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MULTI-OBJECTIVE OPTIMIZATION
APPROACH FOR LAND USE ALLOCATION
BASED ON WATER QUALITY CRITERIA
Prepared by:
Cristhian Villalta Calderón, Ph. D.
Polytechnic University of Puerto Rico
Civil Engineering, Environmental Engineering
and Land Surveying Department
Justification⚫ This research was done in order to develop an integrated
methodology for watershed land use planning decision
making.
⚫ The methodology was focused in the search for optimal
land use distribution and respective allocation based on
water quality objectives and inherent socio-economic
conditions.
⚫ Findings of this research will provide the base work tofind possible solutions to difficult issues related to landuse planning for preservation, forestry, agriculture, urbandevelopment while maintaining the viability of waterquality and quantity.
Overview of the study area
67°5'0"W
67°5'0"W
66°40'0"W
66°40'0"W
66°15'0"W
66°15'0"W
65°50'0"W
65°50'0"W
65°25'0"W
65°25'0"W
17°30'0"N
17°30'0"N
17°55'0"N
17°55'0"N
18°20'0"N
18°20'0"N
18°45'0"N
18°45'0"N
0 10 20 30 405Miles
Legend
Puerto Rico
Watershed Border
Río Limón sub watershed
Río Grande de Arecibo sub watershed
Río Caonillas sub watershed
Río Jauca sub watershed
·
·Legend
Río Limón sub watershed
Río Grande de Arecibo sub watershed
Río Jauca sub watershed
Río Caonillas sub watershed
66°40'0"W
66°40'0"W
18°20'0"N18°20'0"N
Introduction
⚫ Surface water contamination by point and
nonpoint sources of pollution is a major
concern for public and government agencies in
the United States and Puerto Rico. The major
cause of water pollution in the United States is
nonpoint source inputs where species like total
phosphorus cause eutrophication of surface
water around the country (U. S. EPA, 1996).
Introduction
⚫ 70% of the river miles in Puerto Rico are impaired
(PREQB, 2002).
⚫ All our reservoirs fail to meet existing aquatic life criteria
for dissolved oxygen resulting in an eutrophication
condition (list of Impaired Waters of Puerto Rico (305(b)-
303(d)).
⚫ Water quality issues are extremely important for the
general public due to the excessive contamination of
water bodies. Water is an important resource for any
community to support life, economic development,
recreation facilities and aesthetic values.
Objective
⚫ To develop an integrated optimization
methodology for land use planning, at the
Río Grande de Arecibo watershed, using
water quality continuous simulation
analysis based on specific water quality
objectives and using a Multi-Objective
Linear Programming (MOLP) model
implemented in a GIS platform.
METHODOLOGY
Methodology components
⚫ This research has three basic components:– Water quality simulation using HSPF.
– Multi-objective optimization based on a MOLPapproach.
– Land use allocation implemented on a GISplattform.
⚫ All these components together conforms aland use planning model in a environmental,social, political and economic context in theRGA watershed with implemented results in ageo-spatial output.
Data collection and
analysis
Hydrology, sediments
and water quality
simulation
SimulationCalibration/
Validation
Post-
analysis
Multiobjective
Optimization Approach
Land Allocation Model
System Diagnostic
MUNICIPAL ENVIRONMENTAL
CAPABILITY
Methodology components
Sediment and water quality simulation
⚫ HSPF was used to simulate water quality(sediments and nutrients).
⚫ HSPF has various characteristics, including aprocess-based, lumped, continuous modeldeveloped under EPA sponsorship to simulatehydrology and water quality processes inpervious or impervious areas.
⚫ Several reasons were taken into considerationfor HSPF choice.
Input data requirements
Geographical Information System Data
DEMs were obtained from:
U.S. Geological Survey (USGS, 2001)
Based on:
2004 ortho-corrected images (USGS, 2004)
land use maps (PRPB, 1977)
landuse map of RGA (CSA, 2000).
