irrigation system salinity management modelling

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Irrigation System SalinityManagement ModellingMuhammad AslamPublished online: 21 Jul 2010.

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Water Resources Development, Vol. 11, No. 3, 1995

Irrigation System Salinity Management Modelling

MUHAMM AD ASLAM1

& GAYLORD V. SKOGERBOE2

1Department of Irrigation and Drainage, University of Agriculture, Faisalabad, Pakistan ;

2Department of Biological and Irrigation Engineering, Utah State University, Logan, Utah

84322-4150, USA

ABSTRACT A salinity management model is developed for analysing an irrigation

system (small or large), which consists of a hydro-salinity submodel, a soil moisture

chemistry submodel, and a groundwater salinity submodel. The hydro-salinity submodel

calculates water and salt budgets for an irrigation system in order to determine the

recharge rate into the groundwater reservoir. The soil moisture chemistry submodel

predicts soil moisture movement and transport of solutes in the unsaturated soil pro® le

considering the cation exchange, precipitation and dissolution of gypsum and lime in the

soil solution. The three-dimensional groundwater salinity submodel predicts the spatial

and temporal changes in groundwater salinity, as well as temporal variations in the

salinity of pumped water.

Introduction

Irrigated agriculture has been playing an important role in developing the arid

and semi-arid regions of the world, but there is a need to increase agricultural

productivity continuously. For many irrigation system s, one of the most domi-

nant problems that must be contended with is waterlogging and salinity.

It is also necessary to develop a more sophisticated system s approach for

describing salinity phenomenon. Such an approach must differentiate between

the sources of groundwater recharge such as seepage and deep percolation,

predict the chemical changes that occur as water moves through the unsaturated

soil pro ® le, and be capable of taking into considera tion a vertical salinity

gradient, if it exists, in the groundwater reservoir.

This paper focuses on the development of a salinity management model

usable under ® eld conditions, such as an irrigation system, for: (1) assessing

waterlogging and salinity problem areas; and (2) predicting the impact of

alternative management practices for improving the agricultural productivity of

salt-affected soils. The overall salinity management model consists of a hydro-

salinity submodel, a soil moisture chemistry submodel, and a groundwater

salinity submodel. The operation and linkage of these submodels is discussed in

the following sections.

Hydro-salinity Submodel

The detailed evaluation of the hydrologic and salinity ¯ ow system s for an

irrigated area is referred to as hydro-salinity modelling . This modelling de-

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262 M. Aslam & G. V. Skogerboe

scribes the existing water and salt ¯ ows in an area and is necessary for

determ ining the interactions between each component of a hydrologic system .

The hydro-salinity submodel, which describes most of the processes that occur

in an irrigated area, can be used to determ ine the monthly effects of precipi-

tation, river in¯ ow, irrigation, evapotranspiration and subsurface ¯ ows on the

amount and salinity of out¯ ows from the study area.

The hydro-salinity submodel is a slightly modi® ed version of the model

developed by Walker (1970) in order to incorporate the irrigation channel

designations used in the Indian Subcontinent. This submodel is based on the law

of conservation of mass and uses a monthly time-scale for simulations. The block

diagram of a general conceptual hydro-salinity submodel is given in Figure 1,

which represen ts the various hydrologic processes and their ¯ ow pathways, and

also salinity and its pathways in a typical irrigation project.

The hydrologic part of the hydro-salinity submodel computes the water

budgets for an irrigated area using the input information and then performs

calculations within the model. This submodel considers in¯ ows, canal diver-

sions, distributary diversions, watercourse diversions, root zone ¯ ows, ground-

water ¯ ows and out¯ ows from the study area.

The model assumes that all hydrologic components have an associated salt

concentration except for precipitation and evapotranspiration, where the salinity

is considered to be zero. These two processes have an effect on the salt ¯ ow, but

are assumed not to contribute new salt or remove salt from the system .

Therefore, when the water system is satisfactorily modelled, the salinity subpro-

gram performs the salt budgets by multiplying each hydrologic component

considered in the water budget by the salinity concentration, which is measured

in the laboratory as total dissolved solids (TDS).

The operation of the hydro-salinity submodel is illustrated in Figure 2. The

main program reads the input information on land uses (e.g. crops, natural

vegetation, ponds, etc.) in the study area, climatic information required for

potential evapotranspiration calculations, surface water hydrologic components

and their associated salinity concentrations, and the quantity and quality of

water pumped from the groundwater reservo ir.

