EPA-R2-73-168
MARCH 1973             Environmental Protection Technology Series
Prediction  Modeling  for
Salinity Control  in
Irrigation Return Flows

                                  National Environmental Research Center
                                  Office of Research and Monitoring
                                  U.S. Environmental Protection Agency
                                  Corvallis, Oregon 97330

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            RESEARCH REPORTING SERIES
Research reports of the  Office  of  Research  and
Monitoring,  Environmental Protection Agency, have
been grouped into five series.  These  five  broad
categories  were established to facilitate further
development  and  application   of   environmental
technology.   Elimination  of traditional grouping
was  consciously  planned  to  foster   technology
transfer   and  a  maximum  interface  in  related
fields.  The five series are:
                                          -»
   1.  Environmental Health Effects Research
   2.  Environmental Protection Technology
   3.  Ecological Research
   4.  Environmental Monitoring
   5.  Socioeconomic Environmental Studies
                 .»•/'•

This report has been assigned to the ENVIRONMENTAL
PROTECTION   TECHNOLOGY   series.    This   series
describes   research   performed  to  develop  and
demonstrate   instrumentation,    equipment    and
methodology  to  repair  or  prevent environmental
degradation from point and  non-point  sources  of
pollution.  This work provides the new or improved
technology  required for the control and treatment
of pollution sources to meet environmental quality
standards.

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                                                           EPA-R2-73-16*
                                                           March 1973
       PREDICTION MODELING FOR SALINITY CONTROL

                IN IRRIGATION RETURN FLOWS
                 A State-of-the-Art Review
               Arthur G. Hornsby,  Ph.D.
   National Irrigation Return Flow Research Program
   Robert S. Kerr  Environmental  Research Laboratory
                      P. 0. Box 1198
                   Ada, Oklahoma  74820
               Project Number 13030 GJS
                 Program Element  1B2039
        NATIONAL ENVIRONMENTAL  RESEARCH CENTER
           OFFICE  OF RESEARCH AND MONITORING
         U.S. ENVIRONMENTAL PROTECTION AGENCY
                CORVALLIS, OREGON 97331
For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402
            Price 90 cents domestic postpaid or 65 cents GPO Bookstore

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                            FOREWORD

This report has been prepared to fulfill several needs expressed by
the National Irrigation Return Flow Program.  A concise, up-to-date
summation of the current state-of-the-art of prediction modeling as
applied to salinity control in irrigation return flows was needed for
program planning and evaluation.  Secondly, a reference source was
needed by research personnel who are interested in undertaking pre-
diction modeling related to irrigation return flows.  Interdisciplinary
research is being required to solve complex water resource problems
which bridge several scientific disciplines.  Participants of such
research endeavors must have a conversant understanding of some
disciplines other than their own specialties to be an effective part
of the group.  This report can serve as an overview for those not
directly involved in irrigation return flow problems and assist in
bringing about the needed information exchange.

Presentation of equations is primarily meant to aid understanding of
the conceptual models and, therefore, does not include rigid mathe-
matical derivations.  Details of the individual models can be found
in the original publications.  Sections VII and VIII contain refer-
ences cited and a selected bibliography of related references.

Although every effort has been made to include all references
pertinent  to the objectives of this report, the author recognizes
that some  may have been overlooked.  Comments in this regard would
be gratefully received.
                                  iii

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                            ABSTRACT

A review of the current state-of-the-art of prediction modeling as
applied to salinity control in irrigation return flows is presented.
Prediction models are needed to assess the effects of proposed changes
in irrigation management practices on the quality of return flows.  The
processes which affect salinity levels in return flows are enumerated
and their interactions are alluded to.  Models used to predict the quan-
tity and quality of return flows are briefly discussed to show the
development of the current level of technology.  The readers are referred
to the original documents for more rigid development of the models and
incumbent assumptions.  It was concluded that technology of water and
salt flow in soil systems is sufficiently developed to permit formula-
tion of models using systems analysis to evaluate proposed changes in
management practices.  Development of systems models to study irrigation
return flow problems and conjunctive water resource uses was recommended.
A bibliography of selected references is given in addition to the
references cited.

Key words:  Irrigation return flow, prediction modeling, water quality
degradation, resource management.

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                              CONTENTS

Section                                                           Page

  I     Conclusions 	   1

  II    Recommendations 	   3

  III   The Need for Conserving Quality in Return Flows	   5

  IV    Processes Which Affect Salinity Levels in Irrigation
          Return Flows	   9

  V     Models Used to Predict Return Flow Quantity and  Quality  .  11

             Surface Flow	12

             Subsurface Flow	14

                  Mechanics of Water Movement in Soil Systems  .  .  14

                  Mechanics of Salt Movement in Soil Systems.  .  .  16

             System Flow	23

  VI    The Role of Prediction Modeling in Irrigation Return
          Flow Studies	;  .  .  33

  VII   References Cited   	  41

  VIII  Selected Bibliography 	  47
                             Vii

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                                FIGURES




                                                                  Page




1     A TYPICAL IRRIGATION RETURN FLOW SYSTEM	   6




2     HYDROLOGIC AND WATER QUALITY MODELS 	  26




3     CONCEPTUAL DIAGRAM OF GENERALIZED HYDRO-SALINITY MODEL  . .  30




4     CONCEPTUAL DIAGRAM OF A PROCESS MODEL 	  34




5     CONCEPTUAL DIAGRAM OF A SOIL SYSTEM SUBMODEL  	  35




6     CONCEPTUAL DIAGRAM OF AN IRRIGATION SYSTEM MODEL  	  36
                                  ix

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                                 SECTION I

                                CONCLUSIONS

1.  A review of the literature has shown that only recently has prediction
modeling been used to any extent for predicting the quality of irrigation
return flows.  The accuracy of the prediction model depends on the ability
to define the hydrologic system flow as well as the chemical reactions and
interactions taking place within the system.

2.  The theory of movement of water on the surface and in streams, through
the soil profile, and in the groundwater is highly advanced.  The individual
components of flow have been intensively studied by disciplinary scientists
and mathematical models formulated for their behavior.  Many of these models
have been shown to give reliable results for predicting quantity of flow
when applied to actual situations without the usual laboratory restrictions.

3.  The theory of salt movement with the individual components of water flow
is not as advanced as the theory of water movement; however, the past decade
has seen a rapid increase in knowledge in this field.  For irrigation systems,
the movement of salts on the surface can be modeled using a material balance
equation and the surface hydrologic model.  Changes in salinity levels may
be caused by evaporation of water or dissolution of salts previously depos-
ited on the soil surface.  Changes in salinity levels of waters percolating
through the soil profile are not so simple.  In addition to concentrating
the salt by evaporation of water from the soil surface and transpiration of
water from the root zone by plants, the ionic composition of the percolating
water may change significantly.  These composition changes result from ion
exchange with the soil colloid, and precipitation and dissolution reactions
occurring within the soil profile.  Further degradation in quality of per-
colating water is caused by leaching previously accumulated salts from the
profile and salt pickup from zones of natural salt deposits below th§ root
zone.  The above factors, as well as diffusion, dispersion, pore-water veloc-
ity, pore geometry and soil type have been studied in an effort to quantify
the flow of salts through soils.

4.  Flow of salts in the groundwater can be predicted using groundwater
hydrologic models and the materials balance concept.  Mixing the more
saline percolating water with the groundwater can be described by miscible
displacement theory.  After the percolating water is thoroughly mixed with
the groundwater, the salinity level will not change significantly since
salinity is a conservative quantity.

5.  Quantitative data on the quantity and quality of subsurface flows is
difficult and expensive to obtain and its meagerness will limit the appli-
cation of detailed models to this portion of the system.

