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Lake and Reservoir Management
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Effects of climate variation and water levels on
reservoir recreation
Tracy A. Boyer, Richard T. Melstrom & Larry D. Sanders
To cite this article: Tracy A. Boyer, Richard T. Melstrom & Larry D. Sanders (2017): Effects of
climate variation and water levels on reservoir recreation, Lake and Reservoir Management
To link to this article: http://dx.doi.org/10.1080/10402381.2017.1285375
Published online: 01 Mar 2017.
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Date: 02 March 2017, At: 07:14
LAKE AND RESERVOIR MANAGEMENT
http://dx.doi.org/./..
Effects of climate variation and water levels on reservoir recreation
Tracy A. Boyer, Richard T. Melstrom, and Larry D. Sanders
Department of Agricultural Economics, Oklahoma State University, Stillwater, OK
ABSTRACT
KEYWORDS
Boyer TA, Melstrom RT, Sanders LD. 2017. Effects of climate variation and water levels on reservoir recreation. Lake Reserve Manage. 00:1–11.
Climate change; lake levels;
nonmarket valuation;
reservoir levels; South
Central; travel cost method;
visitation
We combined information on valuation, visitation, and time-varying site quality to measure the effects
of climate variation and reservoir water levels on recreational demand at Fort Cobb Reservoir, Oklahoma. A time series model of monthly visitation was estimated to measure the effect of water levels,
rainfall, wind speed, and air temperature fluctuations on visitation to the reservoir. The results provide
no evidence that visitation is affected by rainfall and wind speed but strong evidence that visitation
is affected by water levels and air temperature, even after controlling for seasonality in demand. The
results suggest annual reservoir visitation will increase by 2.3% for a 0.5 C (1 F) increase in average
annual temperature, but that this increase will vary depending on the month and baseline temperatures; managers can expect an increase of 3.5% to occur in October through May, with essentially
no increase in June through September. Visitation increases due to temperatures could potentially
be offset with slight changes in water levels away from normal pool heights, however. To illustrate
the potential use of these predictions in benefit and damage assessments of environmental change,
a nonmarket valuation method was employed to value recreational trips to the reservoir. The results
indicate a trip is worth about $60 per person. With explicit values for recreation, lake and reservoir
managers may find it easier to gauge the economic benefits of managing lake levels for nonconsumptive uses.
Agricultural land use, population growth, and drought
are straining water resources in the South Central
United States (Daugherty et al. 2011, Johnson-Gaither
et al. 2013). Constructed reservoirs, instream flows,
and groundwater are being drawn down to maintain
water allocations to traditional consumptive activities
at the expense of nonconsumptive uses including recreation and wildlife habitat; water use is nonconsumptive when it results in no physical loss of water from
the source (Young 2005). Conflicts among competing
uses are likely to increase in the future because climate change is expected to increase the frequency of
droughts in existing dry regions (IPCC 2014).
To support efficient water allocation, policy makers and managers require information on the economic
effects of water level and climate fluctuations, but studies providing this information for reservoirs in the
South Central United States are scarce. Two exceptions
include Roberts et al. (2008) and Debnath et al. (2013),
which provide estimates of the recreational benefits of
improved water quality and water storage in parts of the
region. Notably, in comparing the economic benefits of
different water uses, Debnath et al. (2013) found that
the value of recreation can exceed the combined value
of hydropower and rural water supply at a reservoir.
This finding suggests that water resources may be misallocated if managers lack information about the value
of water-based recreation. Thus, the need for research
on the economic benefits of reservoir recreation in the
South Central United States is critical.
This study was motivated by the lack of research on
recreation at reservoirs in Oklahoma. Reservoir managers, environmental engineers, and aquatic scientists
in the state are increasingly demanding information
about the impacts of reservoir water allocation decisions on the value of nonconsumptive water uses.
Acknowledgement of these values is widespread, but
actual measurement is hindered by a lack of data
on nonconsumptive water uses and a shortage of
resources to collect this data. Existing models from
other regions could be used to describe visitor behavior
and recreational value, but the insights will be biased
CONTACT Richard T. Melstrom
[email protected]
Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/ulrm.