Soil Survey Geographic
Database (SSURGO)
(USDA-NRCS, 2002)
Input data requirements
Hidrometereological data
* Data from the U.S. Geological Survey (USGS) and the National Oceanic and Atmospheric Administration (NOAA)
Hydro-meteorological series Data time step Data period
Precipitation Hourly 1995/01/01 to 2005/12/31
Potential Evapotranspiration Hourly 1995/01/01 to 2005/12/31
Air temperature* Hourly 1995/01/01 to 2005/12/31
Wind velocity* Hourly 1995/01/01 to 2005/12/31
Solar Radiation Hourly 1995/01/01 to 2005/12/31
Dew Point temperature* Hourly 1995/01/01 to 2005/12/31
Cloud Cover* Hourly 1995/01/01 to 2005/12/31
Sediments and water quality stations
Water quality stations characteristics
Watershed
Name
Outlet USGS
Station
Number
Drainage
Area
at Outlet
(km2)
Geog. Coordinates
Latitude Longitud
Río Grande de Arecibo near
Adjuntas 50020500 32.9 18º10’54” 66º44’12”
Río Grande de Arecibo near
Utuado 50025000 170.9 18º18’11” 66º41’59”
Río Caonillas above Lago
Caonillas 50026050 104.6 18º13’26” 66º38’22”
Río Limón above Lago Dos
Bocas 50027000 85.9 18º19’32” 66º37’24”
Model assembling
•A channel network
creation is the final
step for model assembling.
•For this purpose a
conceptual model need
to be created taking into
account sub-watersheds
created previously by WMS,
rivers and lakes and the
connections between all of
these elements.
MOLP approach
⚫ Multiple scenarios with water quality as the higherpriority were evaluated to obtain sustainable strategiesfor optimal land use growth.
⚫ Two different algorithms were used as solution methodsin combination with several hypothetical scenarios,reflecting spatial, socio-economic, physical and politicalfactors.
⚫ To reflect interregional and spatial characteristics in the study area, the RGA watershed was divided into three sub-areas or sub-watersheds (Río Caonillas, Río Limón and Río Grande de Arecibo) corresponding to three municipalities at the region (Adjuntas, Jayuya and Utuado).
MOLP approach
⚫ Scenarios take into account different combinations inthe land use growth priority as consequence ofhistorical information and future projections abouttendencies in the land use growth pattern.
⚫ For this, a detailed compilation of social characteristicsin the study area, economic sectors inside eachmunicipality tied to the subbasins as well as forecastingfrom local, state and federal agencies in Puerto Ricowere used.
⚫ The uncertainty concept associated to decisionvariables was considered.
Interface for uncertainty analysis consideration
⚫ In order to consider the uncertainty nature of theproblem, the obtained land use export coefficientsintervals from a ten years water quality simulation wereused as the decision variables coefficients inputs in theMOLP model.
⚫ This analysis allows considering multiple randomsamples in those decision variables to generate multipleruns and determine the optimal solution of theconflictive objectives.
⚫ Next equations defines the MOLP problem with theassociated uncertainty in the decision variablescoefficients.
Interface for uncertainty analysis
consideration( ) ( ) ( ) Tn XfXfXfMin ,....,, 21
nxxxX ...,,, 21=
njx
xbb
xaa
j
j
n
j
U
ij
L
ij
j
n
j
U
ij
L
ij
...,,1,0
0,
0,
1
1
=
=
=
=
where:
subject to:
)(Xfn is the n-th objective function
,0,1
=
j
n
j
U
ij
L
ij xaa 0,1
==
j
n
j
U
ij
L
ij xbb inequality and equality constraints, respectively
MODEL
SET-UP
HSPF land
use export
coeffcients
EXCEL DATA
BASE
RANDOM
SAMPLE
GENERATION
EXCEL DATA
BASE FOR
MATLAB INPUT
MOLP automated
solution process
using goal
attainment algorithm
POST PROCESSING
SOLUTION
ANALYSIS
RESULTS
EXCEL DATA
BASE
END
START
MODEL
SET-UP
HSPF land
use export
coeffcients
EXCEL DATA
BASE
RANDOM
SAMPLE
GENERATION
EXCEL DATA
BASE FOR
LINGO INPUT
MOLP automated
solution process
using weighted
goal programming
algorithm
POST PROCESSING
SOLUTION
ANALYSIS
RESULTS
EXCEL DATA
BASE
END
START
MODEL
SET-UP
INPUT
DATA FROM
HSPF
EXCEL DATA
BASE
RANDOM
SAMPLE
GENERATION
MATLAB
DATA BASE
LINGO DATA
BASE
CHOICE MATLAB
ALGORITHM FOR MOLP
SOLVE YES
MOLP automated
solution process
using goal
programming
algorithm
NO
MOLP automated
solution process
using goal
attainment algorithm
POST PROCESSING
SOLUTION
ANALYSIS
RESULTS
EXCEL DATA
BASE
END
START
Scenarios construction
⚫ Summing up, the model considers forest conservation,soil loss targets (sediment loss objectives), waterquality objectives (Nitrogen, Phosphorus lossobjectives), and socio-economic characteristicssubject to:
– Land availability constraints,
– Forest conservation constraints,
– Soil loss constraints,
– Water quality constraints.
