Multivariate drought risk analysis for...

Multivariate drought risk analysis for California

California Water & Environmental Modeling Forum2018 Annual Meeting Program

April 2-4, 2018

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Deepthi RajsekharHongbing Yin

Jay WangRichard Chen, Idy Lui, Liheng Zhong

Outline• What is a drought?• Why analyze droughts?• How to analyze droughts?• Impact of a changing climate on drought• Take-Away

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What is a drought?• Period of prolonged deficit in precipitation, soil moisture, or flow • Natural, recurring, inevitable process• Experienced by all climate regions• “Creeping phenomena”• Impact can be:

• Economic• Social• Environmental

• Multiple physical manifestations

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• Meteorological drought: Precipitation deficit from the norm

• Agricultural drought: Soil lacks moisture that a specific crop need at a specific time

• Hydrologic drought: lack of sufficient surface and/or sub-surface water

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Natural/human-induced climate variability

Precipitation deficiency (amount, intensity, timing)

High T, winds, low relative humidity, greater sunshine

Reduced infiltration, runoff, deep percolation, and GW recharge

Increased evaporation and transpiration

Soil water deficiency

Plant water stress, reduced biomass and yield

Reduced streamflow, inflow to reservoir, lakes, reduced wetlands,

wildlife habitat

Economic impacts Social impacts Environmental impacts

Met

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drou

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Agr

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Why droughts are unique among natural disasters?• No precise and universally accepted definition

• Quantification of impact and mitigation much more difficult• Onset and end of drought difficult to determine• Longer recovery time – impacts may linger for years• Non-structural impacts and spread over a large geographic area

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Motivation• Wide spread social, economical, and ecological impact • Costliest natural hazard - $ 6-8 billion annual damage to US

(FEMA)• Importance of studying droughts in California:

• Major contributor of fruits, nuts, vegetables, and livestock/dairy• 2015 California drought alone caused an economic loss of $2.7

billion• Changing climate likely to cause more severe, more frequent

droughts in future

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How to analyze droughts?

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Define drought events

Quantify drought properties: severity and duration

Fit marginal distributions to severity and duration

Joint and conditional distributions of drought properties – severity and duration

Derivation of drought frequency curves

Plot drought atlas

Study Area

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63 rim watersheds and 30 WBAs to represent Sacramento Valley floor

Shasta

Example step-by-step illustration of drought analysis

Data source: Rim inflows from CalSim3.0 input fileWBA surface runoff from CalSim3.0 Output


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Plot drought atlas

Step 1: Definition of drought events• Use drought indicators for defining drought events• Numerous standardized drought indices like Standardized

Precipitation Index (SPI), Palmer Drought Severity Index (PDSI), Standardized Runoff Index (SRI)

• Choice of index depends on purpose of study• We use SRI for hydrologic drought analysis.

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Standardized Runoff Index (SRI)• Probability based drought indicator

• Runoff time series for each month is fitted to either a parametric or non-parametric distribution.

• Calculate the cumulative probabilities for runoff values• Convert the cumulative probability to a standard normal

distribution variate (with zero mean and unit variance).• The standard normal variate is SRI.

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SRI values ClassificationGreater than 2.0 Extremely wet

1.5 to 1.99 Very wet1.0 to1.49 Moderately wet

-0.99 to 0.99 Near normal-1.0 to -1.49 Moderately dry-1.5 to -1.99 Severely dry

Less than -2.0 Extremely dry

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-3 -2 -1 0 1 2 3

SRI

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Prob

abili

tyExtremely dry Moderately

dryNear Normal Extremely wetModerately

wet

SRI values on normal curve

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-4

-3

-2

-1

0

1

2

3

4

Oct-21 Oct-26 Oct-31 Oct-36 Oct-41 Oct-46 Oct-51 Oct-56 Oct-61 Oct-66 Oct-71 Oct-76 Oct-81 Oct-86 Oct-91 Oct-96 Oct-01 Oct-06 Oct-11

SRI

Time

SRI time series for Shasta


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Plot drought atlas

Step 2: Quantify drought properties• Drought events characterized by: severity, duration• Theory of runs: An event is defined as drought when the value

of interest (SRI) falls below a specified threshold.• Drought event when SRI falls below -0.99

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0 5 10 15

Severity

0

2

4

6

8

10

Dur

atio

n(m

onth

s)

• Each drought event characterized by: • Severity – cumulative SRI for each drought event• Duration – length for which SRI continuously stays below

threshold

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Worst drought in 2012-2015 dry period

Strong dependence between severity and duration


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Plot drought atlas

Step 3: Marginal distributions for drought properties

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Drought property Distribution ParameterSeverity Log-normal µ = 0.9078, σ=0.898Duration Exponential µ = 2.8194

1 2 3 4 5 6 7 8 9 10

Duration (months)

