demand characteristics and future use of colorado … characteristics and future use of colorado...

Demand Characteristics and Future Use of Colorado River Basin Streamflows

James F. Booker

Siena College

Loudonville, NY

American Water Resources Association Annual Conference, Portland, Oregon November 6-9, 2017.

Booker, AWRA 2017

Remembering

Ari Michelsen, past president AWRA Bob Young, Colorado State University

Portland, 2004

Booker, AWRA 2017context: alarm at what the past tells us (NAS, 2007).

Intro and Background Design & model Data Results I Realistic expectations / Conclusions

Booker, AWRA 2017

Questions:

1. How much demand can be supported?

2. Will this be greatly affected by climate changemitigation strategies?

3. What will typical reservoir storage levels look like?

Growing demand, potentially

lower supply


Booker, AWRA 2017

Udall and Overpeck, 2017


Booker, AWRA 2017

context: alarm at what the future may hold

Scenarios for the future must include climate change estimates


Booker, AWRA 2017

Water supply in the BasinHistorical and predicted effects of climate on:

• groundwater recharge (Tillman, Gangopadhyay, and Pruitt, 2017) and

• changes to stream baseflows (Rumsey, et al. 2015) are varied.

But it is increasingly clear that T increases have and will (Udall and Overpeck, 2017; McCabe et al., 2017) dramatically impact total

streamflows.


Booker, AWRA 2017

Growing water demand but declining water supply ...

Christensen & Lettenmaier, Hydrol. Earth Syst. Sci. Discuss. 2007.

Application of specific GCM models to IPCC climate scenarios;

approx. of USBR standard model

Barnett and Pierce, WRR, 2008. “When will Lake Mead go dry?”

Simple reservoir/use model; careful attention to synthetic,

stochastic streamflows with arbitrary flow reductions.


Booker, AWRA 2017

An alternative approach:

ask not

what shortages will occur in the future,

but ask instead

what water use can the Basin support?


Booker, AWRA 2017

Traditional: assume annual “demands” or depletions.

minimize the frequency of shortfalls.

Alternative:maximize utility arising from economic demand


Booker, AWRA 2017

Implementation

Traditional:

1. fixed (exogenous) use

2. sequential simulation

Alternative:

Endogenous depletions in a dynamic model


Booker, AWRA 2017

An alternative dynamic model

• Single stochastic inflow

• Reservoir storage upstream from use

• Loss (e.g. evaporation) is a function of storage

• Single economic demand below reservoir

(abstracting from the rich and complex geographical and institutional environment which I will set aside for the moment)


Booker, AWRA 2017

Model structure

flow variability

(annual)

elasticity

evaporation = f(storage)

elasticity

Inflow (annual)

Reservoir storage

Downstream use: human & environmental


Booker, AWRA 2017

A model maximizing utility

Maximize the beneficial use of

water over time, where marginal

benefits of use in each time are

defined by a demand function:

p(x) = x 1/ , where is the

price elasticity of demand.Intro and Background Design & model Data Results I Realistic expectations / Conclusions

Booker, AWRA 2017

The Model


Booker, AWRA 2017

General solutions (numerical)evaporation loss = 0.05 * storage

source: Booker & O’Neill, 2006.

Booker, AWRA 2017

Data: rule based solution

predefined flow sequences

evaporation = 3% of storage

defined depletions

Inflow (annual)

Reservoir storage



Booker, AWRA 2017

Streamflow in the Colorado River Basin


Booker, AWRA 2017Calibration to “traditional” models

0

10

20

30

40

50

60

1 11 21 31 41 51 61 71 81 91 101 111

years forward (historical hydrology, 1896 start)

Co

mb

ined

Mead

& P

ow

ell s

tora

ge

(millio

n a

cre

feet)

Rule based

CROSS


Booker, AWRA 2017

Data

predefined flow sequences

evaporation = 3% of storage

elasticity = -0.5

Inflow (annual)

Reservoir storage



Booker, AWRA 2017

The future is not the past:use IPCC climate scenarios• B1 - elimination of emission increases by 2100.

• A2 - relatively unconstrained growth.

Historical inflows (1906-2002),2 climate scenarios X 11 GCM generated inflows (Christensen & Lettenmaier 2007)

and ...


