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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”


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 ++++=



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


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.

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