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6.  Systems analysis approach to prediction modeling of salinity in irri-
gation return flows has not been widely used.  Orlob and Woods (1967) were
among the first to develop a prediction model with the system concept.
Walker (1970), Hyatt e_t al_. (1970), and Thomas (1971) have followed this
lead with systems models for quantity and chemical quality of irrigation
return flows.  These models have been successful in predicting the quality
of return water in the test areas and can be applied to other areas to be
studied by making minor adjustments.

7.  Two characteristics of prediction modeling which cannot be overstressed
are:  (1) the potential of evaluating the result of proposed management
practices before they are instituted; and (2) the tremendous savings in
both time and resources over that needed to find the same answers by field
experimentation.  With the pressing need to find immediate solutions to
salinity control problems in the arid west, prediction modeling is an
essential tool.

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                                 SECTION II

                              RECOMMENDATIONS

1.  Comprehensive, systematic prediction models should be developed which
can he easily and unambiguously adapted to field areas, where knowledge of
salinity flow is necessary to institute management practices to reduce
the salinity contributed to river systems by irrigation return flow.  Such
comprehensive models should be sufficiently flexible to permit inclusion
of parameters which might be unique to a given area yet would allow the
model to be generally applicable to any area needing study.

2.  After adequate verification, the prediction models should be used in
lieu of expensive and time-consuming field experiments to:  (a) predict
the salinity contribution of existing irrigation return flow; (b) evaluate
the influence of management practices, such as irrigation scheduling,
irrigation efficiency, application rates, irrigation water quality, etc.,
on the quality of the return flow; (c) evaluate the effect of irrigating
new lands on the quality of the return flow; (d) determine the relative
contributions of the individual processes occurring within the system,
thus identifying those processes which need to be examined closely to
effect better salinity control in return flows; and (e) develop optimal
basin-wide programs of salinity control and management.

3.  Prediction models should be developed using systems methodology and
unified terminology with comprehensive user's manuals developed to permit
widespread usage of the computer programs by water resource researchers
and planners.

4.  Prediction modeling of salinity in irrigation return flows should play
an important role in water resource management where conjunctive use of
the water resource is contemplated since the effect of quality degradation
caused by irrigation on other uses of water resources can be identified
and appropriate measures taken to correct or alleviate the problem.

5.  An increasing commitment must be made to total water resource planning
to assure that maximum benefits are derived from that resource while pre-
serving its quality.

6.  A larger data base of quantitative information on the flow of water
and salts in the groundwater system should be acquired to verify basin
model?

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                               SECTION  III

             THE NEED FOR  CONSERVING QUALITY  IN RETURN FLOWS

Irrigation agriculture uses more water  than any other single  consumer of
water resources.  Ninety percent of the water diverted from impounding
structures and consumptively used  goes  to irrigation  (Wadleigh, 1968) .
Some estimates indicate that as much as sixty percent of  the  total water
applied as irrigation water is. lost to  evapotranspiration.  Water lost by
this process is essentially salt free thus the net effect on  salt concen-
tration could be a 2 1/2-fold increase  in the return flow if  only this
mechanism is active.  Drainage waters usually have some crop  producing
value remaining but, depending upon the fraction of applied irrigation
water that has been evapotranspired, their salt concentration can be from
2 to 7 times greater than  that of  the applied irrigation water (Utah State
University Foundation, 1969).  Thus, the return of highly saline drainage
water to the stream degrades the quality of the stream for further use.
In addition, due to precipitation, dissolution, and ion exchange reactions
occurring in the soil system, the  proportions of the various  salt con-
stituents in the irrigation water  as it becomes drainage water are
usually altered and these  changes  contribute  to the degradation of quality
in the receiving stream.

The demand for irrigation  water in areas where water resources are limited
both in quantity and quality further aggravates the problem.  In many
river basins in the western states, irrigation return flow may contribute
substantially more than half the stream flow  during summer low flow periods-
Nearly all of the summer flow in the lower reaches of the Yakima River in
Washington is composed of  irrigation return water  (Browning,  1970).

Two excellent comprehensive  reviews have been published which describe
the effects and magnitude  of irrigation return flows.  The first was
published in 1960 entitled "Return Irrigation Water—Characteristics and
Effects" by E. F. Eldridge, USDHEW-PHS. and the second published in 1969
was entitled "Characteristics and  Pollution Problems  of Irrigation Return
Flow" prepared by the Utah State University Foundation for the FWPCA-USDI
(now EPA) .  These publications discuss  in detail  the  characteristics and
problems associated with irrigation return flows,  document their findings
from the literature, and set forth recommendations and research needs.
A typical irrigation return  flow system is presented  in Figure 1.

As more new lands are brought under irrigated culture, the demand  for
available water will increase and  return  flows will be increasingly
reused to meet these demands.  The reuse  of return flows  and  the consump-
tive nature of irrigated agriculture  constitutes  a major  contribution  to
salinity increase in western rivers and streams.   The technology of
detection and measurement  of these quality changes is sufficiently
advanced to permit identification  and  quantification  of  the various pro-
cesses which contribute to the increase of salinity.

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                                PRECIPITATION
                             INFLOW TO
                               CANALS
                                            EVAPOTRANSPIRATION
                                               FROM CROPS
  SURFACE RUNOFF
FROM NON-IRRIGATED
       LAND
         IND. 8 MUN.
          WASTES
            FIGURE l.  A TYPICAL IRRIGATION RETURN FLOW SYSTEM
                    NATURAL
                     INFLOW
                                                                                   OTHER
                                                                                EVAPOTRANSPIRATION
                                                                                FROM IRRIGATED LAND
        UPSTREAM
                                               APPLIED TO
                                             IRRIGATED LAND
RIVER
FLOW
DIVERTED FOR
   IRRIGATION
              GROUNDWATER
              CONTRIBUTION
                                                             RIVER FLOW
                                                                                         IRRIGATION
                                                                                        RETURN FLOW
                                                                               DOWNSTREAM

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To anticipate the. changes in salinity that must necessarily occur with
increased use and reuse of irrigation water, prediction modeling provides
a tool to be used in order that management practices can be instituted
in time to prevent serious impairment of water quality for downstream
users.  Prediction models can not only anticipate changes in salinity in
the return flows, but also aid in establishing the relative contributions
of the individual processes that lead to the salinity increase.  Assess-
ment of these relative contributions leads to improved management practices
with the ultimate goal of reducing salinity levels in irrigation return
flows while maintaining a viable agricultural operation.

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                            SECTION IV

    PROCESSES WHICH AFFECT SALINITY LEVELS IN IRRIGATION RETURN  FLOWS

Irrigation return water can be subdivided into  two  general  categories
based on potential degradation levels..  These are  (1) surface return
flow and (2) percolation through the plant root zone.  The  processes
which affect each are varied and are reflected  in  their relative contri-
butions to the increased salinity of irrigation return flows.

Surface return flows contribute relatively little  to the concentration
of salines.  Surface overflows and resulting tailwater will retain
approximately the same levels and composition of salines as the  applied
irrigation water, if relatively short application  times are used.  However,
if the irrigation water is not properly managed the following character-
istics may develop in the receiving stream:

     1.  an increase in sediment load,

     2.  an increase in agrichemical  (pesticides, herbicides, etc.)
         concentration due to adsorption onto particulate matter
         carried in the sediment load,

     3.  a slight increase in concentration of  salines due  to evaporation
         from the free water surface and dissolution of salts previously
         deposited on the surface of the soil,  and

     4.  an increase in the numbers of bacterial organisms  present in
         the surface water.

With correct management practices these contributions can be reduced to
negligible amounts.  Tailwater can be eliminated by regulations  of amount
and rate of application or it can be reused by  pumping back to the point
of initial application or used to irrigate fields  adjacent  to the original
site.  More propitious management can result from modeling  surface flows
to optimize salinity control.

