avan sobre dinamica sequias jsalas

II Congreso Obras de Saneamiento, Hidráulica, Hidrología y Medio Ambiente - HIDRO 2007

01 y 02 de Junio 2007

INSTITUTO DE LA CONSTRUCCION Y GERENCIA - ICGTelefax: (01) 421-7896 / [email protected] / www.construccion.org.pe

Avances Sobre la Dinamica de Sequías Extremas

José D. SalasDepartamento de Ingenieria Civil y Ambiental

Colorado State University

HYDRO II, 2007 Congreso en Lima

Agradecimiento: Projectos financiados por la U.S. Bureau Reclamation y Colorado Experiment Station

Resumen de esta presentacion

• Introduccion- aspectos que intervienen en la dinamica de sequias- ejemplos de impactos

• Caracterizar la dinamica de sequias en el tiempo- metodos- ejemplos

• Caracterizar la dinamica de sequias en el espacio- metodos- ejemplos

• Comentarios finales


01 y 02 de Junio 2007


Introduccion

Ecologic/Environmental Systems Ecologic impacts & feedbacks

Watershed impacts & response

Atmospheric & Hydrologic Systems

Land surface-atmospheric interactions Severity, recurrence, and risk of events

Human Systems Socio-economic impacts & feedbacks

Infrastructure & management

Drought

Introduccion

Meteorological Aspects of Droughts

Precipitation deficiency(duration, amount, intensity, extent)

High temperature, persistent winds, low humidity, more sunshine, less cloud cover

- Less runoff - Less infiltration- Less deep percolation- Less groundwater

recharge- Less baseflow

- Less reservoir storage- Less lake and pond storages- Less soil water storage- Less groundwater storage- Less snowpack- Depletion of glaciers

Hydrological and Ecological Aspects of Droughts

- More reservoirevaporation

- More evaporationand transpirationdemands

Impacts and Consequences of Droughts


01 y 02 de Junio 2007


Introduccion

Economic impacts- Less agricultural production

(plant water stress, reduced biomass and yield)

- Reduced livestock - Unexpected sales of

farmlands and livestock- Increase prices of food- Increased price of water for

municipal consumption and industry

- Decreased revenues of recreational industries such as ski, fishing, etc.

- Loss of jobs (Others)

Social impacts- Urban water shortages

and deficits- Reduced comfort- Less recreational

opportunities- Changes in lifestyles- Deterioration of

aesthetic landscape- Population dislocation- Deterioration of health- Increase of certain

insects, viruses, etc. - Others

Environmental impacts- Increase of wildfires,

forest fires.- Increased soil erosion- Increased dust- Deterioration of air quality- Reduced wetlands- Reduced wildlife habitat- Deterioration of natural

vegetation- Deterioration of water

quality- Others

Drought Mitigation & Adaptation Drought Planning and Management

Hydrological and Ecological Aspects of Droughts

Impacts and Consequences of Droughts

Meteorological Aspects of Droughts

Introduccion

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


01 y 02 de Junio 2007


Niveles del Embalse Mead (Represa Hoover)Rio Colorado, USA

The effects of the drought are dramatically seen at Lake Mead, Nevada, where the shoreline has shrunk so considerably that it has forced a marina to relocate from newly dry land.

Source: The following four pictures are taken from the on-line magazine “Las Vegas Information, Hotels, Apartments, Photos” published by SunSetCities.Com

under the section of Hoover Dam.



01 y 02 de Junio 2007


Source: The following four pictures are taken from the on-line magazine “Las Vegas Information, Hotels, Apartments, Photos” published by

SunSetCities.Com under the section of Hoover Dam.

Niveles del Embalse Mead (Represa Hoover) Rio Colorado, USA


The drought has left docks hanging from newly formed cliffs.


01 y 02 de Junio 2007


Efectos de la Sequia de los 30 en USA

Figure 13. The Dust Bowl - Baca County, Colorado, in 1936. Photo by D. L. Kernodle

Efectos de la sequia reciente(2000-2006?) en USA

Figure 19. Drought affects agriculture production greatlyPhoto Credit: Jahi Chikwendiu / Lexington Herald-Leader

A photo of a wildfire in the west in 2000 due to drought conditions, Aug. 6, 2000 in the Bitterroot Valley National Forest, MT.


