SOLVE THESE in constructing a hydrological model using the data in the table bel
ID: 3184606 • Letter: S
Question
SOLVE THESE in constructing a hydrological model using the data in the table below, it is required to obtain the expected runoff, denoted by Ri during the ith period, as a linear function of obsereved precipitation. from hydrological consideration the expected runoff depends on the precipitation during that period and the previous two periods. so the model for expected runoff is Ri=b0pi +b1pi-1+ b2pi-2where pi eqials precipitation during the ith period; and b0,b1,b2 are the coefficients thar are required to be estimated and i>=3. these coefficients have to satisfy the following constraints from hydrological consideration: b0+b1+b2=1, where b0,b1 and b2>=0.obtaint the best estimates for b0,b1,b2 if the objectives area: to minimize the sum absolute deviations: sum|Ri-b0pi - b1pi-1- b2pi-2|b: to minmize the maximum absolute deviations: max |Ri-b0pi - b1pi-1- b2pi-2|time period123456789101112precipitation3.84.45.75.27.765.45.75.5250.80.4runoff--54.16.95.25.36.46.36.24.63.7
Explanation / Answer
Solution;-
A) Hydrological budget equation P = Q+E+GWO+ds
where P = Precipitation = 72IN/YR
Q = run off = 59IN/YR
GWO = ground water pumping = 3.4IN/YR
E = evoparation = 551in/yr
ds = change in storage
ds = P-Q-GWO-E
ds = 72-59-9.6-3.4 = 0
so there is no change in storage that means hydrological budget is in stedy state
B) E = 55in/yr
Q = 9.6in/yr
GWO = 3.4 in/yr
P = 60in/yr
ds = 60-55-9.6-3.4 = -8 in/yr
so the storage water decreases 8in/yr
i.e the hydrological budget is at a loss stage
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