– Agricultural growth constraints.
– Urban development constraints.
to find the best land use combination according withthe proposed goals.
MOLP formulation
⚫ The scenarios were translated to mathematicalexpressions incorporating all the informationrelated to water quality targets and constraints.
⚫ Two water quality standards were considered inthe analysis:
– a) the existing water quality standards by thePuerto Rico Environmental Quality Board(PREQB, 2003) and the USEPA
– b) a proposed new water quality standarddeveloped by the University of Puerto Rico fornutrient standards (Martínez et al., 2006).
Mathematical model: Decision variables
⚫ X1, The optimal area reserved for forestconservation.
⚫ X2, The optimal area allowed for agriculture.
⚫ X3, The optimal area assigned for urbandevelopment.
⚫ X4, The optimal area reserved for pastures.
⚫ X5, The optimal area reserved for range land.
Mathematical model: Objective functions
⚫ Z1; The objective function of total phosphorus discharge
(TP);
⚫ Z2, The objective function of total nitrogen discharge (TN).
⚫ Z3, The objective function of total discharge of sediment
yield, (TS).
•As mentioned above, the water quality achievement is the
highest priority in this optimization analysis.
•Three objectives functions related to water quality impacts
and total discharges of Nitrogen (TN), Phosphorus (TP) and
Sediment yield from soil erosion (TS) were proposed.
Mathematical model: Constraints
⚫ Two different types of constraints were
incorporated in the mathematical model.
– The first type consists of system constraints
regarding to the actual land use and minimal
areas needed for optimal land management
and development.
– The second type are goal constraints, they
provide a measure of the assimilative capacity
to different pollution impacts (maximum
permissible loads) reaching the water body.
⚫ Those are defined as the system constraints and
goal constraints respectively in a MOLP model
Final mathematical model
5154143132121111 )( XCXCXCXCXCxZMin ++++=
5254243232221212 )( XCXCXCXCXCxZMin ++++=
5354343332321313 )( XCXCXCXCXCxZMin ++++=
Land Use
Total Phosphorus
(TP)
(Kg/Ha*yr)
Total Nitrogen
(TN)
(Kg/Ha*yr)
Total Sediment
Yield (TS)
(Kg/Ha*yr)
Urban 2.94 – 4.65 6.82 – 14.91 14.58 – 789.23
Pasture 1.18 – 3.10 9.53 – 31.65 9.76 – 37.56
Agriculture 1.16 -3.91 14.07 – 41.13 182.85 – 1,390.17
Forestland 0.16 – 0.47 2.02 – 5.41 0.74 – 52.14
Rangeland 0.17 – 0.52 2.12 – 5.56 0.86 – 59.55
Where cij are the land use export coefficients given by the characteristic intervals showed in the Table
RESULTS
Water quality simulation
⚫ Hydrologic, sediments, water temperature andwater quality calibration and validation was donebetween 1995-2005.
⚫ Total nutrients annual loads were calculatedusing the above water quality results.
⚫ Also, land use export coefficients intervals wereobtained by sub-watershed and compared withliterature.
