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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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Applying TxRR to Texas Coastal Basins – Routing to the Streams

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Applying txrr to texas coastal basins routing to the streams l.jpg

Applying TxRR to Texas Coastal Basins – Routing to the Streams

Victoria Samuels

CE 394K.2


Txrr water balance l.jpg

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 l.jpg

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 l.jpg

Direct Runoff

QDi = Pei2 / (Pei + Si)

Pei = Pi – Iai

Iai = abst1 * Si

QDidirect runoff from i precipitation

Peieffective precipitation

Iaiinitial abstraction from i precipitation

abst1initial abstraction coefficient (usually 0.2)

Essentially the SCS Direct Runoff Equation

  • Pi precipitation from i event

INPUT:


Base flow recession l.jpg

Base Flow - Recession

QB2 = QB1 * Kt2 – t1

QB2base flow rate at time t2

QB1base flow rate at time t1

Krecession constant (0.966 subsurface flow,

0.992 groundwater runoff)

t2-t1elapsed 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 l.jpg

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 l.jpg

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 l.jpg

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 l.jpg

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 l.jpg

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 l.jpg

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


Stream flow simulation gamma function l.jpg

Stream Flow Simulation – Gamma Function

ki = 0.5

Ni = 20


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