HW5 - Florida International University Dept. of Civil and...

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Unformatted text preview: Florida International University Dept. of Civil and Environmental Engineering CWR6117 – Statistical Hydrology Assignment No. 5 Lake Valencia is the largest enclosed freshwater lake in Venezuela. It is a very peculiar physical setting, since the lake has no natural stream outflow, i.e., the only natural mechanism for water outflow is evaporation. The surface water elevation‐surface area‐lake volume curve is the following (in tabular form): Elevation (masl) Area (km2) Volume (m3) 370.6 46.6 0.117E9 375.6 95.8 0.473E9 380.6 137.4 1.056E9 385.6 179.0 1.847E9 390.6 221.2 2.848E9 395.6 262.8 4.059E9 400.6 305.7 5.430E9 405.0 345.0 6.922E9 406.7 360.1 7.377E9 410.0 389.0 9.180E9 420.0 475.2 13.719E9 Water level (end of 1994): 407 masl Evaporation from the lake (annual average): 1000 mm/yr According to demographic projections in over 30 towns adjacent to the city of Valencia, and future water management strategies in the lake basin, the following is a series of drainage inflows to the lake for the period 1995‐2025, 31 values, one for each year, in m3/s: 5.501, 5.184, 4.863, 4.545, 4.226, 3.908, 3.929, 3.949, 3.970, 3.990, 4.011, 4.167, 4.323, 4.478, 4.636, 4.792, 4.952, 5.113, 5.273, 5.433, 5.594, 5.756, 5.917, 6.079, 6.240, 6.402, 6.577, 6.752, 6.926, 7.101, 7.276. In addition to this there is an estimated seage/wastewater flow rate of 14 m3/s from the city of Valencia’s metropolitan area (constant throughout the period of analysis). Because of the potential increases in the level of the lake, there is concern of flooding in urban areas located along the lake shore. The Venezuelan environmental ministry has set the maximum lake level to 410 masl, to avoid damages to property and the loss of economically active land farming activities. Develop a stochastic mass balance model for water volume in Lake Valencia, for the period 1995‐2025. Based on this model, formulate a response to the following issues: a) Lake surface water elevation during the period 1995 – 2025 under a no‐action scenario. Develop this model using the methodology discussed in class and generate the 30‐year time series for: (i) the lake mean water volume, (ii) the variance of the lake water volume, and (iii) the covariances between inflow‐volume and outflow‐volume. Use the mean water volume time series to generate the lake surface water elevation time series for the simulation period. b) Use Monte Carlo simulations to obtain the mean lake water volume, the mean lake surface elevation and the variance of the lake water volume over the period 1995‐2025. How do these results compare with those found in part (a)? Discuss similarities and/or differences in detail. c) Action scenario: If the main concern is to control the level in the lake at or below the 410 masl limit, how much water should be pumped out of the lake (constant pumping over the 30 year period)? This water would be pumped out to a waterwater treatment facility (being constructed) for the purpose of reusing this water. In this fashion, the lake operates as a “diluter” of the sewage. Notes: (1) Be very careful with the units in this problem. The inflow rates are given in m3/s, the evaporation from the lake is given in mm/yr, and the time step is t=1 yr. The volume of the lake is expressed in billions m3 (109 m3). (2) When plotting the time series for the simulated lake volume, please also plot in the same graph the +/‐ and +/‐ 2 values to get an idea of the confidence of the prediction of the lake volume by the mean volume. ...
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