ASLO 2012 Slides

Risk, Resource, Governance and Development:
Foundations of Public Policy
Optimal Joint Management of Interdependent
Resources: The Case of Groundwater and
Kiawe (Prosopis pallida)
Kimberly Burnett
James Roumasset
Christopher Wada
Imin Conference Center, Honolulu, Hawaii
December 7-8, 2012
This research was funded in part by NSF EPSCoR Grant No. EPS-0903833
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Overview
• Interacting ecosystems should be jointly managed
o In Hawai‘
‘i, kiawe has been shown to reduce regional groundwater
levels (stock-to-stock), suggesting that the two resources should be
managed jointly
o Groundwater management frameworks often abstract from linkages but
those interactions may not be trivial (e.g. watershed)
• Specific research questions
o How to integrate kiawe uptake into a dynamic groundwater management
framework?
o How does kiawe removal affect optimal withdrawals of water over time?
o What are economic benefits of kiawe management?
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Kiawe (Prosopis pallida)
understory
thorns
seed pods
growing in lava
Photography by Forest & Kim Starr (http://www.hear.org/starr)
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Coastal aquifer cross section
Withdrawals
Kiawe
Natural
Recharge
Uptake
Well
Ground Surface
Return
Flow
Lift
Discharge
GROUNDWATER
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Simple groundwater dynamics
• Equation of motion for the aquifer head level:
γ h&t = R − L(ht ) − qt −U(K t )
R: recharge
L: leakage
q: extraction
U: uptake
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Conceptual framework
• The objective is to choose groundwater extraction (q),
desalination (b) and tree removal (r) in every period t to
maximize PV:


max ∫ e− ρt  B(qt + bt , t) − cq (ht )qt − cb bt − cr (K t )rt  dt
qt ,bt ,rt
1444
424444
3 
 14243
t=0
benefits
of
water
consumption

costs of water extraction, desalination, tree removal
∞
•
•
•
•
Solve with and without kiawe (assume no growth ~ 2mm/yr)
With trees, lower head level (stock-to-stock)
Without trees, higher head + cost of tree removal
Difference in two values is benefit of kiawe management
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Application: Big Island, Hawai‘i
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Kiholo Bay (along the Kona Coast)
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Key equations and parameters
Description
Units
Equation or value
State equation for water
tg/yr
h&t = 0.0000000492[R − L(ht ) − qt ]
Recharge
tg/yr
R = 3, 992, 700
Leakage
tg/yr
L(ht ) = 117,864ht
Extraction cost
$/tg
c(ht ) = 0.00125(1322.5 − ht )
Desalination cost
$/tg
cb = 9.07
Water demand
tg/yr
qt = 850, 983pt−0.7e0.03t
Kiawe uptake (entire region)*
tg/yr
U = 2, 936, 570
*Per acre estimate for saltcedar
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Kiawe removal costs (previous studies)
Authors
Year
Location
Method
Campbell et al.
1996
Australia
Single pull
30
1.57
Double pull
64
3.36
Bulldoze
295
15.5
Aerial spray
133
6.98
Blade-plough
61
3.20
Hand spray
35
Re-treat every 10-12 yrs
1.84
Spray + chain
56
Chain again after 2 yrs;
Spray every 10-12 yrs
2.83
Roller chopping
92
Re-treat every 6-8 yrs
7.60
Root plowing +
reseed
127
Grub every 12 yrs
3.34
Fire
7
Burn every 5-7 yrs
0.68
Grub
106
Re-treat every 10-15 yrs
5.56
March et al.
Teague et al.
1996
1997
Australia
Texas
Cost ($/acre)
Follow-up
*In 2012 US dollars.
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PV (million $)*
Optimal water trajectories
Price paths
Head paths
Water extraction paths
Water consumption
Solid blue: all kiawe removed; Dashed red: no kiawe removed
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Benefits for various removal methods
•
•
Benefits of kiawe removal = Value (no trees) – Value (trees)
Net benefits = Benefits – costs of removal
Method
PV benefit (million $)
PV cost (million $)
NPV (million $)
Single pull
32.5
1.57
30.9
Double pull
32.5
3.36
29.1
Bulldoze
32.5
15.5
17.0
Aerial spray
32.5
6.98
25.5
Blade-plough
32.5
3.20
29.3
Hand spray
32.5
1.84
30.6
Spray + chain
32.5
2.83
29.6
Roller chopping
32.5
7.60
24.9
Root plowing + reseed
32.5
3.34
29.1
Fire
32.5
0.68
31.8
Grub
32.5
5.56
26.9
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Caveats
•
Only direct removal costs are considered (e.g. wages, equipment
rental, materials)
•
Other costs might include: danger to non-target species (all
methods), damage from smoke (fire), reduced quality of underlying
groundwater (herbicides)
•
Kiawe also generates some benefits which are not accounted for:
charcoal and honey production
•
Water uptake estimates not based on field data (not yet available)
•
No kiawe dynamics in application
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Directions for further research
• When to remove?
o Calculations are made under the assumption that kiawe removal
occurs immediately, but immediate harvest is not likely to be
optimal initially, especially if the water table is increasing
o Benefits may be larger in the future when water is scarcer, but
when exactly should (all) kiawe trees be removed?
Preliminary results suggest that it may be optimal to wait at
least a decade before starting removal
o The tradeoff between delaying the costs and benefits of tree
removal will determine the optimal timing for clear-cutting
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Directions for further research (cont.)
• How much to remove?
o It may be beneficial to remove only a portion of the trees in any
given period if we take into account kiawe growth cycles
(previously it was assumed that the growth rate of kiawe was
slow enough to not significantly affect the results)
o Least-cost removal would suggest cutting trees for which the
cutting cost is lowest per unit of water removed (biggest and
oldest?)
o Substantial data requirements: growth function for kiawe, uptake
function for kiawe as related to size of the tree, information on
existing stock of trees beyond acreage (density, biomass, age)
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Mahalo!
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