Multi-Step Automatic Calibration Scheme (MACS)

Sustainability of semi-Arid Hydrology and Riparian AreasSAHRASAHRA

Multi-Step Automatic Calibration Scheme(MACS)Terri S. Hogue

Soroosh Sorooshian, Hoshin Gupta,Claire Tomkins, and Travis Booth

October 22, 2002


Advanced Calibration Techniques NWSRFS

AHPS = Calibration Issues

~ 4000 River Forecast Points

Small % with calibrations

Manual – reliable, quality,

but TIME-CONSUMING

Automatic – reliable, quality,

and EFFICIENT (fewer man-hours)

= Within existing code !!

GOAL:


ManualUser knowledgeExcellent model calibrationsComplicated and highly labor intensiveExpertise not easily transferred

AutomaticUser knowledgeSpeed and power of computerObjective procedureEasy to useResults not generally acceptable

Manual vs. Automatic Calibration


Optimization Algorithm (SCE-UA)

−= ∑=

n

ttobstsim QQnDRMS

1

2,, )(1

Objective Function(Root Mean Square)

Historical Data

Prec

ip. (

mm

)Fl

ow (c

ms)

Time (days)

Automatic Calibration


4.- Flatness Flat near optimum with significantly different parameter sensitivities

3.- Roughness Rough surface with discontinuous derivatives

2.- Local Optima

Many small "pits" in each region

More than one main convergence region

1.- Regions of Attraction

Difficulties in Optimization

5.- Shape Long and curved ridges

Development of “Global Search Algorithm: SCE-UA”Duan, Gupta, and Sorooshian, 1992

Response Surface


Performance: SCE-UA vs. Simplex

Simplex

SCE - UA


Prec

ip. (

mm

)Fl

ow (c

ms)

Time (days)

Results from Automatic single criteria calibration of SAC-SMA model

Good fit to higher flowsPoor fit to low flows

Motivation for Multi-step / Multi-objective


Multi-step Automatic Calibration Scheme (MACS)

3-step automatic calibration process

Use of different objective functions with various model parameters

Process:1) Baseflow Parameters2) High Flow Events – Snow melt, etc.3) Fine-tuning – baseflow, ET parameters …


SNOW-17SCF SIMFMAX MFMIN

SAC-SMA

Upper ZoneUZTWM PCTIMUZFWM UZK

ZPERC REXP

LZTWM LZFSM LZFPMLZSK LZPK PFREE

SAC-SMA

Lower Zone3 - LOG (6)

( )2,,∑ −=tobsQtsimQ LOGLOGLOG

1 - LOG (16)


−= ∑=

n

ttobstsim QQnDRMS

1

2,, )(1

2 – DRMS (10)


Methods for Calibration

15 Headwater Basins – varying size (160-5195 km2)

10 lumped basins5 multi-level basins (elevation bands)

~ 40 years historical dataCalibration: ~ 11 yearsValidation: ~ 40 years (entire period)

RFC parameter ranges RFC statistics / hydrographs for evaluationDRMS, %Bias, Monthly statistics, etc…


Office ofHydrology

Test Basins - NWS

15 Study Sites

Semi-distributed“multi-tiered”** Need for better methodology

2

3

6

1

3


Overall DRMS

0

10

20

30

40

50

60

70

NC-1NC-2NC-3NC-4NC-5NC-6

SE-1SE-2SE-3

CB-1CB-2CB-3

AK-1AK2

Study Basins

DR

MS

RFCMACS

Evaluation of Calibrations


Evaluation of Calibrations

Overall Percent Bias

-30-25-20-15-10

-505

10152025

NC

-1

NC

-2

NC

-3

NC

-4

NC

-5

NC

-6

SE

-1

SE

-2

SE

-3

CB

-1

CB

-2

CB

-3

AK

-1

AK

2

Study Basins

%B

ias

RFCMACS



NCRFC

South River, IA

SERFC

Flint River, GA


AKRFC

Talkeetna River


180 190 200 210 220 230 240 250 260 270 2800

5

10

15

Tra

nsf

orm

ed

Flo

ws

(cm

s) Obs oRFC−−MACS −

Water Year1962

LMRFC

Leaf River


CBRFC – previous work !

• Previous rationale: examine the proportional area and contribution to flow of the three regions. The region considered to make the most significant contribution to flow, which may also comprise the largest proportion of total area, is calibrated initially. Other elevations bands follow, typically lower region next and lastly upper zone.

• In order to not bias the automatic calibration results, mid-point values of each parameter range were used for the parameters not being calibrated in the initial run.


CBRFC Basins

Gila (GILN5)1976-1987 1950-1993

RFC MACS RFC MACS% Bias 6.57 2.68 -4.36 -5.4DRMS 10.186 8.677 8.562 7.315

Virgin (NFUV1)1977-1988 1951-1998RFC MACS RFC MACS

% Bias 4.69 3.98 -15.15 -2.89DRMS 2 1.97 2.239 2.199

Animas (DRGC2)1982-1993 1950-1994

RFC MACS RFC MACS% Bias 1.69 0.76 -0.12 0.72DRMS 10.718 8.82 9.873 9.506


CBRFC Basins

Monthly %Bias: 44-yr. Period Basin DRGC2

-20

-10

0

10

20

30

Jan.

March May Ju

ly

Sept.

Nov.

Month

%B

ias

RFC

MACS

Flow Group %Bias: 44-yr. Period Basin DRGC2

-40

-30

-20

-10

0

10

20

5.54- 17.73- 55.39- 177.26- 553.93+

Flow Group

%B

ias

RFC

MACS

Monthly %Bias: 43-yr. Period Basin GILN5

-60

-40

-20

0

20

40

60

Jan.

Feb.

March

April

MayJu

ne July

Aug.

Sept.

Oct. Nov.

Dec.

Month

%B

ias

RFC

MACS

Flow Group %Bias: 43-yr. Period Basin GILN5

-40

-30

-20

-10

0

10

20

0-1.7

7-5.5

4-17

.73-

55.39

-17

7.26-

553.9

3+

Flow Group

%B

ias

RFC

MACS


CBRFC Basins - Gila


CBRFC Basins - Animas


MACS – Comments

Time-saving, reliable, quality calibrations Application to 15 Basins / 5 RegionsStatistics and Hydrographs comparable to RFCs

Application / Implementation to other RFC regions in progress

More Work on Multi-tiered systems (CBRFC)

Multi-Step Automatic Calibration Scheme (MACS)

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