nws calibration workshop, lmrfc march 2009 slide 1 calibration of local areas 1 2 headwater basin...

NWS Calibration Workshop, LMRFC March 2009 Slide 1

Calibration of Local Areas

1

2

Headwater basin

Local area



Main Steps1. Check routing through local

area

2. Generate local area ‘observed’ hydrograph: this hydrograph reflects the runoff processes in only the local area.

3. Calibrate local area using ‘observed’ hydrograph in step two.

1

2

Headwater basin

Local area


Routing Through Local Areas

• “The ideal approach would be to route the actual observed instantaneous discharge. In this way the volume and timing errors in the simulation would not be propagated downstream.

• However, complete records of observed instantaneous discharge are seldom available.

• Thus, the next best approach is to route simulated discharge that has been adjusted by observed daily discharge and any available instantaneous flow data.”

Source: V.3.3-ADJUST-Q ADJUST SIMULATED DISCHARGE OPERATION



A. Steps with QME data1. Headwater basin

1. Calibrate basin2. Make a final run, save SQIN, declare as output time series. Use for ESP3. Make another final run:4. Add ADJUST-Q operation to combine QME and SQIN data

1. Save Adjusted inst. discharge as QINE (Upstream QINE)2. Declare as output time series3. Retains shape of simulation but has the volume of observed hydrograph (best

estimate of what goes down stream)

– OR1. Use observed QME data (no headwater basin calibration)

1. Change-T: use to convert QME to QINE: Upstream QINE 2. Can’t route QME time series

2. Route Upstream QINE to downstream gage with whatever method to produce ‘Routed QINE’ or ‘Downstream Routed’

3. MEAN Q: Routed QINE to Routed QME

Two cases: Observed QME and Observed QIN


Local Areas, cont’d.

A. Steps with QME data (cont’d)

4. Subtract Routed QME from Observed downstream QME: Local QME time series

5. Verify routing procedure:1. Compare Routed QME to Observed QME

2. Compare Local QME to nearby headwater Observed QME

6. Generate final Local QME; declare as output time series, calibrate local area in same way as a headwater basin.


Local Areas, cont’d.

B. Steps with QIN data1. Route upstream QIN to downstream gage with

whatever method to produce ‘Routed QIN’ or ‘Downstream Routed’

2. Subtract Routed QIN from observed downstream QIN: Local QIN time series

4. Verify routing procedure:1. Compare Routed QIN to Observed QIN2. Compare Local QIN to nearby headwater Observed QIN

5. Generate final Local QIN; declare as output time series, calibrate local area in same way as a headwater basin.


Adjust-Q Operation

Observed QME

SQIN

Flo

w

Time

QINE for routing


CHANGE-T Operation

Observed QME

QINE

Flo

w

Time


Downstream Observed

Downstream Routed QIN or QINE

0

+

-

Q

Diff

eren

ceCheck Routing in ICP PLOT-TS

Time


QME: us, ds

QIN: us, ds, routed

QIN: ds-us


Hydrologic Routing

• Methods combine the continuity equation with some relationship between storage, outflow, and possibly inflow

• Relationships are usually assumed, empirical, or analytical in nature

2


Derivation of Routing Equation

dS

d tI t O t ( ) ( )

dS I t d t O t d t ( ) ( )

Continuity equationfor reservoirs and channels

dS I t d t O t d t ( ) ( )

Integrating right side not analytically possible, so solve over a time interval of t

Rearranging

Take integral

(1)

(2)

(3)

3


Time

Dis

char

geRouting EquationChange of storage during a routing period t

Time

Sto

rage

Inflow

Outflow

Ij+1

Ij

Oj+1

Oj

Sj+1

Sj

jt (j+1)t

Source: Applied Hydrology by Chow, Maidment, and Mays, page 246

(Sj+1-Sj)

t

4



dS I t d t O t d tS j

S j

j t

j t

j t

j t

1 1 1

( ) ( )( ) ( )

S SI I

tO O

tj j

j j j j

1

1 1

2 2

Assumes change in inflow and outflow over time interval is essentially linear

(4)

(5)

5



• collect the unknowns on the right hand side

• Solve left hand side since values are known.

• Must have relationship between O2 and 2S2/t to derive value of O2

I IS

tO

S

tO1 2

11

22

2 2

(6)

6


Time

Dis

char

ge

Outflow: Pure Translation

Translation and Storage Processes in Stream Channel Routing

Lag

Outflow: Pure Attenuation (storage)

Outflow: storage and attenuation

Inflow

7


Lag and K Routing

• Solution to the graphical technique in Lindsey, Kohler, Paulhus, section 9.9

• Flexible – two independent algorithms– lag and no attenuation– attenuation and no lag– constant or variable lag and attenuation– more flexible than Muskingum routing.

3


Lag/K RoutingParameters

• Lag– Based on inflow– Measure of translatory

component of wave motion

– Constant or variable– Units of time

• K– Based on outflow– Same as Muskingum

K– Ratio of storage to

outflow– Constant or variable– Units of time

4


Derivation of K values

Source: Hydrology for Engineers by Linsley, Kohler, and Paulus, page 277

time

disc

harg

e

I-O

K

Observed Inflow (I)

A straight line tangent to the outflow hydrograph at various times is drawn. This line is projected to a discharge value equal to the inflow at that time. K is the time difference between this projection and the inflow. This is done for several historical events.

Outflow (O)

5


Lag/K Routing-Procedure

• Lag algorithm– Inflow hydrograph lagged by constant or

variable time.– Uses lag vs Q table input by user

6


Lag/K Routing-Procedure

• Attenuation (K) algorithm– 1. Takes lagged inflow hydrograph– 2. Reads in K vs Q input table.

– 3. Constructs table of Q2 vs. 2S/Dt + Q2 using equation:

S = KQ or S S K Q Q2 1 2 1 (1)

7


Lag/K Routing-Procedure, cont’d.

• Attenuation (K) algorithm– 4. Solves right hand side of:

– 5. Enter table of Q2 vs. 2S/Dt + Q2

to find value of Q2

I IS

tO

S

tO1 2

11

22

2 2

(2)

8


Oostanaula River Basin, Georgia

Workshop Exercise

RESG1

RTMG1


Notes

• Hourly USGS flow data are provisional and may contain errors. Check against USGS mean daily flow.

• Further downstream local areas will be more noisy

nws calibration workshop, lmrfc march 2009 slide 1 calibration of local areas 1 2 headwater basin...

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