⚫ Results from calibration and validation periodswere good according with the literaturesuggested guidelines and statistical parameters.
Hydrology calibration
USGS Station
Observed
Mean
Daily flow
(m3/s)
Simulated
Mean
Daily flow
(m3/s)
PME
(%)R R2 NSE
RMSE
(m3/s)
MAE
(m3/s)
USGS 50027000
Río Limón above Lago
Dos Bocas
1.32 1.35 1.91 0.82 0.67 0.67 1.05 0.46
Sediments calibration
USGS Station
Observed
Mean
Daily flow
(mg/l)
Simulated
Mean Daily
flow
(mg/l)
PME
(%)R R2 NSE
RMSE
(mg/l)
MAE
(mg/l)
USGS 50020500
Río Grande de Arecibo near
Adjuntas36.74 33.19 -10.70 0.46 0.21 -0.19 103.06 38.58
USGS 50024950
Río Grande de Arecibo below
Utuado
187.73 193.79 3.13 0.73 0.53 0.48 392.71 160.13
USGS 50025155
Río Saliente at Coabey near
Jayuya
25.90 21.51 -20.41 0.29 0.08 -1.54 64.62 24.70
USGS 50026025
Río Caonillas at Paso Palma229.07 241.55 5.17 0.71 0.50 0.50 1,157.91 232.20
USGS 50027000
Río Limón above Lago Dos
Bocas
46.27 49.99 7.44 0.35 0.12 -2.41 153.97 54.96
Land use export coefficients
Land use export coefficients by
subwatershed (Total Nitrogen)
Land Use
Sub-watershed
Río Grande de*
Arecibo
(Kg/Ha*yr)
Río Caonillas*
(Kg/Ha*yr)
Río Limón**
(Kg/Ha*yr)
Urban 6.82 – 14.91 6.12 – 13.08 8.53 – 14.63
Pasture 9.53 – 31.65 6.86 – 34.10 11.33 – 33.10
Agriculture 14.07 – 41.13 5.63 – 39.74 21.65 – 41.06
Forestland 2.02 – 5.41 1.64 – 6.15 3.12 – 6.72
Rangeland 2.12 – 5.56 2.25 – 7.158 3.63 - 5.90
Mean Annual Daily
Flow (m3/s)2.17 – 7.60 1.22 – 4.72 1.70 – 4.46
Land use export coefficients by
subwatershed (Total Phosphorus)
Land Use
Sub-watershed
Río Grande de*
Arecibo
(Kg/Ha*yr)
Río Caonillas*
(Kg/Ha*yr)
Río Limón**
(Kg/Ha*yr)
Urban 2.94 – 4.65 1.39 – 4.15 0.66 – 3.06
Pasture 1.18 – 3.10 0.18 – 2.07 0.14 – 1.88
Agriculture 1.16 -3.91 0.32 – 2.24 0.37 – 1.92
Forestland 0.16 – 0.47 0.05 – 0.36 0.06 – 0.33
Rangeland 0.17 – 0.52 0.06 – 0.22 0.08 – 0.49
Mean Annual Daily
Flow (m3/s)2.17 – 7.60 1.22 – 4.72 1.70 – 4.46
Río Grande de Arecibo land use export coefficients and
literature comparison (Total Nitrogen)
Land UseThis
study
Total nitrogen export coefficients (Kg/ha*yr)
Puerto Rico and New Zealand United States of America
Ramos -
Ginés
Puerto
Rico
(1998)
Ortiz-Zayas
Puerto Rico
(2006)
McDowell
and Asbury
Puerto Rico
(1994 )
Quinn &
Stroud
New Zeland
(2002)
USEPA
(1982)
Beaulac &
Rechow
(1982)
Donigian
et al.