By far, the majority of the increase in salinity in return  flows occurs
during percolation through the soil profile.  Salts are concentrated in
this region by the evapotranspiration process.  Water is in intimate
contact with the soil constituents as it passes through and can  react
with these constituents resulting in degradation in the quality  of the
percolating water.  Processes which may contribute  to some  extent to
this degradation are:

     1.  ion exchange reactions with  the soil minerals,

     2.  precipitation and dissolution reactions occurring  within the
         soil profile,

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     3.   ion composition change due to differential valence charges
         and the lyotropic series effect,

     4.   dissolution and leaching of soluble plant nutrients applied
         as fertilizer,

     5.   leaching to maintain salt balance in the soil profile,

     6.   salt "pickup" resulting from the presence of natural salt
         deposits in the soil profile or near the aquifer which conducts
         the groundwater back to the stream,

     7.   temperature changes which may effect the rate of reaction of
         exchange, precipitation and dissolution processes, and

     8.   filtration and oxidation or reduction of biological and chemical
         components of the applied water.  This process may actually
         enhance the quality of the return water in some cases.

Since many of these processes interact, the net result may not be simply
a summation of the individual process results but rather a complex
situation where the processes are simultaneously operating and interacting.
In managing such a situation, a better comprehension is needed of the
effects  of each process and the degree of interaction with other processes.
This is  best explored by a systematic approach which identifies and quanti-
fies the individual processes and their interactions.  A deterministic
systems  model needs to be developed and verified with experimental data
to predict changes in salinity level and composition of irrigation return
flow water.  The results would lead to a better understanding of the
basic processes and more efficient management of the total system as a
unit.
                                   10

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                                SECTION V

         MODELS USED TO PREDICT RETURN FLOW QUANTITY AND QUALITY

Dissolved solids concentration is one of the major factors affecting the
quality of waters receiving irrigation return flows; therefore, it is
desirable to be able to estimate the concentration of salts in return
flows from existing and new irrigation projects.  Any study of the quality
aspects of return flows must necessarily include the quantity of flow.

Mathematical models have been developed to describe many of the processes
which are active in return flows, and in a few cases they attempt to
describe the system as a whole.  These systems are simulated fay either
stochastic or deterministic models.  Stochastic analysis is aimed at
predicting a probable value of some observable result using statistical
theory.  This approach does not consider the individual processes within
the system at a microscopic level, thus precludes elucidation of the
fundamental processes that occur within.  The result is an expectation
value which is an overall time average for the entire system.

A review of stochastic models used in hydrology has been presented by
Scheidegger (1970).  Investigations of growth and steady state phenomena
in hydrology have revealed that essentially two types of growth models
and one steady state model are possible.  The first two are the cyclic
growth model and the random configuration model,and the third is re-
stricted to a Gaussian type with or without autocorrelation.  The hazard
of extrapolating beyond the time range over which the measurements have
been made was examined.

Upton  (1970) presented a stochastic model for water quality management
under uncertainty, where the variance of stream flow was considered.
Analysis has shown that problems of uncertainty may be dealt with by
selecting a critical value of stream flow and then treating the pollutants
sufficiently to maintain the desired water quality standard.  The economics
of the system was also considered.

These models are concerned with stream flow, but the methods of approach
could be used to study the hydrology of irrigation return flow systems.
Although the results obtained using these models may closely approximate
the measured values, little is learned about the individual processes
within the system.  For salinity control within an irrigation system,
the effect of these processes must be known in order to develop management
practices which will control their effect.  The salinity levels of return
flows are not stochastic in nature in that they do not grow or decay
with time.

Deterministic models, on the other hand, consider the individual
processes within the system and their interaction.  This approach leads
                                   11

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to a clear definition of each process and its contribution to  the system
as a whole.  In deterministic theory, the correct prediction will simply
state the value of the observable result that will be obtained.  The
accuracy of the prediction depends on how well the model represents the
components of the physical system.  Leeds (1970) has described a general
characteristic of a "good" mathematical model as the simplest model that
will adequately describe the real world.  For systems with both spatial
and temporal effects of importance, partial differential equations must
be used to describe the system.

Modeling hydrological systems in general and irrigation systems in par-
ticular has been primarily deterministic in nature.  The model may be a
materials balance type which will account for the material mass transfer
through the system.  The individual processes which contribute to the
quality of the return flows have been studied in depth and will be
presented separately in this review to facilitate development of an
overall model.

Since the flow of salts in the system is directly linked to the flow of
water, prediction of the latter is a necessary part of any prediction
model for salinity.  Following the format set forth previously, prediction
models for water and salt flows will be discussed for surface flows,
followed by a more detailed treatment of deep percolation.

                              Surface Flow

The occurrence and magnitude of surface flows or runoff are affected by
the slope and condition of the surface, antecedent soil moisture content,
infiltration rate, intensity of precipitation or rate of irrigation applied,
vegetative cover, and management practices.  In irrigation systems, sur-
face return flow can be measured and controlled such that prediction of
runoff volume is not a difficult task.  However, for natural precipitation
and ungaged watersheds , prediction techniques are needed to assess the
quantity and quality of surface return flows .

Knisel et^ al. (1969) have elaborated on the model developed by Hartman
et^ aJ^. (I960) to predict runoff volume from daily climatic data.  The
general equation developed for runoff computation is
                     Q = [P(P - P^] / [1/b + (P - P^]              (1)

where Q is the daily runoff volume in inches over the watershed, P is
the daily rainfall in inches over the watershed.  PI is the inches of
rainfall before runoff begins, and b is an empirical constant.  Both
P. and b are functions of available soil moisture.  The accumulation of
moisture in the profile is given by P - Q.  Moisture loss was determined
by the decay type function
                               SM^ = SM Kfc                           (2)
                                 t     o
                                  12

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where SM  Is the soil moisture  at  time,  t;  SM  is the soil moisture at
some initial time,  t ;  and K is the dissipation rate and is a function
of available soil moisture  ,  pan evaporation, and season.   For a reservoir
of soil water defined as  the top three feet of the soil profile, the
dissipation rate is given by the expression

                          K = cQ +  c-jSM + c2PE                        (3)

where SM  is the inches  of available soil moisture in the top three feet;
PE is the average daily open pan evaporation in inches; and cn,  c, , c~
are empirically determined  constants for each season.   The major weakness
of this model is in predicting  the soil  moisture at the beginning of
rainfall.  Greatest errors  in prediction occurred during periods of
extremely high or extremely  low soil moisture levels.

The model was revised to  include a second soil moisture reservoir
(3-5  feet) and equation (2)  was modified as follows

                             SMt =  SMQ -  Ct                           (4)

Where C is a  constant depending on values of K.  The revised runoff
model was tested with data  for  an  11-year period on a native grass-
meadow watershed.   Good agreement  between measured and calculated results
was  found, indicating a valid model.  Accumulated computed amounts for
the  period agreed within  1%  of  the accumulated observed amounts.

Since there is only slight  increase in salinity in surface waters due
to overland flow,  the concentration of salinity in surface return flow
can  be estimated from the concentration  of the applied irrigation water
and  the amount of measured  or predicted  runoff.  This  can be represented
by the equation

                                 SL = QC±                             (5)

where SL  is the salt load in the runoff  water, Q is the daily runoff
volume, and C. is  the concentration of salts in the applied irrigation
water.  In areas where  infiltration rates are low and water must be
ponded for extended periods  to  allow sufficient penetration, equation
 (5)  may be modified as  follows

                        SL  = Q(C±  + ACE  + ACg)                       (6)

where AC,., and AC   are changes in concentration due to the evaporation
of water  and  dissolution  of  salts  on the soil surface respectively.
These changes would be  difficult to quantify since they would be time
variant while infiltration  is taking place.  AC_, would be a function of
time,  evaporation  rate, and infiltration rate; and AC  would be  a
function  of time, solubility rate, and infiltration rate.   The
                                 13

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contribution of these components would need to be determined for each
particular location and condition.  As a first approximation, equation
(5) can be used without great error in most irrigated regions.

