3. water budget of mono lake, ca

mono lake is located in an enclosed intermountain basin near the california-nevada border (see attached map). the shape of the basin is elongate ne-sw, and is approximately 50 km by 30 km long. the lake is also elongate, and is 22 km across e-w and 16 km n-s. the area of the present-day lake is 215 km2, and the basin area is 1748 km2.

in 1941, the los angeles department of water and power began diverting mono lake’s tributary streams 350 miles south to meet the growing water demands of los angeles. with the decreased runoff, lake level dropped by about 40 feet over the next few decades. the volume of mono lake halved, while its salinity doubled. the dropping lake level opened a land bridge to paoha island, which exposed nesting birds to mammalian predation. changes in lake salinity and size also affected the lake ecosystem in a variety of ways. recent legislation has limited the diversion, and requires that the lake level be maintained at 6392’. however, the water budget of the lake is still of great concern to both environmentalists and water management officials. your analysis for this problem set will be based on hydrologic data from 1954-1964 (see table below).

a. write an equation for the water budget of mono lake. use only words, and base your answer on the hydrologic equation (see fetter, page 8). sketch a diagram to illustrate, generically, the fluxes of water into and out of the lake. assume, for now, that groundwater flow is into the lake. [5 pts]

b. how would you find out if net groundwater flow is into vs. out of the lake? what data would you collect or analyses would you conduct? [5 pts]

c. calculate the annual rainfall into mono lake. calculate the total evaporation from the lake over a year. state your results in m3/yr. [5 pts]

d. calculate the natural (pre-diversion) runoff in each of the three gauged streams, and their total (in m3/yr). then account for the diversions to l. a. and calculate the net runoff into the lake. [5 pts]

e. the two additional streams (stream 1 and stream 2) are monitored using weirs (which are less expensive and often used for smaller streams).

stream 1 runoff is measured using a notch weir. discharge through the weir is given by:

where q is in cfs and h is the height of the stream in the weir, in feet.

stream 2 runoff is measured with a cipolletti weir – a rectangular type used for slightly larger flows. discharge for this weir is given by:

where q is in cfs; l is the weir length and h is the water height, both in feet.

calculate the annual runoff for each of these streams, and their total, in m3/yr. [5 pts]

f. several springs also discharge water into mono lake. the combined spring discharge is 5530 gallons/minute. (there are 264 gallons in one m3). convert the spring flow to m3/yr. [5 pts]

g. combine the net runoff from all streams and springs into the lake. [5 pts]

h. the groundwater component of the lake water budget is hard to measure. one approach that is often taken is to define all other terms in the budget equation, and see what’s left over. to do this, you have to define the change in storage. luckily, you have data for lake elevations and lake areas. assuming that the lake basin is defined by a cone-shape (which is a pretty good approximation), determine the change in volume from 1954 to 1964 in m3. the equation for the difference in volume between two cones is:

where r1 and r2 are the initial and final radius of the lake, and h is the height (elevation) change. express your answer in m3. [5 pts] [hint: you will need to define an average or "effective" radius for this calculation, because the lake is not a perfect circle in map view.]

i. using your answer to question 3a, calculate the groundwater flow in/out of the lake with the information you have so far. remember that the volume change you just calculated was in m3 over ten years. [10 pts]

hydrologic data for problem #3: mono lake

mean annual rainfall (from gauges) 18.6 cm/yr

evaporation from lake (from pan experiments) 1.0 m/yr

stream flows into mono lake (annual average):

lee vining creek 87.3 cfs (cubic ft/sec)

rush creek 44.8 cfs

mill creek 37.0 cfs

diversions from these streams to los angeles: 105,305 acre-ft/yr

additional stream inflows:

stream 1 h=6.9"

stream 2 h=3.5"; l=3’

lake level in 1954 6407’

lake level in 1964 6391’

lake area in 1954 89.4 mi2

lake area in 1964 77.0 mi2

total yearly precipitation into basin: 7.6 x 108 m3/yr