01 y 02 de Junio 2007


Sequia en el Rio Amazonas

Foto tomada de un informeDel SENAMHI (G. Chamorro)

Precipitacion annual del Estado de Colorado, USA

Colorado statewide annual precip (1895-2006)

9

11

13

15

17

19

21

23

1895

1900

1905

1910

1915

1920

1925

1930

1935

1940

1945

1950

1955

1960

1965

1970

1975

1980

1985

1990

1995

2000

2005

Time (years)

Prec

ip (i

n)

Deficit Annual precip


01 y 02 de Junio 2007


Precipitacion annual del Estado de Colorado, USA

Colorado statewide annual precip (1895-2002)

9

11

13

15

17

19

21

23

1895

1900

1905

1910

1915

1920

1925

1930

1935

1940

1945

1950

1955

1960

1965

1970

1975

1980

1985

1990

1995

2000

Time (years)

Prec

ip (i

n)

Annual precip5-yr moving averageMean

Caudales Anuales del Rio Poudre, Colorado, USA


01 y 02 de Junio 2007


Caudales Anuales del Rio Colorado, USA

Colorado River Site 20 annual flow (1906-2003)

0

5

10

15

20

25

30

1905 1915 1925 1935 1945 1955 1965 1975 1985 1995 2005

Time (years)

Flow

(mill

ion

AF)

Deficit Annual flow

Caudales Anuales del Rio Colorado, USA

Five-year Moving Average Flow of the Colorado River Site 20 (1906-2003)

0

5

10

15

20

25

30

1905 1915 1925 1935 1945 1955 1965 1975 1985 1995 2005

Flow

(mill

ion

AF)

Deficit

5-yr moving average


01 y 02 de Junio 2007


Caudales Anuales del Rio Niger, Africa

Niger River at Koulikoro annual flows (1907-1999)

0

500

1000

1500

2000

2500

1905

1910

1915

1920

1925

1930

1935

1940

1945

1950

1955

1960

1965

1970

1975

1980

1985

1990

1995

2000

Time (years)

Flow

(CM

S)

Deficit Annual flow

Caracterizacion de la Dinamica de Sequíaspor Metodos Estocasticos

• Analisis estadístico de los datos históricos- datos convencionales, e.g. Q, P, etc.- otros datos, e.g. anillos de árboles

• Analisis estadístico de datos simulados- datos históricos- modelos estocásticos para generar Q, P, etc.

• Solución analítica- datos históricos- modelos estocásticos


01 y 02 de Junio 2007


Definición y Propiedades de Sequías

0

100

200

300

400

500

600

700

800

1950 1952 195 4 1956 1958 1960 1962 196 4 1966

T im e t

x t

L =4

x 0

I

D

Yevjevich’s (1967)


Feller’s (1968)

0

5

10

15

20

25

1 4 7 10 13 16 19Years

Var

iabl

e of

Inte

rest

D D D D

L=2 L=2 L=2 L=2


01 y 02 de Junio 2007



Fernandez y Salas (1999)

0

5

10

15

20

25

1 4 7 10 13 16 19Years

Var

iabl

e of

Inte

rest

d1 d4d3d2 d6d5 d9d8d7 d10

The most extreme 2 years Drought

L=2 L=2

L=2

L=2 L=2

L=2

Distribución de la Duracion de Sequías

0

0.2

0.4

0.6

0.8

1

1 2 3 4 5 6 7 8 9 10 11 12Run Length (years)

Pro

babi

lity

SampleFitted based on the DAR(1) modelFitted based on the DARMA(1,1) model

Sample and Fitted Run Length Distributions of State 0 Based on the DAR(1) and DARMA(1,1) Models Fitted to the Niger River Annual Flows

( ) 10101 1)( −−= l

L pplf

Assume that the sequence of deficits and surpluses are represented by 0s and 1s, and are modeled by a DAR(1) process (Markov chain)