Hyatt et_ al. (1970) estimated surface runoff rates, Qr, by difference
between total rate at which water is diverted from the stream or reser-
voir, Wtr, and the rate at which diverted water enters the soil through
seepage and infiltration, W^, as given by

                          Q  -Of   - W. ) .                        (7)
                          %r     tr    dr
Evapotranspiration losses are included in the W^ term and are accounted
for elsewhere in the overall system model.  Salt carried in the surface
flow can then be estimated by the relationship

                              SQ = Q C                             (8)
                               r   xr s
where S^ is the rate of salt flow from the area, and Cg is the average
water salinity level of the surface flow.

                           Subsurface glow

Mechanics of Water Movement in Soil Systems

The mechanics of flow of water through soil systems has been intensively
studied in the quest for understanding the fundamental physical and
chemical processes affecting the flow behavior of water.  Comprehen-
sive treatises on this subject are given in the books Physical
Principles of Water Percolation and Seepage by Bear, Zaslavsky, and
Irmay; and Soil Water prepared by the Western Regional Research Technical
Committee, W-68, Water Movement in Soils.  Since salt movement through
soil depends upon water as a solvent and vehicle of transport, an under-
standing of the behavior of water flow is tantamount to any study of
salt movement through soils.

Movement of water through soils has generally been described by the
Darcy equation given by

                           Q/At = -K d$/dS                         (9)

where Q is the quantity of flow through a cross-sectional area, A, in
time t; K is the hydraulic conductivity, and d$/d2 is the potential
gradient acting across the system.  In describing steady flow, equation
(9) is strictly valid only when K is independent of time, space,
direction, pressure, flux, hydraulic gradient, and length of flow path.
These assumptions are rarely met in natural soil systems, since K is
known to be a function of water content.  For a saturated soil, however,
K may be considered to be a constant and the equation used to describe
saturated flow.
                                 14

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Using the principle of conservation  of mass  and  the Darcy  equation,  an
equation describing water movement in a partially  saturated  soil  is
given by

                             30    3  3¥    9K
                             W =  3F + 32

where 0 is the volumetric water content, t is time, ¥  is the soil mois-
ture potential, 8 is depth,  and K is the soil water conductivity.  The
effects of hysteresis on ¥(0) and K(0) relationships can be  accounted
for.

Recently, researchers have used numerical  methods  to solve this equation
to predict moisture movement in soils.  Staple (1969)  using  an explicit
finite difference form of equation  (10) computed the expected redistri-
bution of soil moisture following a  period of infiltration.   Agreement
between measured and computed moisture profiles  was  considered satis-
factory.  The computational  procedure required assessing the values  for
conductivity and diffusivity from the ¥ vs.  0 relationships.  Rubin
 (1967, 1968) used implicit finite difference solutions to  equation  (10)
to study redistribution and  transient flow of water in soils.  His work
shows the importance of hysteresis in the  redistribution process.

Wang and Lakshminayana  (1968) developed a  numerical technique to  solve
equation  (10) for the case of unsaturated  nonhomogenous soils.  This
is the situation most prevalent in natural soils in the zone of aeration.
This technique is of more general use since  idealized  soil conditions
are not a requisite for this solution.  The  simulated  moisture profiles
were in excellent agreement  with  the experimental  data of  Nielsen et al.
 (1964).

Hanks e£ al.   (1969) described a  numeric method  for estimating infiltra-
tion, redistribution, drainage, and  evaporation  of water from soil.  The
computed results were compared with  measured values and found to  ade-
quately predict the soil moisture behavior.   Limitations caused by
natural variability of soils are  recognized  by the authors.

Black et  al.   (1969) applied a simplified  flow theory  to both evaporation
and drainage processes and were able to predict  water  storage in  the soil
profile.  Using daily rainfall data, the water storage in  the upper  150 cm
of the profile was predicted over the season to  within 0.3 cm.  The
authors emphasized that evaporation  from the finer textured  soils may
not be described as well as  for the  soil used in this  experiment  and that
layered soils may require special treatment.   However, for the soil
studied, good agreement was  found between  predicted and measured  evapora-
tion, drainage, and storage.
                                    15

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Freeze (1969, 1970) examined the mechanism of natural groundwater recharge
and discharge for a one-dimensional, vertical, unsteady, unsaturated flow
above a recharging or discharging groundwater flow system.  The flow was
simulated with a numerical mathematical model involving transient flow.
The model was verified using both laboratory and field data.  The mathe-
matical model was derived from Darcy's equation and considered both the
unsaturated and saturated zone of the soil profile.  The parameters which
controlled the integrated saturated-unsaturated flow system were found
to be:  the rate and duration of rainfall or evaporation at the upper
boundary; the groundwater recharge or discharge rate; the antecedent soil
moisture conditions and water-table depth; the allowable depth of ponding;
and the hydrological properties of the soil.  It was also concluded that
soil moisture conditions, in general, and evaporation and infiltration
rates, in particular, show areal variations, even under homogeneous
meteorological conditions and soil type due to the influence of areal
variations in the rates of groundwater recharge and discharge.

Bhuiyan et al. (1971a,b) used dynamic simulation language to develop a
computer model that simulated the vertical infiltration of water into
unsaturated soil from both surface and subsurface sources.  The net water
flux through each layer, at any particular time, was established by using
the principles of conservation of mass and Darcy's law.  The water con-
tent and cumulative infiltration was then calculated using a fourth order
Runge-Kutta integration method.  Results obtained compared favorably with
those of Philip (1957a,b) and field data of Nielsen et al. (1961) obtained
for Yolo light clay with surface application of water.  The principle
advantage of the numerical procedure is its complete generality and the
ease with which numerical data on the hydraulic characteristics of the
soil may be used without arbitrary assumptions or function-fitting pro-
cedures.  Water distribution efficiency can be evaluated for subsurface
irrigation systems.

Many other excellent research papers are available where the movement of
soil water has been studied with a variety of imposed conditions and
assumptions, allowing simplified mathematical solutions to be made.  The
description of soil water movement can be considered to be in an advanced
state of development.

Mechanics of Salt Movement in Soil Systems

The movement of salt through the soil profile is affected by many
physico-chemical reactions.  Among these are ion exchange, ion exclusion,
precipitation, and dissolution.  In an irrigated soil system where a
salt balance is maintained, some degree of equilibrium must be obtained
to avoid degeneration of the productivity of the soil.
                                   16

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Under steady-state water flow rates in  an irrigated  area,  the  salt
balance is given by


                         ViCi + Sm - VdCd - Sp  - Sc  =  °
where V. and V, are the volumes of irrigation and drainage waters,
respectively, with corresponding salt concentrations C. and  C,; S  is
the amount of salts dissolved from soil materials; S  is the amount of
salts added to the soil by precipitation from the irrigation water; and
S  is the amount of salt removed by crops.  To  maintain viable agriculture
in an irrigated area, a favorable salt  balance  must  exist  at least in
the root zone of the soil.  This concept has been in use since developed
by Scofield (1940).

Bresler (1967) modeled salt flow through soils  using a salt  balance
relationship applied to individual layers in the soil  profile.

