Water budget using: unit conversions, significant figures, and scientific notation

Objectives: This homework is designed to give you practice using water budgets to solve common problems in water resource management. The homework will use actual data from monitoring stations at Mono Lake, California. In addition, this homework REQUIRES the use of unit conversions, correct application of significant figures, and use of scientific notation (and you thought after high school you’d never do this again).

Hydrology of Mono Lake

Location:
Mono Basin is an intermontane, closed drainage basin in central Mono County, California, and Mineral County, Nevada

The Mono Basin is about 300 kilometers from San Francisco  and forms part of the eastern boundary of Yosemite National Park. Lee Vining and June Lake, CA are the only two towns within the basin.

The shape of the Mono Basin is slightly elongate northeast-southwest . The area of Mono Basin is 1,748 km2. The area of Mono Lake is 215 km2.

The basin floor is relatively flat, sloping gently upward from Mono Lake at 1,948 m (6,390 ft) to the base of the surrounding rim of mountains at about 2,200 m (7,200 ft). West of Mono Lake, the Sierra Nevada rise abruptly from the lake and culminate in snowy crests at elevations near 4,000 m.

Climate:
The climate of the Mono Basin is continental, with cold winters, during which most of the annual precipitation occurs, and dry summers with hot days and cool nights. Average annual precipitation in the basin has been recorded since the early 1950s. The average annual precipitation for the Mono Basin is 44.8 cm.

Water Budget (Inputs-Outputs=Change in Storage):
The variables for the Mono Basin water budget include:
INPUTS: Precipitation (P), discharge from 3 creeks (Q), and groundwater inflow to Mono Lake (G)
OUTPUTS: Evaporation (E), and water diversions from the three creeks before flowing into Mono Lake (D)
CHANGE IN STORAGE: the change in water volume in Mono Lake (V)

ERTH 330: California Water

Spring 2017

Assignment

Your answers must have the correct number of significant figures and use proper scientific notation (e.g. 1.2×106 m3/yr). All the questions are listed here, but you must complete the Mono Lake Water Budget Assignment on iLearn.

1. MonoBasinWatershed.TheMonoBasinisa(n)_____________watershed. a) Open

   b) Closed

2. Water Budget Equation. Write the general water budget for Mono Lake using the specific water budget terms (P, Q, G, E, D, & V).

   a) P+Q+D+G-E=V b) P+(Q-D)+G+E=V c) P+(Q-D)+G+E=V d) P+(Q-D)+G-E=V e) P+(Q-D)-G-E=V

3. Mono Basin Precipitation. Calculate the average annual precipitation in cubic meters per year (m3/yr) for Mono Basin.

   a) 783104000 m3/yr b) 7.83 x 108 m3/yr
   c) 7.831 x 107 m3/yr d) 7.83 x 107 m3/yr
   e) 7.83104 x 105 m3/yr

4. Mono Lake Precipitation. Calculate the average annual precipitation in cubic meters per year (m3/yr) for Mono Lake.

   a) 96320000 m3/yr b) 9.632 x 107 m3/yr c) 9.632 x 104 m3/yr d) 96320 m3/yr
   e) 9.63 x 107 m3/yr

5. EvaporationfromMonoLake.TheaverageannuallakeevaporationfromMono Lake is 0.98 m. Calculate the annual evaporation in cubic meters per year (m3/yr) from Mono Lake.

   a) 210700000 m3/yr b) 2.107 x 108 m3/yr c) 210700m3/yr d) 2.1 x 108 m3/yr e) 2.1 x 105 m3/yr

6. Discharge.ThreelargecreeksflowintoMonoLakefromtheSierraNevada.These creeks are gaged by the Los Angeles Department of Water and Power (DWP), and have the following average annual discharge:

Spring 2017

Lee Vining Creek Rush Creek
Mill Creek

87.3 cfs (cubic feet per second (ft3/sec)) 44.8 cfs
37.0 cfs

Calculate the combined average annual discharge of these three creeks in cubic meters per year (m3/yr).
Note: 1 m3 = 35.3147 cubic feet (ft3), and 1 year = 31,536,000 seconds

a) 1.51 x 108 m3/yr
b) 1.51006170.2 m3/yr c) 151006171m3/yr d) 1.5 x 107 m3/yr
e) 1.510 x 107 m3/yr

7. Diversions.TheLosAngelesDWPhasbeendivertingwaterfromLeeVining,Rush, and Mill Creeks (below the gaging stations) for many years, running the diverted water through the Owens Valley aqueduct to Los Angeles. These diversions average 105,305 acre-feet per year (ac-ft/yr). Note: 1 m3 = 0.000811 acre-foot.

Taking into account these diversions, calculate the average annual flow into Mono Lake from these three creeks in cubic meters per year (m3/yr).

a) 1.29845 x 108 m3/yr b) 1.29 x 108 m3/yr
c) 2.11 x 107 m3/yr
d) 2.1155000 m3/yr

e) 1.38 x 107 m3/yr

8. ChangeinStorage:FromdatarecordedbytheLosAngelesDWP,MonoLake water levels fell 15.7 feet over 10 years. Accounting for the shape of the lake basin, the lowering of the lake level resulted in a change of storage of -103,461,332 m3.

Calculate the average annual change in storage over this 10-year period in cubic meters per year (m3/yr).

a) 103,461,332 m3/yr
b) 10,346,133.2 m3/yr
c) -1.03461332 x 107 m3/yr d) -10,346,133 m3/yr
e) -1.03461332 x 108 m3/yr

ERTH 330: California Water Spring 2017

9. GroundwaterInflow:Usingallthedatapresentedsofar,solvethewaterbudget equation for average annual groundwater inflow to Mono Lake in cubic meters per year (m3/yr). Use the precipitation value for Mono Lake (question 3), NOT the value for the Mono Basin (question 2).

a) 82253866.8 m3/yr b) -82253866.8 m3/yr c) 8.22 x 107 m3/yr d) -8.2 x 107 m3/yr

e) 8.2 x 107 m3/yr

10.Errors with Water Budget Calculations. Which of the variables of the water budget probably contains the largest error? Think about how each variable was calculated.

a) P b) Q c) D d) E e) GÂ