Having input the above mentioned information into the main program, the

potential water consumptive use from irrigated crops, phreatophytes, water

surfaces, and dryland crops in the area is estimated using the potential evapo-

transpiration (ET) subprogram. In the actual ET subprogram, the actual crop

water consumptive use and the amounts of deep percolation water are calcu-

lated by making a comparison between the potential evapotranspiration, root

zone water supply and soil moisture storage for each month. The calculations of

evapotranspiration are needed in order to: (1) perform a root zone water budget;

(2) estimate the salt loading moving below the root zone resulting from salt-con-

centrating effects; and (3) provide inputs to the soil moisture chemistry sub-

model.

After water consumptive use calculations have been made, the water budget

subprogram is invoked in order to evaluate different components of the hydrol-

ogy in the study area. This subprogram provides output information on weekly

potential evapotranspiration and the timing and amounts of irrigation applica-

tions, which are needed as input into the soil moisture chemistry submodel.

Water budgets of the area are developed by calculating monthly values of water

¯ ow components, which are then summed to obtain seasonal and annual values.

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Irrigation system Water supply system

Phreatophyteconsumption

Prim. canalevaporation

Prim. canaldiversions

Prim. canalseepage

Sec. canaldiversions

Prim. canalspillage

Sec. canal seepage

Tert. channeldiversions

Sec. canal evaporation

Sec. canal spillage

Tert. channelseepage

Farmdiversions

Tert. channelevaporation

Tert. channelspillage

Field channelseepage

Root zonesupply

Field tailwater

Deeppercolation

Consumptiveuse

Soil moisturestorage

Groundwater

storage

Groundwateroutflows

Riveroutflows

River inflows

Groundwaterinflows

Tributaryinflows

Precipitation

Imports

Phreatophyteconsumption

Exports

Municipaluses

or or Pumpedwater

Drainagereturn flow

Water flowsSalt flowsSystem boundary

Subsystem boundary

Secondary canal subsys.

Tertiary channel subsystem

Primary canal subsystem

Farm subsystem

Groundwater subsystem

Salinity Management Modelling 263

Figure 1. Block diagram of a genera lized hydro-salinity model (modi® ed from

Walker, 1970).

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Land use dataCrops and soils dataClimatic dataSurface hydrology data and salinity concentrationsPumpage quantities and salinity concentrations

INPUTS

MAIN PROGRAM Reads input information and calls subprogram s

Potential evapotranspiration, PETOutputs

POTENTIAL AND ACTUAL ET SUBPROGRAMS

Evapotranspiration of phreatophytesEvapora tion from water surfacesActual evapotranspiration of croplandDeep percolation from cropland

WATER BUDGET SUBPROGRAM

Weekly evapotranspirationIrrigation schedulesWater budgets by calculating monthly and summingvalues of the hydrologic componentsSubsurface return flowsGroundwater recharge

SALT BUDGET SUBPROGRAM

Salt concentrating budgetsMonthly and annual salt concentrations andload in surface return flows and infiltratinginto the soil

Outputs

Outputs


Figure 2. Schematic diagram of the hydro-salinity

submodel.

Seepage losses from the irrigation conveyance network and deep percolation

losses from the croplands constitute the subsurface return ¯ ows, most of which

becomes groundwater recharge, which is required as input into the groundwater

submodel.

The salt ¯ ows depend upon the water ¯ ows. Therefore, ® rst of all, water

budgets are developed for the area using the water budget subprogram. Then ,

the salinity concentrations are attached to the hydrologic components in order to

obtain salt budgets using the salt budget subprogram. This subprogram pro-

vides information about monthly, seasonal and annual salt loads in the surface

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return ¯ ows, but more importantly the salts in® ltrating into the soils within the

study area.

Soil Moisture Chemistry Submodel

To manage salinity problems in irrigated areas properly, it is necessary to

understand in detail the processes that control the unsaturated movement of

water and salt from the ground surface to the groundwater table, with particular

emphasis upon the root zone of irrigated soils. This detailed understanding

requires the knowledge of chemical reactions taking place in the soil pro ® le

when irrigation water moves through the soil pro ® le. These chemical reactions

in the root zone of an irrigated soil affect soil salinity and the quantity (load) of

subsurface water and salts percolating deep below the root zone en route to the

groundwater reservoir. The process of evaluating the chemical changes in the

subsurface return ¯ ows as they move through the soil pro ® le and are trans-

ported into the groundwater reservo ir is called soil moisture chemistry mod-

elling.