The basic relationship is given by

                    VC - VdCd - S  =  (C1* - CQ*) 6AX              (12)

where V is the depth of irrigation water applied;

      C is the salt concentration in  the irrigation  water;

      AX is the depth of the relevant soil layer;

      V, is the depth of water leached  from AX;

      C, is the salt concentration of drainage  water;

      S  is the amount of salt absorbed by plants per  unit area of soil;
       P
      9 is the volumetric water content;

      Cn* is the initial average salt concentration  in the soil solution
          at water content 6; and

      C1 * is the average salt concentration in  soil  solution at moisture
          content 6 after irrigation water is applied.

To estimate V, and C,, it was assumed that:  (a) the  movement of salt was
with the mass of flowing water and in the downward direction only; (b)
water and salt movement takes place at  moisture content 6  and  that 0
remains relatively constant for the period of movement; (c)  the average
salt concentration of the water which leaches out is the arithmetic
mean of the salt concentration before and after irrigation;  and (d) the
salts are noninteracting.  These assumptions are  clearly not met in the
                                   17

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field; however, the predicted salt distributions in the soil profile
agreed with measured values in direction of change, if not in magnitude.

Bresler and Hanks (1969) developed a model to handle simultaneous flow
of salt and water in a soil system.  For one-dimensional flow, and
neglecting such factors as flow induced anisotropy, the distribution of
pore velocities, and diffusion, the rate of flow of salt is given by

                   [dQ/dt]  - [-D (dC/dx) + V8C + S]                (13)
                          x      p                  x

where Q is the amount of a solute transferred per unit area;

      t is time;

      D  is the effective dispersion coefficient of the solute;

      x is distance in direction of flow;

      V is the average velocity of the solution;

      9 is the volumetric water content;

      C is the concentration of solute; and

      S is the rate of change with time of solute per unit area due to
        all sinks and sources.

By assuming that no sources or sinks exist and that D (dC/dx) « V9C,
equation (13) reduces to                             "

                           [dQ/dt] = [V C] .                        (14)
                                  Xf       A
Equation (14) can be solved by a finite difference scheme.

Comparison of computed with measured data indicated that the source-
sink term, S, should not be omitted.  The procedure gave good agreement
for non-interacting solute in soil.  No accounting was made for evapo-
transpiration losses of moisture or for interacting salts in exchange
reactions or solution-dissolution reactions.  The effects of dispersion
were also neglected but may in some instances become significant.

Hyatt et al. (1970) expressed the deep percolation rate as

                     G  = F  - ET , [M (t) = M  ]
  j                   r    r     r    s       cs                    ,,...
and                                                                 (15)
                         G  = 0, [M (t) < M  ]
                          r    '   s       cs
                                 18

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where 6r is the rate of deep percolation;

      Fr is the rate of infiltration;

      ET  is the actual rate of evaporation;

      Mg(t) is the quantity of water available  for  plant  consumption
        which is stored in the root zone at any instant of  time; and

      M   is the root zone storage capacity of  water  available  to plants.
       Co

The assumption was made that deep percolation occurs  only when  the
available soil moisture is at its capacity level.   No serious error
resulted from this assumption, probably due to  the  fact that most of
the percolation takes place shortly after irrigation  application when
the zone of transmission  is near saturation.  It was  recognized, however,
that percolation continues slowly in partially  saturated  soils.
The flow of salt in this  system would  then be  given by

               S? - tFr - ETcrlCga  = GrCga'  &B™ ' Mcs^
                                                                    (16)

                          Sj =  0,  [MB(t)  < Mcg]
       P
where  S£ is the rate of salt flow from the plant  root zone;

       Cga is the average  salinity concentration within  the soil solution
          at the lower boundary of  the plant root zone;

       ET r is the potential evapotranspiration rate; and

           all other terms are  as previously defined.

This procedure does not account for the individual ion  species and  thus
does not take into consideration changes  in the ion composition of  the
drainage water and resident soil solution.

Lai (1970) considered ion exchange  reactions in a study of salt transport
through soil undergoing miscible displacement.  A model was developed
which  allows prediction of both the solution and  exchanger phase con-
centration of the cation  in question.   Using both implicit and explicit
finite difference techniques, the flow equation was solved considering
exchange reactions.  The  predicted  concentration  distributions gave
good agreement with the measured values.  Non-linear exchange isotherms
were found for both Mg -»•  Ca and Na  -»• Ca systems.  The flow equation,
modified to consider exchange reactions,  is given by
                                   19

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                                                                    C17)


where D is the dispersion coefficient;

      X is the concentration of an individual ion species;

      Z is the distance in direction of flow;

      V" is the average interstitial flow velocity;

      p is the bulk density;

      Q is the cation exchange capacity per unit weight of exchanger;

      a is the pore fraction;

      CQ is the total cation concentration; and

      f! is the slope of the adsorption isotherm.

This model requires assessment of the exchange properties of the soil
and of the flow behavior.  For application to a field situation, the
spatial variation of exchange and flow properties would need to be
evaluated.

Alfaro and Keller (1970) used dimensional analysis to treat a model for
predicting the process of leaching.  The prediction model was verified
for both layered and non-layered soils using physically scaled models.
The use of scaled models to predict leaching from the prototype requires
exact scaling of the soil profile since the accuracy of the prediction
depends upon the closeness by which the prototypes represent the real
world.

Oster and McNeal (1971) have presented three mathematical models which
predict the change in soil solution composition and electrical conduc-
tivity as water content is changed by evaporation or extraction by
plants.  Two of the models included consideration of precipitation of
salts, bicarbonate and carbonate ion pairs of calcium, sodium, and
magnesium, and partial pressure of carbon dioxide.  The third model was
similar but considered only the ion pair calcium sulfate.  The reliabili-
ity of the models was evaluated by comparing calculated electrical
conductivities to those measured with in situ salinity sensors.  The
best model considered the maximum number of ion pairs and used a form
of the Debye-Hiickel equation with individual ion parameters.  This
model resulted in an average error of about 6% when compared to the
average measured value.
                                 20

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Sadler et al. (1965) tested miscible displacement  theory  in a  field exper-
iment designed to study reclamation of  saline  soil.  They concluded that
both hydrodynamic dispersion and  ionic  diffusion contributed salt  to the
effluent that was measured and analyzed during this experiment.  Velocity
flow was most probably responsible for  the bulk of the chlorides removed
from the soil adjacent to the centerline of  the drain.  Diffusion  was of
increasing importance in removing salt  from  the soil more distant  from
the drain.  They indicated a need for further  development of miscible
displacement theory for two-dimensional cases.  However,  it was found
that if proper account was taken  of the two-dimensional nature of  the
field leaching studies, miscible  displacement  theory gives a qualitative
explanation of several observed results.

Simultaneous solute and water transfer  for an  unsaturated soil was exam-
ined by Warrick et al. (1971).  The simultaneous transfer of solute and
water during infiltration was studied both in  the  field and numerically.
The advance of a solute front introduced as  irrigation water was shown
to be nearly independent of the initial soil moisture content, but
highly dependent upon the moisture content maintained at  the soil  surface
during infiltration.  Field results showed that the displacement of
chloride applied in irrigation water and leached with additional chloride-
free water can be quantatively predicted by  linking the equations  of
solute and water movement through an unsaturated soil.  The numerical
simulation provides an examination of the influence of soil moisture on
solute transfer during infiltration.