01 y 02 de Junio 2007


Distribución de la Duracion de Sequías

⎪⎩

⎪⎨⎧ <

=otherwise

yywherex ot

t1

01)1( −−+= ttttt zuyux

],1[/)]}1()1(][1)1(2[

)]0()0()][1(2[{][

10)1()(

)1()(

ixixPHHiWP

HHiWPlLP

li

li

li

lii

=−=−+−=+

−−===

+

+

Assume that the sequence of deficits and surpluses are represented by 0s and 1s, which in turn are modeled by a DARMA(1,1) process

H=transition probability matrix of (x,z) and W=4 state simple Markov chain

∑∞

===

1][][

lii lLPlLE

Distribución de la Magnitud de Sequías

0

12

3

45

6

78

9

0 50 100 150 200 250 300

Deficit (1000 acr-ft)

Prob

abili

ty d

ensi

ty fu

nctio

npd

f (10

-6)

pdf from historical recordpdf from generated sample

Comparison of the probability density function (pdf) of the single year deficit obtained from the generated flow record versus the pdf obtained from the historical record (L=1).


01 y 02 de Junio 2007


Distribución de la Magnitud de Sequías

Probability density function (pdf) of the deficit D obtained from the historical record, generated record, and analytical approximation (L>=1).

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Amount of deficit (104 acre-ft)

Rel

ativ

e fr

eque

ncy

Generated data

Historical data

0 15 30 45 60 75 90 105 120

Eq. (10)

Distribución de la Magnitud de SequíasDada la Duracion (condicional)

⎟⎟⎠

⎞⎜⎜⎝

⎛−⎟⎟

⎠

⎞⎜⎜⎝

⎛Γ

=−

lllllD

dddfl

ααβα

β

exp)(

1)(1

|

( )( ) ( )

( ) 1

11

| ,1)( −+

−−

−

−−=

ll

ll

albdlbad

Bdf

lllD βα

βα

βα

dlD l µµ =|( )

( ) ⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

−

+−−+= 21

22|

1112

φφφρσσ

l

dlDll

Gamma-3:

Beta-4:

Conditional mean and variance of deficit as a function of the mean, variance, and serial correlation of individual deficits:


01 y 02 de Junio 2007


Ejemplo: Rio Niger en Koulikoro(1907-1999)

0

500

1000

1500

2000

2500

3000

3500

1 2 3 4 5 6 7 8 9 10

Drought length (years)

Mea

n of

D

ObservedSimulationEq(31)Eq(20)

0200400600800

100012001400160018002000

1 2 3 4 5 6 7 8 9 10


Var

ianc

e of

D

ObservedSimulationEq(32)

x 103

Eq(21)

Otras Propiedades de Sequías: Periodo de Retorno y Riesgo

0

100

200

300

400

500

600

Time (years)

Flow

s, x

L=3 L=4 L=5

I0

D

I X0

D0

10 20 30 40 50 60 70


01 y 02 de Junio 2007


Otras Propiedades de Sequías: Periodo de Retorno y Riesgo

][][][][ 10

lo ADDPLELEMET

∩>+

==

][]|[][ lLPlLDDPlLDDP oo ==>==∩>

( )( ) ( )

( )∫ −+

−−

−

−−==>

lb

D llo

oll

llds

albslbas

BlLDDP 1

11

,1]|[ βα

βα

βα

Consider the drought event lLDD o =∩>

∑∞

===

1][][

lii lLPlLE

Otras Propiedades de Sequías: Periodo de Retorno

1

10

100

1000

10000

0 1 2 3 4 5 6 7 8 9 10 11Drought length(years)

Ret

urn

peri

od (y

ears

)


Ητ ∀

Ητ ∀0

Ητ ∀0

Eq(27)

Drought length(years)

Ret

urn

peri

od(y

ears

)

γ=0

γ=0.5 γ=1.0

Rio Niger, Africa (Dist. Beta)


01 y 02 de Junio 2007


Otras Propiedades de Sequías: Periodo de Retorno

1

10

100

1000

10000

0 1 2 3 4 5 6 7 8 9 10 11Drought length(years)

Ret

urn

peri

od (y

ears

)


Ητ ∀

Ητ ∀0

Ητ ∀0

Eq(27)

Drought length(years)

Ret

urn

peri

od(y

ears

)

