measures of exiting recreation

traffic. Where possible, observable counts of other measures highly correlated with visitation,

such as fee envelopes, ski lift tickets, or concessionaire reports, are used to reduce variation in

visitation estimates. In addition to showing how sampling units were defined, the authors also

provide calculations they used in developing estimators for the mean and variance of visitation.

Keywords: Monitoring, National Visitor Use Monitoring, NVUM, recreation use, research

methods, sampling, wilderness
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