Scientific Investigations Report 2006-5252
U.S. GEOLOGICAL SURVEY
Scientific Investigations Report 2006-5252
Lake Mead evaporation was computed using micrometeorological data collected at four floating instrumented platforms deployed in Water Barge Cove near Callville Bay, in Boulder Basin near Sentinel Island, in the Virgin Basin, and in the Overton Arm near Echo Bay (fig. 1). Platform station identifier, name, and date of installation are listed in table 2.
The platform in Water Barge Cove (site A) was in a relatively shallow cove protected from prevailing winds (figs. 1 and 2). The platforms in Boulder Basin near Sentinel Island (site B), Virgin Basin (site C), and Overton Arm (site D) were in different areas of the lake that are representative of open-water conditions in each basin. The depth of water at the four platforms fluctuated during the study due to water-level changes of Lake Mead. Lake elevation ranged from less than 1,196 ft in February 1997 to almost 1,216 ft in September 1998 (fig. 3).
Each floating platform was equipped with instruments to measure and record meteorological data and water temperature. Air temperature and relative humidity were measured with a temperature-humidity probe (THP), wind speed and direction were measured with an anemometer and wind monitor, net radiation was measured with a net radiometer, and water temperature was measured at various depths with temperature probes (fig. 4, table 3). A two-point mooring system was used to secure each barge to prevent drifting and maintain the directional aspect of the wind monitor and net radiometer. The number of months with complete data, collected at four floating platforms for 1997–99, used to compute evaporation from Lake Mead is listed in table 4.
The energy-budget method was used to measure evaporation from Lake Mead. This method also was used to quantify evaporation from western reservoirs in the 1950s (Anderson, 1954), and has been used by the USGS on a few long-term lake studies (Sturrock and Rosenberry, 1992; Rosenberry and others, 1993; Swancar and others, 2000). The energy-budget method is the most accurate method for measuring lake evaporation (Winter, 1981). Use of the energy-budget method requires a large amount of data collection, but the effort is important because accurate measurements of lake evaporation are rare. An energy budget is similar to a water budget in that the change in stored energy is equal to the fluxes in and out of the system. Energy drives the process of evaporation because the water at the surface of the lake must absorb a certain amount of energy (latent heat of vaporization; approximately 580 calories per gram) before the water will evaporate. After some derivation, the following equation is used to calculate evaporation from the lake (Anderson, 1954):
E = (Qs – Qr – Qb + Qv – Qθ)/[ρL(R + 1)], (1)
where
| E | is evaporation rate, |
| Qs | is the solar radiation incident to the water surface, |
| Qr | is the reflected solar radiation, |
| Qb | is the net energy lost by the body of water through the exchange of long-wave radiation between the atmosphere and the body of water, |
| Qv | is the net energy advected into the body of water, |
| Qθ | is the change in energy stored in the body of water, |
| ρ | is the density of evaporated water, |
| L | is the latent heat of vaporization, and |
| R | is the Bowen ratio. |
Bowen (1926) expressed the ratio as:
R = γ[T0 – Ta)/(e0 – ea)]P, (2)
where
| γ | is an empirical constant, |
| T0 | is the temperature of the water surface, |
| Ta | is the temperature of the air, |
| e0 | is the vapor pressure of saturated air at the temperature (T0), |
| ea | is the vapor pressure of the air above the water surface, and |
| P | is atmospheric pressure. |
Net radiation (Qn) was measured at Lake Mead evaporation platforms and replaces three energy terms (Qs, Qr, and Qb) in equation 1. Net advected energy (Qv) is disregarded based on the assumption that advected energy is negligible during a 20-minute evaporation period.
Thus, after modifying equation 1 by substituting for net radiation, removing the net advected energy term, and replacing R with equation 2, evaporation can be estimated from measured meteorological and hydrological parameters:
E = (Qn – Qθ)/[ρLγc[(T0 – Ta)/(e0 – ea)] + 1], (3)
where γc, is a psychrometric constant, a product of γ and P (Laczniak and others, 1999, p. 20–21).
Meteorological and water temperature data were used to compute evaporation rates for Lake Mead. Measurements were made every 10 or 30 seconds and were averaged for 20-minute periods. Some of the missing or incorrect 20-minute data were estimated or computed to maximize the amount of data available for the evaporation computation. Where data were missing for short periods, they were estimated from trends of the data before and after the periods of missing or incorrect data. Where data were missing or incorrect for longer periods, they were computed from other available data at that station, data from another station, or data for another year. Typically, a regression was developed with two sets of measurements for a different period, but for similar environmental conditions, using a complete set of data. The regression was then used to estimate the missing or incorrect data from a complete set of data.
Monthly values of meteorological data and water temperatures were computed from 20-minute averaged data collected at each station for 1997, 1998, and 1999 (table 5). Average daily air temperature was about the same at all four platforms (fig. 5), whereas relative humidity and water temperature were similar at the open-water platforms. Generally, water temperature was higher and relative humidity was lower at the sheltered cove platform (Water Barge Cove) than at the open-water platforms.