The primary objective of soil moisture chemistry simulation is to model soil

moisture ¯ ow, the chemical reactions and the transport of salts. A water

movement± salt transport chemistry model developed by Wagenet & Hutson

(1987) is used for simulating water ¯ ow, equilibrium chemistry and solute

transport in one dimension (vertical) in the unsaturated zone of irrigated soils

from the soil surface to the groundwater table.

Modelling Water Flow in Soils

In the soil chemistry submodel, the one-dimensional transient soil moisture

movement in the vertical direction is described using the Richards equation in

the form:

v t

5

zF K( v ).

H

zG 2 A(z, t) (1)

where v is the volumetric water content; t is the time; z is the soil depth; K( v ) is

the hydraulic conductivity; H is the soil hydraulic head; and A(z,t) is a root-ex-

traction term given by the following equation:

A(z, t) 5[Hroot 1 (RRES*z) 2 h(z, t) 2 s(z, t)] [RDF(z, t)k( v )]

( D x D z)(2)

where Hroot is the root water potential at the soil surface; RRES is the root

resistance term de® ned herein as Rc 1 1, where Rc is the ¯ ow coef® cient in the

plant root system assumed equal to 0.05; h(z,t) is the soil matric potential; s(z,t)

is the solute potential; RDF(z,t) is the proportion of the total active roots in the

depth increment D z; and D x is the distance between the plant roots and the point

in the soil where h(z,t) and s(z,t) are measured. The term D x is assumed equal

to 10 mm. To simulate soil moisture movement in the soil, equation (1) is solved

by a ® nite difference numerical technique in which the soil pro® le is discretized

into a number of horizontal segments and the total time period is divided into

short time intervals, which varies from a few seconds during an irrigation event

to a maximum of three hours a few days after the irrigation is completed.

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Modelling Solute Transport in Soils

The one-dimensional salt transport process in the soil chemistry submodel is

described by the following convection-diffusion equation (CDE):

( v c)

t5

zF D ( v ,v)

c

z2 qc G (3)

where v is the volumetric water content; c is the solute concentration; t is the

time; z is the soil depth; q is the volumetric solution ¯ ux; and D( v ,v) is the

combined diffusion and hydrodynamic dispersion coef® cient given by:

D ( v ,v) 5 Do aeb v 1 l v (4)

where v is the average ¯ ow velocity; D o is the diffusion coef® cient for pure

water; a, b are the diffusion constants; and l is a dispersion constant. A

second-order ® nite difference solution of equation (3) simulates the solute

transport process in the soil.

Modelling Soil Chemistry

To simulate the chemical reactions in the soil pro ® le during transient transport

conditions, the solute transport submodel is used to describe the movement of

a chemical ion in solution as a non-reactive species. After the independent

movement of the Ca, Mg, Na, K, Cl, and SO 4 ions as individual species, the

chemistry subroutine, CHEM , and the cation exchange subroutine, XCHANG,

are used to bring the solution species into chemical equilibrium with lime and

gypsum, and to adjust the exchange equilibria.

The soil moisture chemistry submodel is incorporated into the salinity

management model in order to predict the variations in salinity concentrations

in the soil pro ® le and to predict the chemical quality of deep percolating water

through the soil pro® le. The schematic diagram of the soil moisture chemistry

submodel is provided in Figure 3.

In the soil moisture chemistry submodel, the soil moisture subprogram takes

as input information the initial soil moisture contents in the soil pro ® le (or initial

matric head pro ® le), weekly potential evapotranspiration which is output from

the hydro-salinity submodel, crop data and irrigation schedules (timing and

amounts), and provides as output information the soil moisture contents at

different soil depths with time, soil moisture ¯ uxes, and the temporal quantity

of water deep percolating through the soil pro® le and entering the groundwater

reservo ir.