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

CD

F

CDF plot for duration

0 2 4 6 8 10 12 14 16

Severity

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

CD

F

CDF plot for severity


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Plot drought atlas

Step 4: Joint distribution of severity and duration

• Marginal distributions for severity and duration belong to different families

• Use an approach called copula to construct joint distribution• Copulas are mapping functions that preserves the dependence

structure between severity and duration• Different families of copula functions available to develop joint

distribution• Choose the best-fit copula for the data using metrics like log-

likelihood estimate

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Copula family Functionparameter

Log-likelihood estimate

Clayton 4.414 39.13Frank 10.892 45.76

Gumbel 3.207 46.26Gaussian 0.883 39.43

Cumulative joint probability plot

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0 5 10 15

Severity

0

2

4

6

8

10

12

Dur

atio

n (m

onth

s)


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Plot drought atlas

Step 5: Derivation of drought frequency curves• Establishes relationship between severity, duration, and frequency• Analogous to precipitation I-D-F curves• Useful for drought risk assessment, water resources planning, ecosystem

rehabilitation• S-D-F curves based on conditional return period or recurrence interval

Where S and D indicate drought severity and duration, 𝐹𝐹 �𝑆𝑆 𝐷𝐷(𝑠𝑠𝑑𝑑) is conditionaldistribution of severity and duration, n = total number of drought events, N =total length of SRI time series,𝑇𝑇 �𝑆𝑆 𝐷𝐷(𝑠𝑠𝑑𝑑) is the conditional recurrence interval of Sgiven D=d

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• Conditional distribution obtained from joint and marginal distributions• Recurrence interval calculated based on conditional distribution

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0 5 10 15 20 25 30 35 40

Severity

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

P(S/

D)

Conditional distribution plot for drought severity given drought duration

d=1 monthd=2 monthsd=4 monthsd=6 monthsd=8 monthsd=12 months

0 2 4 6 8 10 12

Duration(months)

2

4

6

8

10

12

14

16

18

20

Seve

rity

Drought severity–duration–frequency curves at various return periods for Shasta

T=10

T=25

T=50

T=100


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Plot drought atlas

Step 6: Drought atlas• Compilation of design drought S-D-F curves for different locations• Useful for spatial drought analysis• Example drought map shows the spatial variation of drought severity for a 100-yr return period drought of 12-month duration.• Series of drought maps for a range of return periodsand/or drought durations can be constructed.

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How climate change affects droughts• Growing evidence on climate change leading to more severe and frequent

droughts• Anticipated reduction in precipitation and increase in temperature• As a case in point, we compare the worst drought in 2012-2015 dry period

under current versus mid-century climatology (2045-2074).• 2012-2015 considered one of the driest period in the history of California • We considered the worst case scenario in terms of greenhouse gas concentration

(RCP 8.5).• Climate models chosen from CCTAG recommended list• Rim inflow perturbed for each climate model projection to generate “climate

change rim inflows”

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0 2 4 6 8 10 12

Duration(months)

0

2

4

6

8

10

12

14

16

18

20

Seve

rity


T=10

T=25

T=50

T=100

2012-2015 event

0 2 4 6 8 10 12

Duration(months)

0

2

4

6

8

10

12

14

16

18

20

Seve

rity


T=10T=25T=50T=1002012-2015 event

Current climatology Mid-century climatology

Return period for 2012-2015 drought: 155 yrs Return period for 2012-2015 drought: 108 yrs

For the same drought, the recurrence interval reduces from 155 to 108 years due to climate change.


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Take-Away• Understanding drought properties and their joint behavior essential for

drought management and mitigation• Bivariate computational framework for return period analysis is of key

importance in drought risk assessment.• We also highlight the importance of considering the effect of changing

climate on drought properties.• Significant escalation in the frequency of occurrence of droughts in future

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Thank You!

Disclaimer for analysesDWR makes no warranties, representations or guarantees either expressed or implied, as to thecompleteness, accuracy or correctness of the data, nor accepts or assumes any liability arising from anyincorrect, incomplete or misleading data as interpreted by others or their agents.This presentation is of a framework for multivariate drought risk analysis in California, which represents andis limited by the study/model design, including model assumptions. It has not been Q/A, Q/C by the DWRand is being shared to illustrate the importance of incorporating a multivariate perspective in droughtanalysis.The data, methods, and analyses presented here are research products conducted by the Bay-Delta Office ofthe Department of Water Resources (DWR). These research products are investigatory in nature and do notreflect official DWR policy, programs, or operations. The information presented is qualified as follows:• Any quantitative analyses presented are driven by specific assumptions and the values and trends they

show are subject to change with any new or changed assumption.• The findings presented in these research products are limited to the results shown here.• CalSim 3 is still in Beta-Release form and not final.

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