© Copyright by the North American Lake Management Society 
2
T. A. BOYER ET AL.
if visitation patterns differ between regions. To address
this research gap, this paper presents estimates of the
impact of water levels on the value of recreation at a
reservoir in Oklahoma.
Research on the demand for recreation in other
regions has found the value of reservoir recreation is
closely tied to water levels. An early study of California
reservoirs by Ward et al. (1996) found that the recreational use value of water ranged from $6 to $600 per
acre-foot, depending on the reservoir. In a study of
Nevada reservoirs, Huszar et al. (1999) also found that
the value of and demand for water-based recreation
related significantly to water levels. Jakus et al. (2000)
found that water levels affected the value of reservoir
fishing in Tennessee, although not the overall participation in fishing. Several other studies in the economics
and water resources literature have found that water
levels can affect reservoir visitation (Creel and Loomis
1992, Cameron et al. 1996, Eiswerth et al. 2000, Lienhoop and Ansmann 2011, Miranda and Meals 2013,
Neher et al. 2013). The implication of this research for
water resource planning is that increased or decreased
aggregate reservoir levels will likely impact the economic benefits derived from water-based recreation.
In addition to the geographic focus, this study differs
from prior research on the demand for reservoir recreation in two ways. First, we did not directly identify the
effect of water levels on individual welfare because our
individual visitor data did not vary across time and our
monthly visitation data lacked information on visitor
characteristics. We therefore related changes in recreational use value to reservoir conditions using separate demand models. That is, we initially developed a
monthly visitation model on time-series data to relate
shifts in demand to changes in time-varying site characteristics (e.g., water levels and temperature); we then
assessed the economic damages from fewer trips using
a measure of economic value derived from an individual demand model applied to visitor cross-section data.
Second, we examined the relationship between
reservoir visitation and climate variability, which most
prior studies overlooked. Climate variation or variability refers to climate fluctuations above or below
long-term averages. For example, there are significant
year-to-year variations in average air temperature at
the study reservoir that could have impacted visitation
(e.g., in 2006 temperatures averaged several degrees
below normal, whereas in 2009 temperatures averaged
several degrees above normal). The current study thus
adds to the growing literature reporting on the relationship among weather, climate, and recreation demand.
This study does not, however, address the impacts
of climate change, which is the long-term continuous change in average weather conditions or the range
of weather. Previous work has estimated the potential
impacts of climate change on national park visitation
(Richardson and Loomis 2004) and winter recreation
(Gössling et al. 2012) and the effect of climate variation on sport fisheries (Pendleton and Mendelsohn
1998, Ahn et al. 2000). Although the focus of the current research was on climate variability, the results do
provide insights into the impacts of climate change on
reservoir recreation. With information on how weather
affects water-based recreation, reservoir managers can
better plan for future trade-offs between recreation and
other reservoir uses.
Study site
Fort Cobb Reservoir lies in the upper Washita River
Basin in western Oklahoma (Fig. 1). The reservoir was
constructed in 1958 for water supply, flood control,
fish and wildlife habitat, and recreation. At normal
water elevation (409 m), the area of the lake includes
∼1740 ha of water and 72 km of shoreline (Cofer et al.
2009). The reservoir is managed by the Bureau of Reclamation, although most of the shoreline is operated as
a state park, which maintains 4 boat ramps, a marina,
2 swimming beaches, picnic areas, and several hundred campsites and RV hookups. The reservoir has no
private waterfront, so the recreational use value of the
reservoir comes from lake and shoreline recreation.
Like other lakes in the South Central United States,
Fort Cobb Reservoir lies in a rural, intensively farmed
landscape.
Methods
There were two parts to the investigation. First, we
measured the impact of water levels and climate variation on monthly recreational visitation by combining existing databases of monthly visitation, water levels, and climate factors to estimate a time series model
of recreational trips to the reservoir. Second, we estimated the economic value of a trip to the state park
surrounding the reservoir because no such values have
been reported for similar reservoirs suitable for benefits transfer. Trip values were estimated using the
LAKE AND RESERVOIR MANAGEMENT
3
Figure . Fort Cobb Reservoir in Fort Cobb Watershed, OK.
individual travel cost method applied to a count-data
model of trips.