The solute transport subprogram and the equilibrium soil chemistry subpro-

gram use input data on the chemical composition of irrigation water, initial

concentrations of chemical ions in the soil pro ® le, amounts of lime and gypsum

in the soil pro ® le, initial amounts of exchangeable cations in the soil pro ® le, and

chemical (fertilizer) applications to the soil. These subprograms provide outputs

on the temporal values of solute ¯ uxes between soil nodes, spatial and temporal

ionic concentrations in the soil pro ® le and the chemical composition of deep

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Soil physical properties

INPUTS

INPUTSINPUTS

INPUTS

INPUTS

OUTPUTS

OUTPUTS

SOIL TRANSPORTSIMULATION

SOIL MOISTURE MOVEMENTSIMULATION

Potential ConsumptiveUse(Climaticdemand)Information

Irrigationwater chemistrydataFertilizerapplications(time andamounts)

Chemistry programsimulatesSolution phase

Cation exchangePrecipitationDissolution

(Solves moisture flow equation)

Soil moisture contents at nodes

Soil moisture fluxesDeep percolation amounts withtime

(Solves solute transportequation)

Solute fluxesChemical ionic concentrationsChemical composition ofgroundwater recharge with time

Initial soilchemistryinformation

Rainfall andIrrigation WaterApplication Data


Figure 3. Schematic diagram of the soil moisture chemistry submodel.

percolating water reaching the bottom of the soil pro ® le with time, which

becomes input (recharge) to the groundwater salinity submodel.

Groundwater Salinity Submodel

The analysis of groundwater ¯ ow and solute transport under variable ¯ uid

density conditions is a complex phenomenon, which requires the solution of two

simultaneous non-linear partial differential equations that describe groundwater

¯ ow and solute transport through porous media. Many researchers have devel-

oped various groundwater ¯ ow and solute transport models to study the

transport of solutes in a groundwater ¯ ow system . A ® nite-difference density-

dependent groundwater ¯ ow and solute transport model, HST3D (Heat and

Solute Transport in saturated 3-Dimensional Groundwater Flow System) devel-

oped by Kipp (1987) is adapted to simulate the solute transport in the ground-

water ¯ ow system with pumping wells.

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Groundwater Flow Equation

The major reason for selecting a three-dimensional groundwater model is for

cases where a vertical salinity gradient exists in the groundwater reservo ir. In

many arid areas, higher salinity concentrations, which are also slightly more

dense, are encountered at deeper depths in the groundwater reservo irs. In some

cases, these higher salinity concentrations are largely the result of salts taken into

solution from the underlying geologic formations, particularly when they are of

marine origin. If pumping occurs, there is a high potential for salinizing the

groundwater reservo ir after a few decades unless the groundwater is carefully

managed, which usually requires lower discharge capacity wells (e.g. fractional

tubewells of perhaps only 10 litres per second in some areas of the Punjab in

Pakistan as reported by McWhorter [1980]).

In the HST3D model, the groundwater ¯ ow equation, which is based on the

conservation of total ¯ uid mass in a volume element, coupled with Darcy’s law

for ¯ ow through a porous medium, is expressed as:

( « r )

t5 , r

k

m( , p 1 r g) 1 q r * (5)

where p is the ¯ uid pressure; t is the time; « is the porosity; r is the ¯ uid density ;r *is the density of a ¯ uid source; k is the porous-medium permeability; m is the

¯ uid viscosity; g is the gravitational constant; and q is the ¯ uid-source ¯ ow-rate

intensity (positive for in¯ ow and negative for out¯ ow). In HST3D, the pore or

interstitial velocity is obtained from Darcy’ s Law as:

v 5 2k

« m( , p 1 r g) (6)

where v is the interstitial velocity vector.

Solute Transport Equation

The HST3D solute transport simulation is based on advective-dispersive mecha-

nisms of solute transport. Ignoring adsorption, dissolution, production and

decay of solute species, the mass of solute stored in a particular volume of solid

matrix may change with time because of ambient water with a different

concentration ¯ owing in, injected water having a different concentration, change

in the total ¯ uid mass in the element, solute diffusion, or dispersion in or out of

the volume.

In HST3D, the partial differential equation, which describes the solute trans-

port in the porous medium, is expressed as:

( « r w)

t5 , « r D s , w 1 , « r DmI , w

2 , « r vw 2 l « r w 2 r bR fs 1 q r *w*(7)

where w is the mass fraction of solute in the ¯ uid phase; w* is the mass fraction

of solute in the ¯ uid source; D s is the mechanical dispersion coef® cient; Dm is the

molecular diffusivity of the solute; l is the decay rate constant; R fs is the transfer

rate of solute from the ¯ uid to the solid phase per unit mass of solid phase;r b is the porous medium bulk density ; and I is the identity matrix.