Daily air temperature, water temperature, and relative humidity at the Sentinel Island station were compared for 1997, 1998, and 1999 (fig. 6). Air temperature varies from year to year, but the seasonal pattern is consistent. The maximum daily air temperature occurs about mid-July, with some daily average air temperatures exceeding 95°F, and the minimum daily air temperature occurs from late December through February. Water temperature did not vary much from year to year. Maximum daily water temperature occurs in late July to early August and the minimum daily water temperature occurs in late February. Relative humidity fluctuated from day to day and differed greatly from year to year (fig. 6). However, there is a seasonal pattern of high relative humidity in January that gradually decreases to a low at the end of June, followed by a gradual increase to higher relative humidity in December.
Daily average wind-speed and direction data for 1999 are plotted in figure 7. Points are plotted a distance from the origin relative to the wind speed and in the direction from the origin that represents wind direction (measured with zero degrees (0°) corresponding to a north wind). Thus, a daily average wind speed of 5 mi/hr with a direction of 120° would be plotted on the circle representing 5 mi/hr and in the lower right quadrant. Daily average wind speeds of less than 1 mi/hr were not plotted to avoid a dense cluster of points at the origin. Wind direction was predominately from the southeast to the southwest, occasionally from the northwest, and rarely from the northeast. Most daily wind speeds were less than 10 mi/hr. The Virgin Basin location experienced more daily wind greater than 10 mi/hr than other locations.
Evaporation rates were computed at 20-minute intervals to evaluate diurnal fluctuations of lake evaporation. The 20-minute period evaporation rates also were used to identify periods of poor or missing energy-budget data. Daily evaporation rates are the sum of 20-minute periods, monthly rates are the sum of daily evaporation and annual rates are the sum of monthly evaporation.
Daily evaporation rates at the four evaporation stations were compared for calendar year 1999 (fig. 8) and showed similar daily fluctuations. However, the magnitude of fluctuations in daily evaporation was greater at Virgin Basin and Sentinel Island than at Overton Arm or Water Barge Cove. Daily evaporation was greatest from late June through early July and was least from mid-December through late January.
To evaluate the temporal variation in monthly evaporation at each station, monthly evaporation rates for each station were averaged and compared to the total evaporation rate for each month of data collection. Temporal data were available for Water Barge Cove, Sentinel Island, and Virgin Basin stations (table 6); however, monthly data were insufficient for the Overton Arm station to compute average monthly evaporation. Total monthly evaporation rates at three stations, with some exceptions, generally were within 10 percent of average monthly rates; consequently, annual variation in monthly evaporation typically was minimal between 1997 and 1999. Some months, however, exhibited significant differences between average and total evaporation. These differences were as great as 31 percent at Water Barge Cove (February 1997; fig. 9A), 14 percent at Sentinel Island (January 1998 and 1999; fig. 9B), and 22 percent at Virgin Basin (December 1998 and 1999; fig. 9C). Some of the difference in monthly evaporation rates from year to year may be due to errors in meteorological and water-temperature data collected at each station, but year-to-year differences for most months likely are due to actual differences in evaporation.
To evaluate the spatial variation in evaporation, total monthly evaporation rates at all four stations were averaged for every month of data collection and the average was compared to the total monthly evaporation rate at each station (fig. 10A). For each station, total monthly evaporation rates compared well to average monthly rates with correlation coefficients of 0.96 or higher. However, total monthly evaporation at Water Barge Cove generally was less than total evaporation rates at the open-water stations when rates were less than 6.5 in. Total monthly evaporation rates for all three open-water stations were nearly equal and compared well to average evaporation rates (fig. 10B); correlation coefficients for Sentinel Island and Overton Arm were 0.98, and for Virgin Basin was 0.96. This evaluation suggests that the spatial variation in evaporation is minimal for open-water areas of Lake Mead.
The monthly volume of evaporated water was computed using the average monthly open-water evaporation rate, in feet, and the average monthly surface area of Lake Mead for July 1997 through December 1999, in acres, (calculated from water elevation data at URL: <http://www.usbr.gov/lc/riverops.html> and the Reclamation area capacity tables, Bureau of Reclamation, 1967). The volume of water evaporated in 1 month ranged from 46,000 acre-ft in February 1998 to 126,000 acre-ft in July 1998.
The average monthly rates for the Lake Mead open-water evaporation stations were computed for 1998 and 1999. For open-water stations, the sum of the average monthly rates for 1998 was 88.9 in. (7.4 ft) and the sum for 1999 was 90.7 in. (7.6 ft; table 7). For these 2 years, the average annual Lake Mead evaporation rate was 89.8 in. (7.5 ft). Monthly evaporation rates were available for only the Sentinel Island station for January–March 1998, and those rates are used instead of an average rate.
Evaporation rates at the Sentinel Island station are generally representative of evaporation of the lake as a whole. For April 1998 through November 1999, the total evaporation at the Sentinel Island station was 161.3 in., whereas, the total of average monthly evaporation for the open-water stations was 159.9 in. The difference of 1.4 in. is less than 1 percent of the total average open-water evaporation.
The annual volume of water evaporated from Lake Mead exceeded 1.1 million acre-ft in 1998 and 1999 (table 7), which probably is higher than a long-term average annual evaporation due to higher-than-normal lake elevations and corresponding larger-than-normal surface area for the period. For example, the average surface area of Lake Mead was 125,000 acres from 1942 to 1995 and the computed average annual evaporation rate was 7.5 ft from 1997 to 1998, which would equal a long-term average annual volume of 937,500 acre-ft of evaporated water.
U.S.
Department of the Interior | U.S. Geological
Survey
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