Time series data
The visitation data are from the Oklahoma Tourism
and Recreation Department (OTRD). Total visitation is
calculated by the OTRD monthly using information on
campsite rentals, car counters at park entry points, and
visiting group sizes. Visitation is measured in aggregate
and does not distinguish visits by sociodemographic
variables, trip origin, or the purpose of the visit. It
is therefore not possible to use a valuation method
with the OTRD data or to distinguish between visits
taken for different onsite activities (addressed later).
Visitation data were available for each month between
July 1998 and June 2014. The variable visits measured
monthly visits to the state park. These data indicate an
average of ∼58,000 unique visits to Fort Cobb State
Park in a month, although the actual amount can vary
widely (Table 1). All recreation activities take place at
the lake, either on the water or on the shore. There are
no trails, and all camping sites lie adjacent to the lake
shore. The park would not exist without the lake and,
although not every visitor goes out on the lake, most do
(72% boat on the lake and 72% fish at the lake; Table 2),
and other visitors camp, swim, or picnic by the lake.
Water level data were obtained from the US Army
Corps of Engineers (USACE 2014). Data on water
elevation for Fort Cobb Reservoir are reported in
daily and monthly averages extending back to 1994.
Monthly average water levels were used here, measured in meters above sea level by the variable level
(Table 1). Normal water elevation, the height of the
water at which the reservoir is considered full, is 409 m
(1342 ft). A scatter plot of visits and level (Fig. 2) shows
that maximum visitation tends to occur near normal
water elevation. To account for possible nonlinearity in
the relationship between water levels and visitation, the
square of the variable level centered on the mean (to
reduce multicollinearity) was included as a regressor in
the monthly visitation model. This method is consistent with prior research, which used a quadratic function to capture the concave relationship between water
Table . Summary statistics of monthly visitation, environmental,
and economic data for Fort Cobb Reservoir.
Table . Summary statistics of the characteristics of individual visitors at Fort Cobb Reservoir ().
Visitation model measuring water level and climate
impacts
Variable
Mean
SD
Min
Max
Visits
Level (m)
Temperature (C)
Rainfall (cm)
Wind speed (km/h)
Unemployment (%)
Gas price ($)
,
.
.
.
.
.
.
,
.
.
.
.
.
.
.
.
− .
.
.
.
.
,
.
.
.
.
.
.
Note. SD = standard deviation.
Variable
Mean
SD
Min
Max
Trips
Travel cost
Substitute cost
Group size
Age
Boating
Fishing
Overnight
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.


.






.
.





4
T. A. BOYER ET AL.
monthly visitation. These variables included gas price,
which measures the average monthly retail gas price
observed in the Midwest (Energy Information Administration 2014) and unemployment, which measures
Oklahoma’s seasonally adjusted monthly unemployment rate (Bureau of Labor Statistics 2014).
Model specification
State park visitation at Fort Cobb Reservoir was modeled as:
ln (vt ) = α + γw wt + γc ct + γx xt + γd dt + εt ,
Figure . Monthly visitation and water levels at Fort Cobb Reservoir, OK, during –. Levels are measured as meters above
sea level, with a normal elevation (pool height) of  m a.s.l. The
months with the largest number of visitors tend to be the months
when water levels are at or near normal elevation.
levels and recreational activity (Debnath et al. 2013,
Miranda and Meals 2013).
Climate data were collected from the Oklahoma
MESONET network of weather stations (Brock et al.
1995), consisting of 120 automated monitoring stations covering the state, including one station ∼1 km
from Fort Cobb Reservoir. Every 5 minutes, each
station collects data on, among other variables, air
temperature, rainfall, humidity, wind speed, and wind
direction. These data were assembled into monthly
summaries up to April 2014. The weather variables
considered in the study included air temperature,
rainfall, and wind speed. Specifically, the variable
temperature measures average daily temperature in
degrees Celsius, rainfall measures average daily rainfall
in centimeters, and wind speed measures average wind
speed in kilometers per hour (MESONET variables are
normally measured in US customary units and were
converted to metric for this application). Data summaries show that temperature and rainfall have enough
month-to-month variability in this region to plausibly
affect visitation (Table 1). Wind speed is relatively less
variable month-to-month, so measuring an impact
at a monthly time scale may be difficult. To test for a
nonlinear effect of temperature (anticipating that temperature increases from a low base increase visitation
but further increases make camping uncomfortable
and decrease demand), the square of temperature was
also included as a covariate in the regression model.