The groundwater salinity submodel is incorporated within the salinity man-

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G R O U N D W AT E RM O V E M E N TS IM U L AT IO N

IN P U T S

IN P U T S

O U T P U T S

S O L U T E T R A N S P O R TS IM U L AT IO N

O U T P U T S

(s o lv e s s a tu ra te df lo w e q u a t io n )

F lu id p re s s u red is tr ib u t io n

w ith t im e

(s o lv e s s o lu tetra n s p o r t e q u a t io n )

Te m p o ra l s a l in i tyd is tr ib u t io n ing ro u n d w a te r

S a lin ity c o n c e n tra t io nin p u m p e d w a te r w ith t im e

A q u ife r p h y s ic a ld im e n s io n s

P o ro u s m e d iap ro p e rt ie sW e ll in fo rm a tio nF lu id p ro p e r t ie sR e c h a rg e ra te s

In it ia l s a lt c o n c e n tra t io nin th eg ro u n d w a te rS o lu te tra n s p o rtp a ra m e te rsTe m p o ra l s a l in i tyc o n c e n tra t io n o fg ro u n d w a te rre c h a rg e


Figure 4. Schematic diagram of the groundwater salinity submodel.

agement model in order to predict the distribution of salinity concentrations in

the groundwater and in pumped groundwater with time. Recharge resulting

from seepage and deep percolation are obtained from the hydro-salinity sub-

model, while the salinity concentrations of this recharge are obtained from the

soil moisture chemistry submodel. Pumping rates and salinity concentrations are

measured in the ® eld, but predictions of future salinity concentrations of

pumped water must come from the groundwater salinity submodel. A schematic

diagram of the groundwater salinity submodel is given in Figure 4.

The groundwater ¯ ow simulation portion of the groundwater salinity sub-

model uses input information on the physical dimensions of the aquifer in the

study area, properties of the porous media, properties of the ¯ uid, well data and

recharge to the groundwater reservoir. This simulation provides predictions on

the spatial and temporal pressure distribution in the aquifer, which re¯ ects the

movement of groundwater in the aquifer.

The solute transport portion of the groundwater submodel employs input data

on initial salinity concentration distribution in the groundwater body, solute

transport parameters, and the chemical quality of recharge water entering the

groundwater. The solute transport subprogram predicts the salinity concen-

tration distribution in the groundwater system of the area with time, as well as

the temporal variation of salinity in producing wells present in the groundwater

aquifer.

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Salinity Management Model

The schematic diagram of the irrigation system salinity management model is

presented in Figure 5, which depicts the linkages between the three submodels.

First of all, the hydro-salinity submodel is run by inputting land use infor-

mation, crops and soils data, climatic data, surface hydrology and associated

quality data, and the amounts and quality of pumped groundwater. The output

that will be obtained from this hydro-salinity submodel consists of water and

salt budgets representing the existing conditions regarding water and salt ¯ ow

systems of the area, weekly values of potential evapotranspiration, timing and

amounts of irrigation applications for croplands, and the groundwater recharge

resulting from conveyance system seepage and cropland deep percolation.

In order to simulate soil moisture movement and solute transport through the

soil pro® le, soil physical and chemical data, irrigation chemistry data, solute

transport coef® cients, crop data including weekly potential evapotranspiration,

and the timing and amounts of irrigation events obtained from the hydro-salin-

ity submodel are manually input into the soil moisture chemistry submodel.

This submodel considers the chemical reactions of cation exchange, precipitation

and dissolution of chemical salts during the movement of salts through the soil

pro ® le. The soil moisture chemistry submodel provides the predictions of soil

moisture contents at different soil depths with time, temporal salt pickup, spatial

and temporal salinity concentration distribution in the soil pro ® le, quantities and

qualities of subsurface return ¯ ows, and groundwater recharge and its chemical

quality that becomes input into the groundwater salinity submodel.