(1990)
Omernick
(1976)*
Agriculture5.6 -
41.16.9 – 8.6 26.9 – 39.7 ------
6.76 (Mixed
agriculture)9.0 – 20.2 2.5 – 41.5 5.6 – 78.4 4.2 – 38.0
Urban 6.1-14.9 6.6 – 17.1 4.8 - 33.0 ------ ------ 4.5 - 11.2 1.6 – 38.5 5.6 – 28 2.0 – 17.0
Pasture6.9 -
34.1------ ------ ------ 10.0 – 35.3 2.2 – 6.7 2.0 – 30.8 1.7 – 7.8 ----
Forest 1.6 – 6.7 2.7 ------ 4.4 – 9.8 2.1 – 3.7 0.6 – 2.2 1.6 – 6.5 0.2 – 5.6 ----
Rangeland 2.1 – 7.2 ------ ------ ------ ------ ------ ------ ------ ------
MULTI-OBJECTIVE
OPTIMIZATION RESULTS
(SCENARIO 1)
Scenario1
Sub-watershed Land Use
2005 2025
Actual
Value
(Ha)
Lower
Bound
(Ha)
Upper
Bound
(Ha)
Interval
(Ha)
Mid. Value
(Ha)
RGA
Forest 14,653.1 14,689.4 14,699.2 9.8 14,694.3
Agriculture 1,286.3 1,363.5 1,416.6 53.1 1,390.1
Urban 883.7 948.8 978.4 29.6 963.6
Pasture 11.7 35.8 78.5 42.7 57.2
Rangeland 1,713.3 1,452.4 1,482.7 30.3 1,467.6
CAONILLAS
Forest 8,155.7 8,159.6 8,160.1 0.5 8,159.9
Agriculture 643 710.8 733.1 22.3 721.9
Urban 283.7 409.1 414.8 5.7 411.9
Pasture 180.9 197.3 198.3 1.0 197.9
Rangeland 2,970.9 2,762.5 2,792.2 29.7 2777.4
LIMON
Forest 7,627.0 7,676.7 7,682.5 5.8 7,679.6
Agriculture 694.7 728 763.4 35.4 745.7
Urban 165.2 174.8 187.9 13.1 181.35
Pasture 102.3 104.7 110.9 6.2 107.8
Rangeland 784.9 654.6 676.3 21.7 665.45
Scenario 1
Land use
Sub-watershed land conversion (Ha)
TOTALRGA Caonillas Limón
Forest 38.3 (0.26%) 4.1 (0.05%) 52.5 (0.69%) 94.9
Agriculture 104.0 (8.09%) 78.9 (12.28%) 50.9 (7.34%) 233.8
Urban 79.6 (9.00%) 128.2 (45.20%) 16.1 (9.76%) 223.9
Pasture 45.4 (388.3%) 16.9 (9.33%) 5.51 (5.4%) 67.8
Rangeland -245.4 (14.33%) -193.6 (6.52%) -119.42 (15.2%) -558.4
Barrenland -24.5 -34.1 -5.6
Water 0.0 (0%) 0.0 (0%) 0.0 (0%) 0.0
Land use probable conversion based on mean optimization modeling
output. (Forest conservation + agriculture and urban growth)
RGA Scenarios summarize
Land use optimization results
by Scenario, RGA sub_watershed
-300
-250
-200
-150
-100
-50
0
50
100
150
200
Forest Agriculture Urban Pasture Rangeland Barrenland
Land Use Name
LU
Ch
an
ge
(Ha
)
SCENARIO 1 SCENARIO 2 SCENARIO 3
MOLP Conclusions
⚫ A Multi-objective Linear Programming (MOLP) approachwas incorporated in this research in order to be used as amathematical tool for the evaluation of a series ofhypothetical scenarios searching for the optimal land usecombination for the year 2025.
⚫ The proposed methodology incorporates the uncertaintyassociated with the model decision variables in the exportcoefficients for each land use category.
⚫ By considering uncertainty this methodology produces betterresults compared with a deterministic formulation where aunique solution is available instead of multiple optimalpossible combinations.
MOLP Conclusions
⚫ The methodology is flexible and could be adapted to thedecision maker priorities, producing multiple optimalpossible solutions.
⚫ The number of total random runs is defined by themodeler and combined with the scenarios producing anextensive data base of results.
⚫ The versatility of the program allows exploring the effectto make flexible one or two of the water quality goals.