The set of model variables was enhanced with proxies for macroeconomic conditions expected to affect
(1)
where vt is the number of visits in month t, wt is a
vector of water level measures (level and level-squared),
ct is a vector of climate factors, xt is a vector of economic conditions, dt is a vector of time effects, and ε t is
the error. The climate factors included the 3 variables
drawn from the MESONET database discussed earlier
plus the square of temperature. To control for timedependence in visitation, equation 3 was estimated
with different specifications of dt . We reported an initial specification that ignores all time effects, but this
inevitably biases γ because visitation and temperature
are both seasonal. That is, there may be unobserved factors that vary with the seasons for reasons unrelated to
temperature (for example, employment contracts) that
need to be included in the model. Failure to control for
these factors by excluding seasonal indicator variables
could lead to endogeneity. Subsequent specifications of
equation 1 therefore included seasonal effects (month
dummy variables; Neher et al. 2013) and seasonal
effects plus a yearly trend (Jollands et al. 2007). We considered including several interaction variables to test
whether, for example, the effect of water level could
depend on temperature; however, most of the interactions were highly collinear with the original variables, and none meaningfully improved the fit of the
model.
All monthly visitation models were corrected for
autocorrelation. Although the ordinary least squares
(OLS) estimator is unbiased in the presence of autocorrelation, assuming the explanatory variables are exogenous, it is not efficient and its standard errors are no
longer valid (Neher et al. 2013). We used the DurbinWatson test statistic to check for first-order autocorrelation. Based on initial OLS regression results, the
test rejected the hypothesis of no autocorrelation at
the 1% level for all model specifications. We therefore
LAKE AND RESERVOIR MANAGEMENT
applied the Prais-Winsten method to correct for firstorder autocorrelation (Rogers et al. 2014).
Applying the travel cost valuation method to a trip
demand model
Visitor cross-section data
To quantify some of the economic impacts on recreational visitors from changes at the reservoir, we
measured the economic benefit of trips. For this we
used individual visitor data collected over 2 nonconsecutive weeks in June and July 2014 (including
weekdays and weekends). A sample of visitors was
collected by recruiting participants at the swimming
beaches and picnic and camping areas around Fort
Cobb State Park. To ensure compliance with Institutional Review Board rules for human subjects research,
student interviewers were instructed to only contact
and interview adult visitors at least 18 years old.
Interviewers worked throughout the day but were
instructed to not approach people performing some
sort of work, specifically launching a boat or setting up
a tent, because past experience showed these individuals were unlikely to participate in interviews, leading
to sample selection bias in favor of visitors who do not
engage in boating or camping. Sample selection will
not bias the parameters in the model, however, if all
variables that determine the probability of selection are
included as explanatory variables (Wooldridge 2002).
The individual trip demand model includes variables
for visitors who use a boat and stay overnight, so sample selection on the basis of these variables will not bias
the trip value estimates. These procedures resulted in
187 survey responses; refusals were not recorded, but
most of those contacted by the interviewers agreed to
participate.
The survey was kept short to minimize the burden
of participation; it took about 10 minutes to administer.
The survey instrument asked about visitors’ activities at
the lake, time spent on site, travel group size, residential
location, and demographics. One battery of questions
asked about the number of trips to Fort Cobb Reservoir in the previous year (2013) and the number of trips
anticipated for the current year (2014). The questionnaire also asked about trips to other lakes.
Before analyzing the data, the responses were
checked for appropriateness. Several responses could
not be used because they did not include quantitative
information or the answers were considered infeasible.
5
For example, several respondents did not report the
frequency of trips to the lake while others reported the
number as “multiple” or “a lot.” For nonresponses to a
demographic questions, missing values were filled in
with the average reported by the other respondents; this
practice affected 9 observations used in the analysis, so
multiple imputation was not considered necessary. The
usable sample size was 162.
Several variables used in the demand model were
created from a combination of survey and external
data. The variable travel cost was calculated using individual information on travel distance, travel time, a
driving cost, and a value for travel time. Travel distance
and time from the centroid of each respondent’s home
zip code to the lake was calculated using the PC∗ Miler
program (ALK Technologies 2012). Driving costs
included the average fuel price plus marginal depreciation and maintenance costs as reported by the American Auto Association (AAA), totaling $0.25 per mile. A
large body of literature has investigated the appropriate
value of travel time (Smith et al. 1983, McKean et al.
