Crater Lake: Hydrogeology

Introduction

The purpose of this memorandum is to provide a summary of the hydrogeology of Crater Lake located in Crater Lake, Oregon in support of the project questioning whether to sell Crater Lake's water to California providing a landfill for waste or keeping the lake for its recreational value. The hydrogeology of this project is used to predict some of the figures that are used with the other team members' components. Determining these values can be used to create a logical answer for this project. The values that were of most importance in this project were of volume and drainage longevity of the lake's water content. Consumption rates for the State of California are of extreme interest to the project in order to determine an appropriate time period to drain the lake. In order to understand the hydrogeology of Crater Lake, the investigation of groundwater movement and flow of the lake's water was a key factor. The public claims that springs are resurfacing from the lake's water content. With the information that is available, the investigation of outflows and inflows of hydrothermal variability is explained to establish a better truth than that created by the public and community.

Methodology

Volume of Crater Lake. The volume of Crater Lake was determined by assuming that the lake was a frustum of a cone (see attached diagram). The formula for the volume of a frustum of a cone is: ⅓h(r^2 + rR + R^2) (see diagram). The complexity of finding volume of Crater Lake's frustum shape consisted of locating information available stating different dimensions of the lake. Two radiuses were to be determined; one radius of the surface water (R) and one radius of the lake's bottom (r). The dimensions of the surface water were found to be 6.02 miles by 4.54 miles (National Park Service). There were no clear dimensions of the current floor of the lake, but at the time of the creation of the caldera the width of the base was approximately 5.0 miles wide. The depth of the lake is 1,932 feet (National Park Service), which is the "h" in the equation.

The radius is equal to half the length of the diameter. To generate an estimated model of the frustum of the cone the average of the two diameters of the surface water had to be found. This was done by adding 6.02 mi and 4.54 miles and dividing that value by 2. This value is 5.28 miles, which is the diameter of this estimated frustum model. The radius value for the surface water (R) of the frustum model is then 2.64 miles. The bottom of the lake's diameter is 5.0 miles, which then is divided by 2 to determine the radius (R). R then equals 2.5 miles. However, these quantities must be converted to feet. The conversion of miles to feet is that there are 5,280 feet per mile (Chicago Turnite). 2.64 miles is 13,939 feet and 2.5 miles is 13,200 feet.

With these values the volume of Crater Lake can be found. So again, the formula for volume of a frustum of a cone is: ⅓h(r^2 + rR + R^2) (see diagram). With this formula the quantities from above can be plugged in: ⅓(1,932)[(13200*13200) + (13200*13939.2) + (13939.2*13939.2)]

The answer to the equation is 1,117,896,372,000 ft^3. This number needed to be converted to gallons. Given from that 7.48 gallons are in one cubic foot, 1,117,896,372,000 ft^3* 7.48 gallons would equal 8,361,864,862,000 gallons. The volume of Crater Lake is 8,361,864,862,000 gallons. (Detailed components of equations on spreadsheet.)

California Water Consumption. Research was done in order to determine the State of California's consumption rate. The California Energy Commission provided the figures for this annual rate. "In total, California uses about 42.6 million acre-feet of water per year for agricultural, municipal, and industrial purposes, weighing some 550 million tons." (California Energy Commission)

Drainage of Crater Lake. After determining that the State of California consumes 42.6 million acre-feet of water annually, the amount of time it would take to drain Crater Lake could be revealed. One acre foot is equal to 325,851 gallons (Chicago Turnite). With that in mind, 42,600,000 acre-feet * 325,851 gallons will be 13,881,252,600,000 gallons. This value is the amount of gallons being consumed per year by the State of California.

Assuming that the State of California consumes the same amount of water each month, 13,881,252,600,000 gallons/12 months, the amount of water consumed will be 1,566,771,050,000 gallons per month. So the amount of time it will take to drain Crater Lake is determined by volume of the lake divided by the amount of water California consumes per month: is 8,361,864,862,000 gallons/1,566,771,050,000 gallons per month = 5.34 months. It will take only a little over five months to drain the lake.

Crater Lake Flow. There have been many assumptions and unsubstantiated rumors of springs to resurface near the Klamath River due to Crater Lake. These reports of hydrothermal outputs by Crater Lake are very difficult to provide substantial evidence that they are true. However, there are many reports on the activity of the thermal inputs to Crater Lake that cause temperature variability. There are several hypotheses for the thermal fluctuations in the near-bottom waters of the lake. Some of these hypotheses include the "convection of waters through cooling magmatic bodies that underlie Crater Lake" (Collier and Dymond, 60). Other hypotheses suggest that "a landslide may provide a more permeable pathway for heated water from ring-fracture sites reach the lake-floor surface" (Bacon et. al. 38). One other hypothesis from Collier and Dymond suggested that "the observed temperature pattern of the deep lake is a consequence of conductive heat flux through the lake bottom and does not involve any fluid injection" (60). Crater Lake does have hydrothermal variability, to which none of which can be found to result in a distinguished springs outflows.

Discussion

Given the data above, there are formative values that create a basis of how the water content and time period of drain Crater Lake can affect the decision of this project. The volume of Crater Lake creates issues in the decision making process of whether to sell the lake or to keep it. The lake's volume is massive and has great value to either side of the project. In order to find the volume of Crater Lake a series of steps were taken to perform the volume of a frustum equation. The volume of Crater Lake is 8,361,864,862,000 gallons. This volume is based on an average year. The number of gallons can depend on various