simulacion_estocastica_jsalas

7/24/2019 Simulacion_Estocastica_JSALAS

1/34

II Congreso Obras de Saneamiento, Hidrulica,

Hidrologa y Medio Ambiente - HIDRO 200701 y 02 de Junio 2007

INSTITUTO DE LA CONSTRUCCION Y GERENCIA - ICG

Telefax: (01) 421-7896 / [email protected] / www.construccion.org.pe

Stochastic Modeling andStochastic Modeling and

Simulation of theSimulation of the

Colorado River SystemColorado River System

T.S. Lee, J.D. Salas, J. KeedyT.S. Lee, J.D. Salas, J. Keedy

Colorado State UniversityColorado State UniversityD.D. FrevertFrevertand T.and T. FulpFulp

U.S. Bureau of ReclamationU.S. Bureau of Reclamation

IntroductionIntroduction

Important source of water supply for 7 statesImportant source of water supply for 7 states It runs through semiarid and arid zonesIt runs through semiarid and arid zones Subject to climatic and hydrologic extreme events such asSubject to climatic and hydrologic extreme events such as

those of the 1982those of the 1982--83 (flood) y 200083 (flood) y 2000--2005 (drought)2005 (drought)

Law of the River in the 1920s (Colorado River Compact)Law of the River in the 1920s (Colorado River Compact) Upper Colorado (sites 1Upper Colorado (sites 1--20) Lower Colorado (sites 2120) Lower Colorado (sites 21--29)29) Large number of diversions works, dams, and reservoirs suchLarge number of diversions works, dams, and reservoirs such

as Lakes Powell and Meadas Lakes Powell and Mead

MultipurposeMultipurpose StreamflowStreamflowscenarios that may occur in the future are neededscenarios that may occur in the future are needed

for testing the Colorado River system operationfor testing the Colorado River system operation


2/34





UC CRSS stream gauges

LC CRSS stream gauges

9

10

1

1312

2

3456

78

14

15

1617

1819

20

21

22

23

24

25

26

2728

29

ObjectivesObjectives

To build a simulation model for the Upper and Lower ColoradoTo build a simulation model for the Upper and Lower Colorado

River System: 29sitesRiver System: 29sites

To simulate 100 samples 98To simulate 100 samples 98

--years long of monthlyyears long of monthly

streamflowsstreamflows

forfor

the entire 29the entire 29--site systemsite system

To compare the historical and generated yearly and monthlyTo compare the historical and generated yearly and monthly

statistics for both intervening flows (IF) and accumulated flowsstatistics for both intervening flows (IF) and accumulated flows

(AF)(AF)


3/34





Overall Modeling ProcedureOverall Modeling Procedure

Transformation

Multisite CAR(1)

Adjustments (optional)

Spatial-Temporal

Disaggregation

Temporal-Spatial

Brief Description of the ModelsBrief Description of the Models

MultisiteMultisite Model (Annual Time Scale)Model (Annual Time Scale)

Contemporaneous Autoregressive Model (CAR) forContemporaneous Autoregressive Model (CAR) for

modeling yearly flows at key or index sitesmodeling yearly flows at key or index sites

EYY BA 1+=

where A is a diagonal matrix and

B is a lower triangular matrix

+

=

2

1

2221

11

1

2

1

22

11

2

1

0

0

0

e

e

bb

b

Y

Y

a

a

Y

Y

For example, for 2 sites


4/34





Brief Description of the ModelsBrief Description of the Models(Annual to Monthly / Spatial)(Annual to Monthly / Spatial)

Disaggregation modelsDisaggregation models

Valencia andValencia and SchaakeSchaake (1973)(1973)

MejiaMejia--RousselleRousselle (1976)(1976)

Lane (1990)Lane (1990)

GreygierGreygier and Stedinger (1990)and Stedinger (1990)