1995, Bockstael et al. 1987, Fezzi et al. 2014). Cesario
(1976) suggests travel time to be valued at one-quarter
to one-half the wage rate; one-third the wage rate is
common in recreation demand studies (e.g., Vesterinen et al. 2010, Melstrom et al. 2015). Other work, however, recommends the full wage rate (Larson 1993). To
compromise between these extremes, this study used
one-half the wage rate as the value of visitors’ time. The
wage rate was calculated as respondents’ income (measured as the midpoint within their reported income
category from the survey) divided by 2000, which is
the total amount of working hours in a year. Income
groups were classified into <$19,999; $20,000–$39,999;
$40,000–$59,999; $60,000–$79,999; $80,000–$99,999;
and ࣙ$100,000. Finally, travel cost was calculated as
the round-trip distance multiplied by the per-unit driving cost, plus round-trip travel time multiplied by the
assumed value of time. There is no entrance fee to the
site.
A number of studies have shown the importance of
controlling for substitute prices in individual demand
models (Liston-Heyes and Heyes 1999). The estimated
own-price effect will be biased if omitted substitute
prices are correlated with the cost of visiting the site
in question. To control for possible substitution effects,
the travel cost to Lake Eufaula in Oklahoma was used to
generate the variable substitute cost, following the same
procedures used to generate travel cost. Lake Eufaula
6
T. A. BOYER ET AL.
was used because respondents most often identified
visiting that lake in the past.
The other covariates used in the individual demand
model were a combination of demographic and behavioral variables (Table 2). The variable group size is the
number of individuals with whom the respondent was
traveling, and age is the respondent’s age. Two dummy
variables indicate whether the respondent engaged in
boating or fishing in the event that trip demand varied
among individuals who used the lake for those activities. The dummy variable overnight, which equaled
1 for trips lasting >1 day and 0 otherwise, was
used to distinguish between the average number of
observed trips for overnighters and day trippers. Summary statistics indicate >90% of visitors stayed multiple days, which is consistent with the nature of this state
park.
individual trip data) produces standard errors biased
downward. As a remedy, we bootstrapped the standard
errors (Efron and Tibshirani 1993). We also estimated
equation 3 as a negative binomial regression accounting for truncation and endogenous stratification, which
accommodates overdispersion by allowing the variance
to be a function of the mean (Martinez-Espineira and
Amoako-Tuffour 2008).
When individual demand is modeled in this manner, the economic value or willingness to pay (WTP)
for a trip by a visiting group is −1/β tc (Haab and
McConnell 2003). We report 3 measures of WTP: WTP
per group, WTP per visitor (measured by dividing
WTP per group by the respondent’s group size), and
WTP per visitor-day (measured by dividing WTP per
visitor by the respondent’s days onsite for the current
trip; Melstrom 2014).
Model specification
Demand was modeled as a count data process to
account for the integer nature of individual trips, measured as the total number of trips to the reservoir
in 2013 and 2014. Because the data were collected
onsite, observed trips were truncated at 0 and more
frequent visitors were oversampled (Englin and Shonkwiler 1995, Parsons 2003). We therefore used Poisson
regression with corrections for truncation and endogenous stratification:
Results
f(ni |xi ) = exp (−λi ) λini −1 /(ni − 1) !,
(2)
which is individual i’s probability of taking ni trips,
with the expected number of trips denoted by λi . It is
typical to express λi as an exponential function of the
demand shifters λi = exp(βxi ) (Haab and McConnell
2003). Considering the variables from the onsite survey, the expected number of trips to Fort Cobb Reservoir was specified as:
⎡
⎤
β0 + βtc travel costi + βsc substitute costi
⎢ +βg ln group sizei + βa ln agei
⎥
⎥.