Dutt  (1962a,b, 1964) and Dutt et_  al.  (1962,  1963)  studied the  effects of
changes in the ionic composition  of percolating irrigation waters.  Begin-
ning with simple models for water percolating  through soil containing
gypsum and exchangeable Ca*"1" and  Mg"^,  computer programs  were  developed
to predict the quality of the percolating water.   The procedure for
making these predictions assumes  that the total activity  coefficient of
the ionic species in the soil solution  can be  calculated  by the Debye-
Hiickel theory.  Predictions made  in this manner were found to  be within
the experimental error of measured values found for soil  systems con-
taining Ca4^, Mg^, Na+, 80*-"-, Cl~, and CaS04'2H20 at saturation
moisture content.  Some deviation from  the predicted values was expected
since the constants used were developed from solution chemistry and do
not consider the effects of the interacting  clay surfaces.  Dutt and
Anderson  (1965) found that the soil solution does  not differ greatly
from true solution for a range of 15-33 percent gravimetric moisture
content.  This was determined by  electrical  conductance methods using
both true solutions and soil solutions.

Tanji e£ al. (1967a) developed a  computer method to predict the salt
concentration in soils at variable moisture  contents.  The calculations
were based on ionic activities, solubility product constant of CaS04'2H20
                                    21

-------
 (gypsum), dissociation constant of CaSO/, and cation-exchange equations.
Five agricultural soils were used to test the procedure and excellent
agreement was found between predicted and experimental values for  all
ions examined.

Precipitation of CaCO, resulting from high bicarbonate water has been
examined by Tanji and Doneen (1966).  The overall reaction for precipita-
tion of CaC(>3 in an open system is

                   Ca++ + 2HC03~ $ CaC03+ + C02* + H20             (18)

This reaction proceeds stepwise through several equilibria stages.  Using
Debye-Htickel theory and ionization constants from solution theory, the
authors developed a computer prediction model which gave excellent agree-
ment with measured values.  Precipitation reactions were important in
solution composition changes which may lead to increased sodium levels
in the soil profile.

Stratified soils present a special problem in predicting the quality of
the percolating water.  The complexity of flow due to changes in hydraulic
and mineralogical properties from layer to layer are difficult to model.
Tanji et al. (1967b) developed two computer models to predict chemical
changes in percolating water due to stratified soils.  The first program
predicts the chemical changes induced by saturation of an initially
moist stratified profile and the second program predicts the solute con-
centration in the effluent from the stratified profile as percolation
occurs, and the subsequent changes in chemical properties of the soil
profile.  These programs have been verified by laboratory studies of
a two-layered, salinized, gypsiferous soil model.  The above procedure
may be extended and modified to include additional variables, reactions,
and more complex conditions.  This is exemplified by Tanji (1970) where
the approach was used to predict the leaching of boron from stratified
soil columns.  A Langmuir adsorption isotherm was assumed and predicted
results were in good agreement with experimental values.

Tanji and Biggar (1972) developed a specific conductance model for
natural waters and soil solutions of limited salinity levels.  They
point out that specific conductance (electrical conductivity) is one of
the most widely used parameters monitored to estimate the salinity of
water and soils, thus it is appropriate to develop a model with this
parameter.  One disadvantage of specific conductance as a measure of
salinity is that it is a measure of only the ionic activity of the
solute species and thus may underestimate the analytically determined
salt concentration.  This would be of particular importance when ion
association or ion-pairing is prominent.

The model estimates temperature-dependent conductance from measured or
predicted solution composition in water and soil solutions.  The specific
                                   22

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conductance in multicomponent aqueous  systems  is  given by

                               n       n
                           L = I   JL, « Z' A..CJ                      (19)
                              1=1  x   i=1 11


where L is the conductance in micromhos/cm,  and £j,  AJ,  and  Ci  are,  respec-
tively, the ionic specific conductance in micromhos/cm,  ionic equivalent
conductance in cm2/equiv-ohm, and concentration in meq./liter for  the
ith solute species.  The term A£  may be related to concentration by  the
equation

                             X± = Xj - aCj/2                      (20)

where x9 is the ionic equivalent  conductance of the  ith ion  species  at
infinite dilution in cnr/equiv-ohm, and the  coefficient,  a,  is  an
adjustable empirical coefficient  for salt concentration and  ion associa-
tion effects.

Equations (19) and  (20) are applicable at a  reference  temperature,
usually 25°C.  Variations caused  by temperatures  other than  the reference
may be expressed by

                       LT = L25 + 0.02(T  - 25)L25                 (21)

where LT and L£5 are the specific conductances at some temperature T
and at 25°C, respectively.

This conductance model was tested on representative  river waters and
soil solution extracts from the Western United States.   Over a  limited
salt concentration range, the conductance was  predicted satisfactorily
by the model.  For high salt concentrations, the  coefficients must be
adjusted to obtain a good fit.  The model has  been described by the
authors as a compromise between analytical and empirical approaches.

                               System  Flow

In an assessment of the characteristics and  pollution  problems  of  irri-
gation return flow, the Utah State University  Foundation (1969) described
both the quantity and quality of  irrigation  return flow as dependent
variables, with the soil and soil moisture playing important roles in
the functional relationship.  The quality of irrigation return  flow
                                   23

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can be described as:

               IRFq = f(Qig, Cgq, Bq, Ta, Ma, Smq, Scc, ET,


                      V V V F*' Pa' Cf V

where IRF  is the irrigation return flow quality;
         q
      Q.  is the quality and quantity aspects of applied irrigation water;

      Csq is the canal seepage quality change;

      Bq is the bypass water quality;

      TQ is the time of application;
       3.

      Ma is the method and rate of application;

      Smq is the soil moisture quality;

      Scc represents the additional soil characteristics such as cation
          exchange capacity, basic soil compounds, bacteriological activity,
          chelation, fixation, oxidation, and other factors which may
          alter the soil-chemistry-bacteria-water system;

      ET is the evapotranspiration;

      D   is the quality of water percolating below the root zone;

      C_ is the crop influence on quality;

      Fpq is the farm practice effect on quality;

      FQ is the fertilizer application;
       a,

      P  is the pesticide application;

      Cf is the climatological factors; i.e., temperature, precipitation,
         wind, radiation, etc.; and

      Q± is other influences; i.e., elements carried from the air to the
         farm land, by precipitation, industrial pollution of soils and
         water, municipal inputs from runoff or sewage, etc.

The intricate nature of the soil-water quality complex makes prediction
of return flow quality variables very difficult.  Equation (22) indicates
the complexity of the system and the possibility of interactions among
the variables which combine to effect a given quality in irrigation return
flows.
                                   24

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A general model which will  simulate  the water quality in irrigation  sys-
tems is needed for planning and maintenance of viable irrigated  agricul-
tural areas.  Such a model  should  include all the identifiable subsets
or units which contribute to the water quality behavior  of  the system as
a whole.  This would result in a systemized approach for predicting  the
quality response  of this system of units to changes  in irrigation practices.

Or lob and Woods  (1967)  have presented such a model where an idealized
hydrological  "unit" is  composed of three basic storage elements — surface,
soil moisture, and groundwater — between which water  is transferred either
according to  operational plan or in  accord with physical relationships.
For each of the  storage elements in  the system it is possible to write a
continuity equation such that


                                 f - SQ                          (23)

where S is She total stored water, Q is the flow into or out of  the  unit
by any mechanism, and  t is  time.

The storage elements are given by  the following equations.

Surface water:


                   <*ci  - Qco + Qs + Qg - Qd + Qi - Qp + Pf - E      (24)
 Soil Moisture:


                   3F1 ' Qsi - Qs + Qd + Qr - u + p ~ QV           (25)

 Groundwater :
 where the subscripts c, g, and s refer to surface, ground, and soil water
 storage elements, respectively; i and o refer to inflow and outflow from
 the element;  d refers to diversion for irrigation use; p denotes extrac-
 tions from surface water element for export to other units; v denotes
 vertical flow; r denotes recirculation; P1 denotes precipitation onto a
 free water surface, P denotes precipitation on a land element; E denotes
 evaporation from a surface element; and U denotes evapotranspiration from
 a land element.  A sketch of this hydrologic model is given in Figure 2.