)'(

1

)()( BA

++= YEYY C

+++=

=

1

1

,1,,,

u

uuWDBCA XYZXY

)()( BA

EYY +=

1,,, ++= YEXY BCA

[ ]TYYY

,2,1,

)(L=Y

],[ ,11,1)'(

1

= YYY

Software Utilized: SAMS 2005Software Utilized: SAMS 2005

Data analysisData analysis

--Annual and monthly sample statisticsAnnual and monthly sample statistics

-- Surplus, drought, and storage related statisticsSurplus, drought, and storage related statistics

-- Data transformations as neededData transformations as needed

Stochastic modelingStochastic modeling

-- Single site andSingle site and multisitemultisite modelsmodels

--Yearly and seasonal temporal scalesYearly and seasonal temporal scales

-- DisaggregationDisaggregation models: Vmodels: V--S, MS, M--R, Lane, GR, Lane, G--SS

--Alternative modeling schemesAlternative modeling schemes

Stochastic simulationStochastic simulation


5/34





Brief Summary of DataBrief Summary of Data

The original data base of naturalized flows had unequal recordThe original data base of naturalized flows had unequal recordlengthslengths

The data has been extended to the period 1906The data has been extended to the period 1906--20032003

(Lee and Salas, 2006)(Lee and Salas, 2006)

Data base in two forms:Data base in two forms:

-- intervening flows: gains or losses between sitesintervening flows: gains or losses between sites

-- accumulated flows: total flows through the stream networkaccumulated flows: total flows through the stream network

Upper Colorado River: sites 1Upper Colorado River: sites 1--2020Lower Colorado River: sites 21Lower Colorado River: sites 21--2929

Two sites are intermittent (22 and 27)Two sites are intermittent (22 and 27)

Brief Summary of DataBrief Summary of Data


6/34





1.000.0Log15

0.75-3781.2Power290.500.0Power14

0.70-3871.0Power280.60-45.4Power13

0.200.0Power270.60-207.3Power12

0.75-3799.6Power260.75-324.6Power11

0.75-3307.6Power250.85-193.7Power10

1.00-55.4Log240.85-234.2Power9

0.80-3205.1Power230.75-1427.8Power8

0.300.0Power220.45-43.6Power7

1.00-3.3Log210.75-335.4Power6

0.80-2990.0Power200.75-193.9Power5

0.50-103.6Power190.85-144.8Power4

0.65294.1Power180.70-36.8Power3

0.30-4.2Power170.65-1069.7Power2

0.70-1026.1Power160.75-591.1Power1

baTransIDbaTransID

CoeffManualCoeffManual

Transformation for Annual FlowsTransformation for Annual Flows


7/34





Scheme 1Scheme 1


8/34





Scheme 2Scheme 2

Grouping of Sites forGrouping of Sites for

Model 2 and 3Model 2 and 3

Scheme 3Scheme 3

Temporal Disaggregation

(G-S)

AF20_mon Jan

AF20_mon Feb

AF20_mon Mar

AF20_mon Apr

AF20_mon May

AF20_mon Jun

AF20_mon Jul

AF20_mon Aug

AF20_mon Sep

AF20_mon Oct

AF20_mon Nov

AF20_mon Dec

TF29'_mon Jan

TF29'_mon Feb

TF29'_mon Mar

TF29'_mon Apr

TF29'_mon May

TF29'_mon Jun

TF29'_mon Jul

TF29'_mon Aug

TF29'_mon Sep

TF29'_mon Oct

TF29'_mon Nov

TF29'_mon Dec

Spatial disaggregation (MR) of the total

upper basin monthly inflows to the

monthly flows of 3 index sites

Colorado Rockies : Sum ( IF_mon 1,

2, 3, 4, 5, 6,12, and15)

Green River / Uintas : Sum

( IF_mon 9, 10, 11, 13, 14, 16 ,

and 17)

Dolores/SanJuan : Sum (IF_mon 7,

8 , 18, 19, and 20)