γ=0

γ=0.5 γ=1.0

Rio Niger, Africa (Dist. Beta)Niger River at Koulikoro annual flows (1907-1999)

0

500

1000

1500

2000

2500

1905

1910

1915

1920

1925

1930

1935

1940

1945

1950

1955

1960

1965

1970

1975

1980

1985

1990

1995

2000

Time (years)

Flow

(CM

S)

Deficit Annual flow

Otras Propiedades de Sequías: Riesgo

0.0

0.2

0.4

0.6

0.8

1.0

0 1 2 3 4 5 6 7 8 9 10 11


Dro

ught

ris

k

0.00 0.25 0.50 0.75 simulated 1.00 1.35 1.50 0.75 (historical)

Symbol λ

]25)...,2,1([ 000 yearsinocurrwillllLandDDPR =≥>=

Rio Poudre, Colorado, USA


01 y 02 de Junio 2007


Otras Propiedades de Sequías: Riesgo

0.0

0.2

0.4

0.6

0.8

1.0

0 1 2 3 4 5 6 7 8 9 10 11


Dro

ught

ris

k

0.00 0.25 0.50 0.75 simulated 1.00 1.35 1.50 0.75 (historical)

Symbol λ

]25)...,2,1([ 000 yearsinocurrwillllLandDDPR =≥>=

Rio Poudre, Colorado, USA

0100200300400500600700800

1884 1893 1902 1911 1920 1929 1938 1947 1956 1965 1974 1983 1992 2001

Time (years)

Stre

amflo

ws

(100

0 ac

re-ft

)

Variabilidad (dinamica) Espacial de la Severidad de Sequías: PDSI


01 y 02 de Junio 2007





01 y 02 de Junio 2007


Definicion y Propiedades de Sequíasen el Espacio: Sequia Regional

zt(1)*

zt(2)*

zt(3)*

zt(4)*

a(1)*

a(2)*

a(3)*

a(4)*

ft(1)*

ft(2)*

ft(3)*

ft(4)*


⎩⎨⎧

⎭⎬⎫

≥=<=

)k(f)k(zfor0)k(I)k(f)k(zfor1)k(I

ttt

ttt)k(I)k(aaM

1ktt ∑

=

⋅=

Area (fraction del area total) en deficit en el tiempo t

where: k = estationM = numero de estacionesa(k) = area (fraccion) de la estacion k (0 ≤ a(k) ≤ 1)

,

zt(k) = precipitacion normalizada y estandarizadaft(k) = representa la demanda (e.g. quantil de z)

Deficit Areal (espacial) en el tiempo t

)k(I)]k(z)k(f[)k(aDM

1ktttt ∑

=

⋅−=


01 y 02 de Junio 2007



L=5

ac

at

1 2 . . . . ti tf … N

Dt

∑=

=f

i

t

tttDD

Magnitude sequiaregional

Duracion sequiaregional

L=5

t

tL

Propiedades de Sequíasen el Espacio: Sequia Regional

Ejemplo: Estado de Colorado, USA


01 y 02 de Junio 2007





01 y 02 de Junio 2007


Comentarios Finales

• Se ha avanzado bastante en la literatura para caracterizar ladinamica de sequias mediante metodos estocasticos. e.g. el periodo de retorno (T) de sequias es un concepto reciente.e.g. las formulaciones analiticas para estimar T y el riesgo R

• Areas donde se necesita mayor atencion y estudio incluyen:

- definiciones alternativas de sequias tanto para una o masvariables asi como para un sitio o sitios multiples.

- metodos para cuantificar la severidad de sequias paraescalas multiples de tiempo (e.g. estaciones, meses, etc.)

- metodos para cuantificar la severidad de sequias regionales ycontinentales.

Comentarios Finales

Areas donde se necesita mayor atencion y estudio incluyen:

- desarrollar metodos para cuantificar la incertidumbre de la severidad de sequias.

- desarrollar metodos para definir y estimar la severidad de sequias

teniendo en cuenta las variaciones hidroclimaticas de bajafrecuencia (persistencia, cambios bruscos, procesosno estacionarios, etc.)

avan sobre dinamica sequias jsalas

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