 Changes in water quality in an irrigation system are closely related to
 the hydrologic behavior of that system.  A water quality model which has
                                    25

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Qgi
                  Hydrologic Model
             Water   Quality    Model
         FIGURE 2.  HYDROLOGIC AND WATER QUALITY MODELS
                            26

-------
the same storage elements as  the hydrologic model  can be used.  The amount
of salt in a given element is given by  the product of the  storage quan-
tity and the concentration of salt in that element.  The flow of a salt
ion from one element to another might be at a rate defined by

                               fx " qXKxCx                        (27)
where q  is the flow from  the hydrologic model, Cx  is the concentration
of a salt species, and K^  is the distribution coefficient.  Each of these
quantities may be space and time dependent  in the system.  The total flow
of salt in an element would be  given by


                                F -  Z  f                           (28)
                                   x=l  x

where the subscript x denotes the particular ion specie.  The water qual-
ity model is shown in Figure 2.  Subscripts are the same as for the
hydrologic model except a  and e which represent salt additions or removal
from an element respectively.

Such a combined hydrologic-salinity model facilitates inclusion of the
individual processes which contribute to salinity flow in the system.
Sensitivity analysis on these individual processes  can result in know-
ledge of the relative contribution made by  each process to the system
as a whole.  Such knowledge is  necessary to make efficient management
decisions and to develop control measures which would lead to reducing
the salinity level of the  return flow.

Dixon and Hendricks  (1970) considered the spatial and temporal changes
in water quality within a  hydrologic unit.  A water quality simulation
model was developed in conjunction with a hydrologic simulation model
and verified with actual field  data from a  prototype system.  Dissolved
oxygen concentration, biochemical oxygen demand, temperature, and dis«
solved mineral concentration were selected  as the water quality parameters
to be measured.  The simulation submodel for each water quality param-
eter has an input phase and an  in- transit phase.  The input phase simu-
lates the time distribution of  the quality  parameters in each component
of flow, while the in-transit phase deals with changes in the water
quality parameters as it is carried through the reach being simulated.

In irrigated agriculture,  dissolved mineral concentration (salinity) is
an important measure of water quality.  Because salinity, and thus
specific electrical conductance, is not subject to  dissipation or decom-
position, no in-transit phase model need be developed.  The conductivity
of the outflow from the reach is the sum of the conductivities and flows
of the input streams. Assuming  complete mixing, the conductivity of the
                                   27

-------
combined flows is calculated by
                           n             n
                     ECI = 2 EC   •  q./ S q.                      (29)
where ECI is the conductivity of the combined flows; EC, is the conduc-
tivity of the jth hydrologic input stream; q. is the rate of flow for
that input; and n is the number of inputs to the reach being simulated.
Good agreement was found between measured and simulated values for the
parameters studied.

Margheim (1967) studied some of the major factors which affect the qual-
ity of irrigation return flows and expressed them in mathematical forms
which could be fitted into an overall computer program to predict the
quality of the return flows.  The four-phase system is composed of (1)
a solution phase, (2) an exchange phase, (3) a crystalline salt phase,
and (4) a groundwater-deep percolation phase.  Consideration of exchange
phase-solution phase and crystalline salt phase-solution phase relation-
ships was in the form of an extension of the theory developed by Dutt
(1962).  The groundwater-deep percolation phase submodel was developed
using Maasland's (1965) data.  This allowed determination of the fraction
of the flow which is groundwater at any given time.  The concentration
of effluent from the groundwater aquifer was determined by the equation

                     Ct = C1 + f (C2 - C^                         (30)

where C.  is the effluent concentration at any given time in ppm; C^ is
the concentration of the recharge water at any given time in ppm; G£ is
the concentration of the groundwater in ppm; and f is the fraction of
flow which is groundwater at any given time.

The method used to calculate the volume of the return flow was developed
by Glover (1960) and later used by Hurley (1961, 1968).  With the hydro-
logic characteristics of the system known, i.e., the coefficient of
permeability, k, in feet per second; the effective porosity, n; the
original saturated depth, D, in feet; and the half spacing between drains,
L, in feet; then the fraction of the original volume returned (1-P) to
the drain, in time t, is given by
            (1-P) = 1 -  Z     ~Y-    exp   "m "^   ;  m-1,3,5,7.. (31)
                         m=l   mil              4L n

where P is the fraction of original volume of water remaining in transient
storage.  Using data from Dutt's (1962) column studies the computer  program
developed gave good agreement between theoretical and experimental results.
                                  28

-------
The deviation present was attributed to  evaporation losses.   The  effects
of continuous versus intermittent  recharge were  examined.  Glover's
method has been successfully  applied to  field  conditions by  the United
States Bureau of Reclamation  (Hurley,  1968)  and  was found  to be well
suited to areas of known homogeneous aquifer characteristics and  well-
defined uniform drainage patterns.

A hydro-salinity model, Figure  3,  of the Grand Valley  in Colorado was
developed by Walker  (1970) where the various parameters of water  and
salt budgets were examined.   Since the budgets for  the whole of the Grand
Valley are generalized, the model  or budgeting procedure is  simply the
adjustment of the water and salt flows according to a  set  of weighted
data to arrive at a  fair representation  of the area.   The  budgets are
characterized by inflows and  outflows.  The  inflows represent the total
water available for  use within  an  area and the salts carried with this
water.  Outflows represent the  total water leaving  the area  and the salts
carried with it.

Inflow waters may come from rivers,  tributaries,  groundwater, imports,
and precipitation.   Outflows  are in the  form of  evapotranspiration,
river outflow, exports, and groundwater  flowing  under  the  gauging station.
The model consists of a main  program which inputs data to  and controls
subroutines which compute various  parameters of  the water  and salt bud-;
gets .  The subsurface characteristics of the area must be  identified in
sufficient detail to be capable of mathematically describing the  entire
water system and thus detect  errors in surface water flow  estimates.
The time unit in the computations  is on  a monthly basis and  as such
gives a long term average of  the hydraulic conductivities.   This  is
sufficient for the saturated  zone,  however,  can  be  very erroneous in
the unsaturated zone where conductivity  is a strong function of water
content.

Hyatt et al. (1970)  developed a computer simulation model  of the  water
and salinity flow systems within the upper Colorado River  basin using an
analog computer.  The model is  macroscopic in  scale using  monthly time
increments and large space increments and is based  on  fundamental and
logical mathematical representation of the hydrological processes and
routing functions.   The physical processes modeled  are not specific, thus,
the model can be translated to  another hydrologic unit.  The basic con-
cept of the model is the conservation of mass  in the total flow through
the system.  For this study the total flow was divided into  (1) surface
flows,  (2) subsurface flows,  and  (3) groundwater flows.

Mathematical representations  were  developed  for  inflows and  outflows for
each of the three components  of the total flow.   These representatipns
were sensitive to the physical  processes which impinge upon  the components
of flow and require  determination  of the coefficients  and  constants.
                                   29

-------
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j

.,
Ground Water
Inflows
i
i
1
i


Imports
i



Precipitation



<
Phreatophyte
Consumption

i

t t
Exports

i

River
Outflows
* *
Municipal
Uses

FIGURE 3-   CONCEPTUAL DIAGRAM OF GENERALIZED HYDRO-SALINITY MODEL
                            30

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The flow of salts in the system was modeled  similarly  so  that  the influ-
ence of water flow on salt flow could be properly assessed.  This was
accomplished by superimposing  the salinity model  upon  that of  the hydro-
logic model.  The two models are linked by relationships which express
salinity as a function of water flow rate.   Thus,  the  rate of  salt flow
at any point is the product of the water flow rate times  the appropriate
concentration of total dissolved solids at that point  in  the hydrologic
system.  The authors note that additional  research is  needed to relate
the role of irrigation to increased salt loading  within the agricultural
system and point out that physical constants and  coefficients  and water
quality data must be ascertained in order  to adequately verify the model
to the area simulated.  Factors such as irrigation practices,  soil types,
leaching of salts, ion exchange within the soil complex, efficiency of
water use, and other parameters related to the irrigation system, all
require additional investigation to provide  the proper perspective of the
role of agriculture in the salinity flow system.