λi = exp ⎢
⎣ +βb boatingi + β f fishing
⎦
+βo overnight i
i
(3)
Poisson regression of equation 3 was carried out
by maximum likelihood estimation; however, simple
Poisson regression often suffers from the misspecification that the conditional mean and variance are equal,
which in cases of overdispersion (a common feature of
Monthly visitation model
Most of the estimates in the 3 monthly visitation models have the expected parameter signs
(Table 3). First consider the results of the baseline model specification. The variables level and
level-squared are jointly statistically significant
(P < 0.01). The parameters predict visitation is
highest when water levels are about 409.3 m (1343
ft), or about 30 cm higher than normal water
elevation, holding other variables constant. The
effects of temperature and temperature-squared
are also jointly statistically significant (P < 0.01).
The model predicts higher gas prices negatively
impact visitation, which is consistent with our
expectations.
The second specification adds in month dummy
variables to control for seasonality in visitation. For
brevity, the dummy estimates are not reported here. All
the parameter signs were unchanged from the baseline
model, with notable differences in the estimates. A test
of the joint hypothesis that the effects of level and levelsquared are 0 was again rejected (P < 0.01). A similar joint test for temperature and temperature-squared
was also rejected (P < 0.01). The parameters imply that
visitation is highest when water levels are at 409 m.
Furthermore, the predicted apex on the quadratic temperature effect was 27 C (80 F), which is within the
observed range of variability (Table 4). The effect of
LAKE AND RESERVOIR MANAGEMENT
7
Table . Fort Cobb Reservoir monthly visitation (–) model results.
Baseline model
Variable
Level
Level-squared
Temperature
Temperature squared
Rainfall
Wind speed
Unemployment
Gas price
Constant
Year trend
Seasonal (monthly) effects
Observations
R-squared
Durbin–Watson statistic (corrected)
Effect of  cm ( ft) lake level change from avg. elev.
Effect of . C ( F) increase from sample avg. temp.
Effect of . C ( F) increase from  C ( F)
Model with seasonal effects
a
Coef.
SE
.∗∗
− .∗∗∗
.∗∗∗
− .∗∗
.
.
− .
− .∗∗∗
− .∗
.
.
.
.
.
.
.
.
.
Coef.
SE
.
− .∗∗∗
.∗∗
− .∗
.
.
− .∗∗
− .∗∗∗
− .
.
.
.
.
.
.
.
.
.
No

.
.



Model with time trend
a
a
Coef.
SE
.
− .∗∗
.∗∗
− .∗
.
.
.∗∗
− .
− .
− .∗∗
.
.
.
.
.
.
.
.
.
.
Yes

.
.


−
Yes

.
.



Note. SE = standard error. ∗∗∗ , ∗∗ , ∗ denote significance at the %, %, and % levels, respectively.
aCalculated using White’s heteroskedasticity-robust estimator.
unemployment was negative and significant (P < 0.01),
and the effect of gas price remained negative as in the
baseline model.
The third specification added in a yearly trend.
Although the estimated parameter signs were
unchanged, several effects lost significance. A joint
test of the effects of temperature and temperaturesquared was again rejected (P < 0.01), but level and
level-squared lost significance (P < 0.05). The estimates indicate visitation is highest when water levels
are at 408.9 m (1341.5 ft, or slightly below normal pool height), and when temperatures are at 26 C
(78 F). These peaks fall within the range of the observed
values.
Table . Individual trips to Fort Cobb Reservoir demand model
results.
Poisson
Negative binomial
a
Variable
Coefficient
SE
Coefficient
SE
Travel cost
Substitute cost
Ln(group size)
Ln(age)
Boating
Fishing
Overnight
Constant
− .∗∗
.
.
.
.∗∗
.∗∗
.∗
− .
.
.
.
.
.
.
.
.
− .∗∗
.
.
.
.∗∗
.∗∗
.
− .
.
.
.
.
.
.
.
.
Observations
b
Pseudo R-squared

.

.
Note. ∗∗∗ , ∗∗ , ∗ denote significance at the %, %, and % levels, respectively.
aStandard error calculated from  bootstraps.
bMcFadden’s pseudo R-squared; calculated as 1 − ln L(model)/ln L(null).
