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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
Intro and Background Design & model Data Results I Realistic expectations / Conclusions
Booker, AWRA 2017
Udall and Overpeck, 2017
Intro and Background Design & model Data Results I Realistic expectations / Conclusions
Booker, AWRA 2017
context: alarm at what the future may hold
Scenarios for the future must include climate change estimates
Intro and Background Design & model Data Results I Realistic expectations / Conclusions
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.
Intro and Background Design & model Data Results I Realistic expectations / Conclusions
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.
Intro and Background Design & model Data Results I Realistic expectations / Conclusions
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?
Intro and Background Design & model Data Results I Realistic expectations / Conclusions
Booker, AWRA 2017
Traditional: assume annual “demands” or depletions.
minimize the frequency of shortfalls.
Alternative:maximize utility arising from economic demand
Intro and Background Design & model Data Results I Realistic expectations / Conclusions
Booker, AWRA 2017
Implementation
Traditional:
1. fixed (exogenous) use
2. sequential simulation
Alternative:
Endogenous depletions in a dynamic model
Intro and Background Design & model Data Results I Realistic expectations / Conclusions
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)
Intro and Background Design & model Data Results I Realistic expectations / Conclusions
Booker, AWRA 2017
Model structure
flow variability
(annual)
elasticity
evaporation = f(storage)
elasticity
Inflow (annual)
Reservoir storage
Downstream use: human & environmental
Intro and Background Design & model Data Results I Realistic expectations / Conclusions
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
Intro and Background Design & model Data Results I Realistic expectations / Conclusions
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
Downstream use: human & environmental
Intro and Background Design & model Data Results I Realistic expectations / Conclusions
Booker, AWRA 2017
Streamflow in the Colorado River Basin
Intro and Background Design & model Data Results I Realistic expectations / Conclusions
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
Intro and Background Design & model Data Results I Realistic expectations / Conclusions
Booker, AWRA 2017
Data
predefined flow sequences
evaporation = 3% of storage
elasticity = -0.5
Inflow (annual)
Reservoir storage
Downstream use: human & environmental
Intro and Background Design & model Data Results I Realistic expectations / Conclusions
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 ...
Intro and Background Design & model Data Results I Realistic expectations / Conclusions
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)
Intro and Background Design & model Data Results I Realistic expectations / Conclusions
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
Intro and Background Design & model Data Results I Realistic expectations / Conclusions
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)
Intro and Background Design & model Data Results I Realistic expectations / Conclusions
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
Intro and Background Design & model Data Results I Realistic expectations / Conclusions
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!
Intro and Background Design & model Data Results I Realistic expectations / Conclusions
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.
Intro and Background Design & model Data Results I Realistic expectations / Conclusions
Booker, AWRA 2017
But ...the real world doesn’t have perfect foresight
Intro and Background Design & model Data Results I Realistic expectations / Conclusions
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
Intro and Background Design & model Data Results I Realistic expectations / Conclusions
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
Intro and Background Design & model Data Results I Realistic expectations / Conclusions
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.
Intro and Background Design & model Data Results I Realistic expectations / Conclusions
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.
Intro and Background Design & model Data Results I Realistic expectations / Conclusions
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.
Intro and Background Design & model Data Results I Realistic expectations / Conclusions
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.
Intro and Background Design & model Data Results I Realistic expectations / Conclusions
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.
Intro and Background Design & model Data Results I Realistic expectations / Conclusions
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