Applying TxRR to Texas Coastal Basins – Routing to the Streams

1. Applying TxRR to Texas Coastal Basins – Routing to the Streams Victoria Samuels CE 394K.2

2. TxRR Water Balance • It Rains! Pi at ti • Initial Abstractions subtracted • Runoff produced • Excess goes to Infiltration • Base Flow calculated from SM parameters • Base Flow + Direct Runoff = Stream Flow Precipitation P Initial Abstraction Ia Direct Runoff QD Infiltration F Maximum Soil Moisture SMMAX = Soil Moisture SM + Soil Retention S Stream Flow Base Flow QB Percolation (not modelled)

3. Time Variables Precipitation Event “i-1” Precipitation Event “i” Precipitation Event “i+1” In “i-1” time (t1): QB2, SM2 QB1, SM1 Time between Precipitation Events = ti = t2 – t1 In “i” time (t2): QB2, SM2 QB1, SM1

4. Direct Runoff QDi = Pei2 / (Pei + Si) Pei = Pi – Iai Iai = abst1 * Si QDi direct runoff from i precipitation Pei effective precipitation Iai initial abstraction from i precipitation abst1 initial abstraction coefficient (usually 0.2) Essentially the SCS Direct Runoff Equation • Pi precipitation from i event INPUT:

5. Base Flow - Recession QB2 = QB1 * Kt2 – t1 QB2 base flow rate at time t2 QB1 base flow rate at time t1 K recession constant (0.966 subsurface flow, 0.992 groundwater runoff) t2-t1 elapsed time • Part of the streamflow that flows out long after a precipitation event • Can be groundwater runoff, subsurface runoff, or a combination of the two

6. Base Flow – Reaction to Precipitation • Base flow increment either proportional to amount of precipitation or infiltration • Related to soil moisture, ie base flow is larger when soil moisture is larger QBnew = wB * Fi * (SM2i/SMMAX) QBnew = wB * Pi * (SM2i/SMMAX) QBnew base flow increment wB base flow coefficient or weighting factor SM2isoil moisture right before i precipitation SMMAX maximum soil moisture

7. Infiltration Equation is more conceptually correct However, when Fi 0, QBnew  0, despite if there is a large amount of precipitation (initial abstraction is large enough to take all of the precipitation, soil retention large enough) If a large initial abstraction is realistic, use Fi equation. If not realistic, use Pi equation Base Flow – Which Equation? QBnew = wB * Fi * (SM2i/SMMAX) QBnew = wB * Pi * (SM2i/SMMAX)

8. Base Flow - Computations New Base Flow: QB1i = QB2i + QBnew Amount of New Base Flow (volume): QBV = (QB2 - QB1) / ln K Used for daily continuous simulations Total volume of Base Flow from initial base flow as t2  inf, QB2  0: QBV = -QB1 / ln K Used for event by event simulation

9. SCS Unit Hydrograph Assumption that 37.5% of direct runoff reaches outlet before peak flow is reached In hours Tl= lag time = b * A0.6 b coefficient from 0.4 – 1.5 A drainage area (sq mi) Tp = time to peak = 12 + Tl Tb = base time = 5 * Tp Qpeak = 484 * A * QD / Tp Stream Flow Simulation - Then time rainfall Tl Qpeak runoff time Tb Tp

10. Stream Flow Simulation - Now • Cascade of identical completely mixed linear reservoirs • ki = detention time of each reservoir, Ni = number of reservoirs, t = time increment, ui(t) = discharge • Gamma distribution allows Ni to be a non-integer value, (Ni-1)! is replaced by the gamma function G(Ni) • Input to each reservoir is output from reservoir upstream Acknowledgements: Dr. Francisco Olivera

11. Stream Flow Simulation - Reservoirs C2,out = Co(t/q)e-t/q Cout = Coe-t/q CN,out …………….. N =N N = 2 N =1 CN,out = Co * 1/(N-1)! * (t/q)N-1 * e-t/q Substitute: q = ki, N = Ni, using the relationship Q/V = 1/ki, and a little handwaving: ui(t) = 1/ki * e-t/ki * 1/(Ni-1)! * (t/ki)Ni - 1 Acknowledgements: Dr. Desmond Lawler

12. Stream Flow Simulation – Gamma Function ki = 0.5 Ni = 20