After running the soil moisture chemistry submodel, thereby obtaining the

aforementioned outputs, the monthly groundwater recharge volumes resulting

from deep percolation and seepage are known from the hydro-salinity sub-

model, while the temporal variation in recharge rate and associated salinity

concentrations are predicted by the soil moisture chemistry submodel. This

information is manually input into the groundwater salinity submodel. In

addition, information is input on aquifer physical dimensions, porous media and

¯ uid properties, well information and initial groundwater chemistry infor-

mation. The groundwater salinity submodel provides outputs of spatial and

temporal salinity concentration distribution in the groundwater reservo ir, as

well as the temporal variations in the salinity concentrations of pumped water

by wells installed in the irrigation system (or study area). These predictions help

in establishing groundwater management requirem ents for continued use of the

aquifer on a long-term basis.

The interpretation of the results obtained from model studies using the

irrigation system salinity management computer model developed herein will

provide considerable insight into the surface hydrology, unsaturated soil pro ® le

hydrology and subsurface groundwater hydrology, as well as their associated

impacts on salinity. For example, the hydro-salinity submodel will provide

information about how much water is diverted from the canal system into the

irrigated area concerned and how much of this diversion becomes seepage, how

much surface runoff occurs, how much water effectively in® ltrates into the soil

for crop use, and how much of this in® ltrated water percolates deep into the

groundwater system . The model will also give information on the amounts of

salts concentrated in the soil root zone due to evapotranspiration.

The soil moisture chemistry submodel will provide insight into the chemical

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INPUTS:

INPUTS:

INPUTS:

OUTPUTS:

OUTPUTS:

OUTPUTS:

HYDRO-SALINITY SUBMODEL

SOIL MOISTURE CHEMISTRY SUBMODEL

GROUNDWATER SALINITY SUBMODEL

Land use data, crops and soils data, climatic data, surfacehydrology data and salinity concentrations of surface watersinformation, and pumpage quantities and salinity concentrations

Water and salinity budgetsWeekly potential evapotranspirationIrrigation schedules (amounts and times) Recharge rate (from DP and seepage)

Soil physical informationSoil chemical informationWeekly potential evapotranspiration(from hydro-salinity submodelIrrigation schedules(from hydro-salinity submodel)Chemical quality of irrigation water

Soil moisture profile with time, salt pickup andsalinity concentration profile with timeQuantity and salinity of subsurface return flows Temporal groundwater recharge and salinity concentrations

Aquifer physical dimensions, porous media properties,well information, fluid properties, initial saltconcentration distribution in groundwater, recharge rate(from hydro-salinity and soil moisture chemistry submodels)

Spatial and temporal salinity concentration distributionin groundwaterSpatial and temporal salinity concentration in pumpedgroundwater


Figure 5. Schematic diagram of the irrigation system salinity management model.

changes which occur during unsaturated ¯ ow in the soil pro ® le. Information

will be provided on both soil salinity and salt pickup in deep-percolating water

moving through the soil pro ® le and entering the groundwater reservo ir under-

lying the study area.

The groundwater salinity submodel will predict long-term trends in ground-

water salinity, thereby providing guidance in groundwater resource manage-

ment on a long-term sustained basis for both domestic and irrigation purposes.

This submodel will predict the impact of salinity management measures in

controlling groundwater salinity and, consequently, in alleviating the ground-

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water salinity contribution to receiving streams, onto irrigated lands resulting

from pumping, or domestic groundwater supplies.

Based on all of the above-mentioned information, various salinity control

measures, such as lining of the conveyance system , drainage, improved irri-

gation practices, etc., can be evaluated for their effectiveness in alleviating the

salinity problems by using the locally calibrated irrigation system salinity

management model.

References

Kipp, K.L. (1987) A Computer Code for Simulation of Heat Transport and Solute Transport in

Three-dimensional Groundw ater Flow Systems, US Geological Survey, Water Resources Investiga-

tions Report 84-4095 (W ashington, DC, US Governm ent Printing Of® ce).

McW horter, D .B. (1980) Summary of Skimming W ell Investigations, Water M anagement Technical

Report No. 63 (Fort Collins, CO, Colorado State University).

Wagenet, R.J. & Hutson, J.L . (1987) LEACHM: Leaching Estimation and Chemistry M odel, User’s m anual

(Ithaca, NY, Center for Environment Research, Cornell University).

Walker, W.R. (1970) Hydro-salinity model of the Grand Valley. M S thesis submitted in partial

ful ® lment of the requirements for the degree of M aster of Science in Agricultural and Irrigation

Engineering, Colorado State University, Fort Collins, Colorado.

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