Booker, AWRA 2017

Application to Colorado River Basin under Climate Change

Historical inflows (1906-2002), plus 2 climate scenarios X 11 GCM generated inflows (Christensen & Lettenmaier 2007)


Booker, AWRA 2017

This study: uses GCM derived streamflows for the Colorado River Basin (Christensen & Lettenmaier, 2007)

B1 scenario

0

0.5

1

1.5

his

toric

cnrm

csiro

gfd

l

gis

s

hadcm

3

inm

cm

ipsl

miroc

mpi

mri

pcm

GCM

rela

tive s

tream

flo

w

A2 scenario

0

0.5

1

1.5

his

toric

cnrm

csiro

gfd

l

gis

s

hadcm

3

inm

cm

ipsl

miroc

mpi

mri

pcm

GCM

rela

tive s

tream

flo

w

annual means and +/- one standard deviation

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1 4 7

10

13

16

19

22

25

28

31

34

37

40

43

46

49

52

55

58

61

64

67

70

73

76

79

82

85

88

91

94

97

no

rma

lize

d f

low

year

Historic

B1-CNRM


Booker, AWRA 2017

Inflow and use (perfect foresight)

0.60

0.70

0.80

0.90

1.00

1.10

0.60 0.70 0.80 0.90 1.00 1.10

normalized inflow

me

an

us

e

B1 scenario

A2 scenario

Mean inflow determines mean water use

(history means nothing)


Booker, AWRA 2017

0.40

0.50

0.60

0.70

0.80

0.90

1.00

1.10

1.20

0.60 0.70 0.80 0.90 1.00 1.10

me

an

us

e

normalized inflow

B1 scenario

A2 scenario

Historic

Variability in depletions (error bars show 1sd; perfect foresight)

Could this possibly be reasonable?

recall: 80% of Basin use is agriculural


Booker, AWRA 2017

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0 0.5 1 1.5 2 2.5 3

nu

mb

er

normalized storage

Historic

B1-cnrm

B1-csiro

Reservoir storage(pdf; perfect foresight)

Mode is about 12% of capacity!


Booker, AWRA 2017

0.00

0.20

0.40

0.60

0.80

1.00

0 0.5 1 1.5 2 2.5 3

fre

qu

en

cy

normalized storage

Historic

B1-cnrm

B1-csiro

Reservoir storage(cdf; perfect foresight)

Median is below 20% of capacity.

Mostly empty reservoirs are the norm.


Booker, AWRA 2017

But ...the real world doesn’t have perfect foresight


Booker, AWRA 2017

Approach to finding use x*(t)

Guess what future annual flows s(t) will be:

1. Assume that each year in the future will be “average”

or

2. Try out a sample of possible perfectly known futures: a Monte Carlo approach.

UCRB projections under alternative emission scenarios; Udall and Overpeck, 2017


Booker, AWRA 2017

Dynamic model with limited foresight

s(t) = actual (current)assumed (future)

Find x(t) which maximizes U(t) over current and all future periods.

Fix x*(t) for current period

t = t + 1


Booker, AWRA 2017

Mean annual use (B1 climate)

0.60

0.80

1.00

1.20

his

toric

pcm

inm

cm

mri

ipsl

hadcm

3

csiro

gfd

l

gis

s

mpi

cnrm

miroc

GCM model

mean

an

nu

al u

se (

no

rmalized

)

Perfect foresight

Rule based

Average

MC(30)

Rule based reservoir operations result in lower mean annual use.


Booker, AWRA 2017

Utility (B1 climate)

-1.000

-0.800

-0.600

-0.400

-0.200

0.000

his

toric

pcm

inm

cm

mri

ipsl

hadcm

3

csiro

gfd

l

gis

s

mpi

cnrm

miroc

GCM model

tota

l u

tility

Perfect foresight

Rule based

Average

MC(30)

2. Simple expectations are almost as good as perfect foresight!

1. Rule based reservoir operations do poorly using a utility metric.

3 Simple expectations are as good as complex expectations.


Booker, AWRA 2017

Mean storage

0.00

1.00

2.00

3.00

4.00

5.00

his

toric

pcm

inm

cm

mri

ipsl

hadcm

3

csiro

gfd

l

gis

s

mpi

cnrm

miroc

GCM model

mean

sto

rag

e (

no

rmalized

)

Perfect foresight

Rule based

Average

MC(30)

Mean historic storage is not what we’ll see in the future.


Booker, AWRA 2017

Maximum storage

0.00

1.00

2.00

3.00

4.00

5.00

his

toric

pcm

inm

cm

mri

ipsl

hadcm

3

csiro

gfd

l

gis

s

mpi

cnrm

miroc

GCM model

maxim

um

sto

rag

e (

no

rmalized

)

Perfect foresight

Rule based

Average

MC(30)

If Basin water resources are managed to maximize utility it is unlikely that we will ever again see full reservoirs.


Booker, AWRA 2017

Conclusions

• Dynamic solutions with realistic expectations appear to

outperform existing management.

• Declining average water resources cannot be mitigated by

reservoir storage.

• New reservoir construction will likely result

in reductions in overall basin water availability.

• Current Colorado River Basin reservoir levels

may be typical of future conditions.


demand characteristics and future use of colorado … characteristics and future use of colorado...

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