Spatial disaggregation (MR) of the

total lower basin monthly inflows to

individual intervening monthly flows

IF21_mon

IF22_mon

IF23_mon

IF24_mon

IF25_mon

IF26_mon

IF27_mon

IF28_mon

IF29_mon

Spatial disaggregation(MR) of the monthly flowsin Colorado Rockies

IF1_monIF2_monIF3_monIF4_monIF5_monIF6_monIF12_monIF15_mon

Spatial disaggregation ofthe monthly flows inGreen River/Uintas flows

IF9_monIF10_monIF11_monIF13_mon

IF14_monIF16_monIF17_mon

Spatial Disaggregation of

the monthly flows in

Dolores/San Juan

IF7_mon

IF8_mon

IF18_mon

IF19_mon

IF20_mon

CAR(1) model for the yearly

total flows of the upper

(AF20_yr) and lower basin

(TF29'_yr : Sum [IF_yr

21,22,23,24,25,26,27,28,29])

AF20_yr

TF29'_yr

Temporal

Adjustment

Spatial

Adjustment


9/34





ResultsResults

Selected Upper Colorado Rive SitesSelected Upper Colorado Rive Sites

Site 15 : AccumulatedSite 15 : Accumulated

Site 20 : Accumulated and InterveningSite 20 : Accumulated and Intervening

Selected Lower Colorado Rive SitesSelected Lower Colorado Rive Sites

Site 26 : Accumulated and InterveningSite 26 : Accumulated and Intervening

Site 27 : AccumulatedSite 27 : Accumulated


10/34






11/34






12/34






13/34






14/34






15/34






16/34






17/34






18/34






19/34






20/34






21/34






22/34






23/34






24/34






25/34





Scheme 2 Scheme 3

Historical

Scheme 2 Scheme 3

Historical


26/34





Historical

Scheme 2 Scheme 3

Scheme 2 Scheme 3

Historical


27/34





Summary and ConclusionsSummary and Conclusions

Overall schemes 2 and 3 are better than scheme 1 in reproducingOverall schemes 2 and 3 are better than scheme 1 in reproducingannual and seasonal statisticsannual and seasonal statistics

The annual statistics for the accumulated and intervening flowsThe annual statistics for the accumulated and intervening flowsare better reproduced for Scheme 2 than Scheme 3.are better reproduced for Scheme 2 than Scheme 3.

The monthly means, s. deviations,The monthly means, s. deviations, skewnessskewness, and month, and month--totomonth correlations are fairly well reproduced by schemes 2 and 3month correlations are fairly well reproduced by schemes 2 and 3except for the correlation for the first month of the year forexcept for the correlation for the first month of the year forscheme 3.scheme 3.

The crossThe cross--correlations are somewhat better reproduced bycorrelations are somewhat better reproduced byscheme 3.scheme 3.

Both schemes 2 and 3 produce quite reasonableBoth schemes 2 and 3 produce quite reasonable streamflowstreamflow

scenarios that may be useful for operational studies of thescenarios that may be useful for operational studies of theColorado River system.Colorado River system.

Currently we are trying to improve some parts of the modelingCurrently we are trying to improve some parts of the modelingschemes especially those related to modeling intermittent sitesschemes especially those related to modeling intermittent sites

Grouping of Sites for Model 2 and 3 (Yearly)Grouping of Sites for Model 2 and 3 (Yearly)

UC CRSS stream gauges

LC CRSS stream gauges

9

10

1

1312

2

345678

14

15

1617

1819

20

21

22

23

24

25

26

2728

29

Scheme 2


28/34






29/34






30/34






31/34





Scheme 1

Scheme 1


32/34





Scheme 1

Scheme 1


33/34





Scheme 2


34/34



INSTITUTO DE LA CONSTRUCCION Y GERENCIA ICG

Scheme 2

Scheme 3

simulacion_estocastica_jsalas

Documents