Attachment A
	Recreation

Use Estimation Modeling (Webster Reservoir)

Use estimating models apply multiple regression techniques to estimate statistical relationships between recreation visitation and a wide range of explanatory variables, including reservoir water levels.

Monthly data on visitation by recreation activity from January 1980 to December 2000 was obtained from the reservoir manager at Webster. Recreation activities include camping, swimming, boating and waterskiing, picnicking, warm water fishing, and wildlife observation. Monthly information for the same time period was gathered on reservoir water levels, total monthly precipitation, and average monthly air temperature. Using this data, the following monthly model was statistically estimated for each activity.

Monthly Visitation_am =

where:

Activity: a = 1,...,l

Month: m = 1,...,n

(Note: Given the various recreation activities are pursued at different times of the year, each model was designed to reflect the sequence of months associated with that activity.)

Dependent variable: Total visitation in activity a in month m

Explanatory variables:

Year = Year of monthly data. This variable was intended to reflect a trend variable, used in lieu of socioeconomic variables. Expected sign: unknown. Both population and income could potentially affect recreation use. Populations in the adjacent counties to Webster have been fairly stable or even declining in recent years. Conversely, income levels have been gradually rising. The combined effect leads to an unknown sign for this variable.

WL = End of month (EOM) water levels measured in terms of feet above mean sea level. Expected sign: Positive. This implies that as WL increases, so would visitation. While this relationship typically holds across most water level ranges experienced by recreators, it may become negative at high water levels.

WL² = EOM water levels squared. Expected sign: Negative. The positive and negative signs on the WL and WL² variables produces a bell-shaped function where visitation increases, peaks, and decreases with increasing water level.

Precipitation = Total monthly precipitation in inches. Expected sign: Typically negative, but may be positive for some activities (e.g., fishing).

Temperature = Average monthly air temperature. Expected sign: Positive.

Monthly A series of qualitative (0,1) variables for each month of the recreation dummy season for each activity. Expected sign: unknown since certain months

variables = may be positive but others negative.

Information on average water levels by month for each alternative was modeled by Reclamation hydrologists. This water level information, along with historic monthly averages for temperature and precipitation, were multiplied by each model's coefficients to estimate visitation by activity and month for each alternative.

Model Selection

Model Selection Criteria

For each recreation activity, the following criteria were used to select the "best" model:

Significant Water Level Variable - Since water levels were the primary factor under control of reservoir managers, it was critical to have a significant water level variable within the model. Fortunately, many of the different models attempted resulted in significant water level variables. Significance was assumed at the 90 per-cent confidence level or higher (P[|Z|>z] column at .10 or lower).

Quadratic Water Level Term - Based on existing literature, it is generally hypothesized that the relationship between water level and recreation visitation would be bell-shaped. The quadratic function with a positive water level variable and a negative water level squared variable results in such a function.

Number of Significant Variables - In addition to the water level variables, the number of other significant variables influenced model selection.

Expected Signs - Based on the literature, a positive or negative relationship for each explanatory variable was assigned. Given these assumed relationships, statistically significant variables for each of the models were evaluated in terms of expected signs.

Coefficient of Determination (Adjusted R²) - A commonly used measure of the goodness of fit of the estimated function to the underlying data.

Model Selections

Based on a comparison using the above criteria, the following models for each activity at Webster Reservoir were selected as "best":

Camping.--

Dependent variable: Visits

Model is usable across the following water level range: 1859.2 feet to 1906.8 feet

Explanatory variables: # of observations: 105

Swimming.--

Dependent variable: Natural log of visits (Note: The analyst will need to take the antilog of predicted values to estimate predicted visits)

Model is usable across the following water level range: 1859.2 feet to 1906.8 feet

Explanatory variables: # of observations: 105

Boating and Waterskiing.--

Dependent variable: Visits

Model is usable across the following water level range: 1859.2 feet to 1906.8 feet

Explanatory variables: # of observations: 105

Picnicking.--

Dependent variable: Visits

Model is usable across the following water level range: 1859.2 feet to 1906.8 feet

Explanatory variables: # of observations: 105

Warm Water Fishing.--

Dependent variable: Visits

Model is usable across the following water level range: 1859.0 feet to 1906.8 feet

Explanatory variables: # of observations: 168

Wildlife Observation.--

Dependent variable: Natural log of visits (Note: The analyst will need to take the antilog of predicted values to estimate predicted visits)

Model is usable across the following water level range: 1858.8 feet to 1906.8 feet

Explanatory variables: # of observations: 252

Facility Availability Analysis (Kirwin Reservoir)

The facility availability analysis used for Kirwin Reservoir forecasts recreation use by water- based activity through evaluation of changes in water access. Basically, the approach fore-casts the availability of water access facilities, such as boat ramps, marinas, and swimming beaches, using high- and low-end usability thresholds for each facility in conjunction with end-of-month water level forecasts by alternative developed by Reclamation hydrologists. Table A-1 lists water access facilities and their respective high- and low-end water usability thresholds.

Forecasted monthly availability of each facility is linked with estimates of historical visitation by facility and activity to estimate monthly visitation by activity and alternative. After linking forecasted facility availability by alternative with historical visitation by activity and facility, a final adjustment is made to account for possible movement of visitation between facilities (i.e., facility substitution). Table A-1 also provides information as to the percentage of use by facility at different water levels.

Given the approach centers on water access, only water-based activities, such as boating, fishing, and swimming, are evaluated. While land-based, but water-influenced activities, such as picnicking and camping, may be somewhat affected by fluctuating water levels, it was assumed the impact would be fairly negligible except with severe drawdowns. As a result, water-based activities were assumed to incur the majority of the impact. Furthermore,

it was decided, in consultation with recreation planners working at Kirwin, that the primary impacts of fluctuating reservoir water levels would accrue to motorized boating and boat fishing. The assumption was made that shoreline activities, such as swimming and shoreline fishing, would not be significantly impacted by declining water levels since the recreators could simply walk out to the water if necessary. Potential impacts by recreation activity are summarized in table A-2. These assumptions, at least to some extent, limit the scope of the recreation analysis at Kirwin, but as noted previously, the lack of data precluded a full- scale modeling effort.