MIT OpenCourseWare http://ocw.mit.edu 1.020 Ecology II: Engineering for Sustainability Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Civil and Environmental Engineering 1.020 Ecology II: Engineering for Sustainability Problem Set 1 –Salination in Irrigated Agriculture Due: 5PM Tuesday Feb. 19, 2008 Problem Description This modeling exercise considers the problem of salt accumulation in irrigated agriculture. The system of interest includes a river and two farms that divert irrigation water from the river and discharge drainage water back to the river. Water and salt accumulate in the soil below each farm. Relevant mass flows and storages are shown in the figure below. Each box is a separate mass balance control volume. E1, SE1 E2, SE2Farm 1 Soil Farm 2 Soil VS1, SS1 VS 2, SS 2 Q1, SR1 D1, SS1 Q2, SR2 D2, SS 2 11 , SRR 11, RR SV 12 , SRR 22 , RR SV 23 , SRR 33 , RR SV 34 , SRR River section 1 River section 2 River section 3 VRi Volume of water in river section i (m3) SRi Salt concentration in river section i (mg L-1) Ri Flow into river section i and out of river section i-1 (m3 sec-1) SR1 Upstream salt concentration (mg L-1) VSi Volume of water stored in soil at Farm i (m3) SSi Salt concentration in soil at Farm i (mg L-1) Ei Evaporation rate from soil at Farm i (m3 sec-1) SEi Salt concentration in water evaporated from soil at Farm i (mg L-1) -- note SEi = 0 Di Drainage rate from Farm i (m3 sec-1) Qi Irrigation diversion rate into Farm i (m3 sec-1) Model Specifications Construct a MATLAB model that simulates the salinity history in the soil at each farm and in each section of the river, over a 100 day period. 1Assume: • All water mass balances are in steady-state (time derivatives are zero) but salt balances are dynamic (time derivatives are not zero) • River and farm soil salt concentrations at beginning of first day all = 30 mg/L • River section volumes each = 3000000 m3 • Soil storage volumes each = 6000000 m3 • SR1 = 30 mg/L • R1 = 15 m3/sec • Nominal values of E1 = E2 = 3.5 m3/sec • Nominal values of Q1 = Q2 = 7 m3/s • SEi = 0 for all i (plants do not evaporate salt) • Use 1 day time steps and assume salt concentrations in flows between control volumes are equal to the concentration value computed at the beginning of the day, throughout the day. • The maximum soil salinity Ssi must always be less that 230 mg/L or the crop will die. Make sure this requirement is met when you adjust Q1and Q2. • In the model code, derive crop revenue for each farmer from the following yield equation: Ni =γEi exp ⎡⎢[− Ssi 22 ⎤⎥ ⎣ 2S0 ⎦ where Ssi is the maximum salinity over the 100 day growing period and S0= 36 mg/L. . • γ = 0.015 $/(m3/day) Using the Model 1. Nominal case: Plot the time histories of soil salt concentration at each farm and in each river section for the nominal values of E1, E2,Q1 and Q2 given above. What are the nominal farm revenues N1 and N2 for both farms? 2. Alternative case: Suppose that Farm 1 doubles its production by irrigating more land. Then its evaporation increases to E1= 7 m3/s. Adjust the Farm 1 diversion Q1 to ensure that Q1 ≥ E1 and that Ss1 ≤ 230 mg/L. What are the new farm revenues for both farms when E2 and Q2 are held fixed at their nominal values? What is the penalty paid by Farm 2 when Farm 1 increases production? What do you think is a fair way to deal with this “externality”? Submit via Stellar your MATLAB source file, the requested plots (as *.fig files), and a text file with a few sentences summarizing your answers to the questions in the “Using the Model” section. Be sure to define all variables and to identify all major calculations in comments included in your MATLAB file (comments will be considered in the grade).