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Applying TxRR to Texas Coastal Basins – Routing to the Streams. Victoria Samuels CE 394K.2. TxRR Water Balance. It Rains! P i at t i Initial Abstractions subtracted Runoff produced Excess goes to Infiltration Base Flow calculated from SM parameters

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Presentation Transcript
txrr water balance
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)

time variables
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

direct runoff
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:

base flow recession
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
base flow reaction to precipitation
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

base flow which equation
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)

base flow computations
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

stream flow simulation then
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

stream flow simulation now
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

stream flow simulation reservoirs
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