Individual demand model and trip value
The individual demand model estimates (Table 4) show
that the own-price effect of travel cost was negative and
statistically significant at the 0.05 level in both specifications. The results indicate the demand for trips to
Fort Cobb Reservoir was uninfluenced by the proximity of Lake Eufaula to visitors’ homes. The effects of
boating and fishing indicate that visitors who fish or
boat on the lake tend to visit more frequently. The effect
of overnight implies that overnighters take more trips
on average. Including overnight in the model had little effect on the other parameters. Note also the variable overnight could be interacted with travel cost to
test whether the demand function varies in slope for
day-trippers and overnighters. We tested this specification but found it did not improve the fit of the
model.
For a single visitor, the value of a trip was about $60
(Table 5). Per day, the value of a trip to a single visitor
was about $20. All trip value estimates had wide and
upwardly skewed confidence intervals.
Table . Trip economic benefit estimates (in  dollars) from the
individual trip demand models.
Poisson
Negative binomial
a
a
Trip welfare measure
Average
% CI
Average
% CI
WTP/visiting group
WTP/visitor
WTP/visitor/day



–
–
–



–
–
–
aConfidence interval calculated from  bootstraps.
8
T. A. BOYER ET AL.
Discussion
The various specifications of the monthly visitation model make several common predictions. The
quadratic effects of level and temperature were generally
significant, suggesting that reservoirs’ water levels and
ambient air temperature have a nonlinear impact on
visitation. Specifically, the models predicted increases
in water levels from a low base will have a large positive effect on visitation but increases past normal levels will lead to a fall in demand. Likewise, for temperature, increases from a cool base will encourage
greater visitation but further increases once temperatures are already hot will have a small (and possibly
negative) effect on demand. Our preferred visitation
model included the seasonal effects and time trend, in
which the concave relationships between visitation and
temperature and water level falls within the observed
range of values.
The results imply that precipitation and wind speed
do not affect the demand for reservoir recreation, at
least month-to-month. No specification estimated a
statistically significant effect of rainfall or wind speed.
Rain and severe wind events likely affect the demand
for day-to-day recreation, but this effect would be
masked by the relatively coarse time scale of the visitation model if postponed trips are made up later in
the month. Moreover, many visitors may have been
compelled to make their trip regardless of rain and
wind events because of reservations they made weeks in
advance of their trip (recall that >90% of visitors in the
onsite sample stayed multiple days and likely needed
reservations). The results may have been different if
the Fort Cobb Reservoir received a greater share of day
visitors.
The impacts of several hypothetical water level and
temperature changes were predicted from the monthly
visitation model (Table 3). Consider the estimates from
the second and third specifications that controlled for
seasonality by including month dummy variables.
Moving away from normal water elevation reduces
recreation demand by 725–1918 visits per 1200 m3 (1
acre-foot) per month, which is about a 1% to 3% decline
in visits. Given a trip value of about $60 per visitor, this
decline in demand suggests that a 30 cm (1 ft) change
in average monthly water level from normal elevation
reduces the recreational value of Fort Cobb Reservoir
by between $43,500 and $115,100 per month.
The effect of average monthly temperature on visits was nonlinear and quadratic. The interpretation is
that warmer weather increases visitation when temperatures are already low, so during most of the year (in
winter, spring, and fall) increasing temperatures lead
to more visitors. Increasing temperatures in months
that are already hot (Aug and Sept), however, can have
the opposite effect (i.e., visitation falls). These results
suggest visitation at Fort Cobb State Park may experience an overall increase with global climate warming, which is consistent with some other recreation
demand studies (Richardson and Loomis 2004). Based
on the HadCM3 and GFDL-CM2 general circulation
models’ climate change projections, the South Central
United States is expected to experience a several degree
increase in average temperatures in the next several
decades (TACCIMO 2014). The Fort Cobb monthly
visitation models predict a temperature rise of 2 C
(about 3 F) will increase visitation by 7% to 8% percent,
or several thousand visits per month on average, with
most of the increase occurring in the cooler months
and little change in the warmest months. Overall, this
increase in visitation would raise the recreational trip
value of Fort Cobb reservoir by about $3 million per
year. The negative time trend in the third specification,
however, suggests a decline in visitation that may offset this gain. These projections also raise an interesting
question about the design life (lasting to 2060) of the
reservoir.
There are several important caveats to the economic
values reported here. First, the visitor values were
estimated on a sample of summer visitors because
resources limited the frequency that Fort Cobb State
Park could be surveyed, possibly affecting the reliability
of the trip value estimates. Second, the demand models
in the study were incapable of predicting changes in
use value arising from site quality changes. Some people may experience a welfare loss but continue to visit
the site after a reduction in site quality; this welfare
loss was not included in our estimates. The changes in
site value reported here were only measured in terms
of adjusted visitation numbers with the value of a visit
held constant, which understates the full welfare effects
of a change in site quality. Third, climate change will
encompass more than temperature changes; although
the models suggested that other climate variables had
little impact on visitation, long-term climate change
could affect the natural environment around Fort
Cobb Reservoir, which would affect visitation in ways
not captured in the monthly visitation model. Nonuse
value may also be associated with the reservoir, so the
LAKE AND RESERVOIR MANAGEMENT
recreation value reported here should be interpreted as
a lower bound for nonmarket value of the site because
it does not provide an estimate of the total recreation or
nonuse value. Finally, the monthly visitation data did
not distinguish between visits intended for different
recreation activities, although visitors who actively
use the lake are probably more sensitive to water level
changes than other visitors. Ignoring visitor heterogeneity could therefore mask the substantial effect
water level has on certain types of users.
Conclusion
This study analyzed the impact of fluctuating reservoir conditions on the recreational value of Fort Cobb
Reservoir in Oklahoma. We found that peak visitation was associated with water levels at normal pool
elevation and average monthly air temperatures at
27 C. Visitation declined when water levels fluctuated from normal elevation, probably because water
access is restricted when water levels are too low, and
beaches and picnic areas flood when water levels are
too high. The effect of temperature on visitation was
also curvilinear, in that rising temperatures during cool
weather increased visitation but at a decreasing rate.
Eventually, rising temperatures led to a fall in visitation because camping is uncomfortable in hot weather.
Overall, these findings demonstrate the importance of
accounting for nonlinear site quality effects in modeling the demand for reservoir recreation.
Changing water levels implies changes in the recreational value of a reservoir. Our case study implies that
to maximize the recreational value of a reservoir, managers should maintain water levels at or near normal
pool height while also balancing the benefits of water
for flood control, hydropower, and other consumptive
uses. Lowering or raising water levels may be necessary
to support other water uses, although often allocations
for recreation receive the lowest priority (Roberts et al.
2008). Overlooking the value of recreation in deciding water levels, however, will lead to adjustments in
pool height that occur too rapidly and equilibrium levels that are too high or too low compared to what is
economically desirable (assuming water levels were at
normal pool height before the change). The visitation
model in this study can be used to estimate the economic costs of lost recreation from changing water levels. Hence, this information can be used to enhance
political support for managing reservoirs for recreation
9
or to carry out benefit–cost analyses of allocating water
from multiuse reservoirs.
Oklahoma and the region of the semiarid and arid
US South have recently been marked by extreme climate variability, including periods of extreme temperature and drought. Projections made by the Oklahoma
Water Resources Board in the State’s Comprehensive
Water Plan have brought the issue of water rights and
appropriations to the fore. The Oklahoma Comprehensive Water Plan finalized in Oct 2011, the recent water
rights lawsuit brought by the Chickasaw and Choctaw
Nations, and other past and potential water conflicts in
the South Central region highlight the need to define
economic and environmentally optimal water withdrawals (OWRB 2012). With explicit values for lake
recreation, nonconsumptive use values can be brought
into the policy discussion, otherwise decision makers
will have poor knowledge of the in situ value of water
resources. Furthermore, rural communities that rely on
water-related tourism to diversify their economy must
be prepared for changes in the value of their natural resources—and the opportunity cost of their use—
which our study confirmed is related to changes in
water levels and climate. This information will become
increasingly important in water management decisions
as changes in climate exacerbate water use conflicts.
Acknowledgments
The authors would like to thank Kangil Lee for valuable research
assistance.
Funding
Funding provided by the USDA NIFA National Integrated
Water Quality Program Project #2013-51130-21484, the USDA
National Institute of Food and Agricultural Hatch project
#OKL02852, the Division of Agricultural Sciences and Natural Resources at Oklahoma State University, and the National
Science Foundation Grant No. IIA-1301789. The econometric
analysis was conducted in Stata, and the data are available from
the corresponding author upon request.
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