Comparison of computed and measured water  and salt flows  for the study
areas used shows good agreement, indicating  that  the analog simulation
technique can predict with considerable accuracy  the salinity  level in
the hydrologic system.  Decreasing the time  and space  increments of the
study and better evaluation of the physical  constants  and coefficients
will lead to better agreement  between predicted and measured results.

Thomas et al. (1971) developed a hybrid computer  program  to predict the
water and salt outflow from a  river basin  in which irrigation  was the
major water user.  A chemical  model which  predicted the quality of water
percolated through a soil profile was combined with a'general  hydrologic
model to form a system simulation model.   The chemical model considered
the reactions that occur in the soil, including the exchange of calcium,
magnesium, and sodium ions on  the soil complex, and the dissolution and
precipitation of gypsum and lime.  The chemical model  was developed from
the work of Tanji £t al.  (1967) and Tanji, Doneen, and Paul (1967).  The
chemical composition of the outflow is a function of these chemical pro-
cesses within the soil, plus the blending  of undiverted inflows, evapora-
tion, transpiration, and  the mixing of subsurface return  flows with
groundwater.

The quality of the outflow water was calculated from the  following
relationship
                               n            m
                  Qso Pso. -   Z QS,PS   +  Z QG PG                  (32)
                         J   i-1  X  1J    k-1 k   k

where QS. is amount of water from surface  source  i in  the inflow;

      QG, is amount of water from underground source k in the  outflow;

      Qso is the quantity of surface outflow;
                                    31

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      Pso. is concentration of chemical  constituent  j  in  the outflow;

      PS. . is concentration of chemical  constituent  j  in  QS.;  and

      PG, . is concentration of chemical  constituent  j  in  QG~.

The j subscripts on the quality factors  refer  to  the different ions being
modeled.  The i subscripts refer to the  various sources of surface inflow
and the k subscripts refer to the groundwater  inflow sources.

Six^ommon ions found in western waters, namely calcium CCa++) > magnesium
(Mg""^), sodium (Na+), sulfate CS04=), chloride (Cl~) ,  and bicarbonate
(HCO-j"") were studied.  The total dissolved solids in the  outflow  was
obtained by adding the individual ions.  The overall model operates on
monthly time increments.  In a test using data from  a  portion  of  the
Little Bear River Basin in northern Utah, the model  sucessfully simulated
measured outflows of water and each of the six ions  for a 24-month
period.  Only sodium, which occurred in  small concentrations,  exhibited
significant discrepancies between predicted and observed values.   All
other ions agreed within 10 percent on a weight basis  for the  two-year
period, with correlation coefficients ranging from 0.87 to 0.97.   With
minor adjustment the model can be used in other areas.

A digital computer systems model developed by Dutt et  al. (1970)  describes
the dynamic soil-water system along a vertical flow  line  from  the surface
to a nonfluctuating water table and predicts the  distribution  and concen-
tration of the constituents in the effluent reaching the water table.
The constituents considered were: Ca"1"1", Mg*"1", Na+, NH^+,  S0^=, C03=,
HC03~, Cl~, N03~, CaS04 • 2H20, CaC03, CO(NH2)2,  and Organic-N.   The
processes considered were (1) moisture additions; (2)  evapotranspiration;
(3) nitrogen transformations; (4) changes in solute  concentration of
soil-water due to ion exchange, solubility of gypsum and lime  (CaC03),
and dissociation of certain ion pairs; and (5) nitrogen uptake by crops.
Each major process was calibrated individually and the model was  verified
against cropped lysimeters treated with  15N enriched fertilizers.   The
computer model consists of two programs.  The first  is a moisture flow
program whose output serves as input data to the  second which  is  the
biological and chemical program.  The moisture flow  program uses  a finite
difference method to solve the moisture  flow equation.  The behavior of
inorganic constituents except nitrogen was developed from thermodynamic
considerations.  The behavior of organic and inorganic nitrogen was
developed from statistical treatment of  data found in  the literature.
The model was corrected and verified by  comparing its  predicted output
with observed data from the literature.  Comparison  of computed and
measured data for Ca"*"1", Mg"**, Na+, ammonia and nitrate-nitrogen resulted
in a correlation coefficient of better than 0.97.
                                   32

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                                SECTION VI

    THE ROLE OF PREDICTION MODELING IN IRRIGATION  RETURN  FLOW STUDIES

Irrigation, return flows are  the result of a  multitude  of  natural  flow
phenomena and humanly  controlled management  practices.  The movement of
water and salts in soils  is  influenced by soil  properties such as texture,
bulk density, water content, hydraulic conductivity, and  exchangeable ions,
as well as, soil moisture and  gravitation potentials.   These parameters
may vary considerably  from one location to another within an irrigated
area further complicating the  flow behavior.  The  loss  of water from the
surface by evaporation and from the root zone by plant  transpiration not
only interrupts the flow  behavior  but  also concentrates salts in  the
remaining soil water.  Thus, the characterization  and prediction of the
quality of irrigation  return flow  waters are considerably more difficult
than quantity of water flow, although  the two are  closely related.  Both
are dependent upon a large number  of variables  which may  be interrelated.

Study of such a system composed of many variables  and  interrelationships
dictates the use of systems  analysis techniques whereby the individual,
fundamental processes  occurring within the system  can be  identified and
examined in detail and the degree  of interrelationship  can be assessed.
Each fundamental process  occurring in  the system can be represented by
the process model given in Figure  4.  Associated with  the model are input
variables, internal variables, model parameters, and output variables
which characterize the particular  process being modeled.  The sophistication
of the model depends upon the  completeness of identifying these variables
and parameters as well as formulation  of the mathematical equations which
represent their interrelationships. The accuracy  of the  model output is
dependent upon the accuracy  of the input and internal variables used as
well as the accuracy with which the model parameters and  mathematical
relationships represent the  process being modeled.

Many processes occurring  in  irrigated  agriculture  are  closely related.
Sometimes they share the  same  input or output variables and can be grouped
to show this close association. A conceptual diagram  of  a soil system
submodel, Figure 5, shows the  interrelationship of several process models
which depend upon each other.   The net result of this  soil system submodel
is the combined responses and  interactions of the  individual processes to
the input variables imposed  on the system.  System submodels such as this
can be easily handled  by  digital computer programs which  provide  simul-
taneous output for the individual  process models as well  as the total
system submodel output.   This  capability provides  insight into the cause
and effect relationships  occurring within the system and  individual pro-
cess which are particularly  sensitive  to changes in input variables can
be readily identified.

Several related system submodels may be grouped to form a system  model.
An irrigation systems  model  is presented in  Figure 6 and  is composed of
                                   33

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U)
                 input
               variables
internal
variables
  model
parameters
 output
variables
                                   FIGURE  4.  CONCEPTUAL DIAGRAM OF A PROCESS MODEL

-------
OJ
  Input
Variables
                                  Ion
                                Exchange
                                 Process
                                 Model
                               Dissolution
                              Precipitation
                                 Process
                                  Model
Moisture
Movement
 Process
  Model
                                                           Evapo  -
                                                        Transpiration
                                                           Process
                                                            Model
                                                          Nitrogen
                                                        Transformation
                                                           Process
                                                            Model
  Output
Variables
                           FIGURE 5.  CONCEPTUAL DIAGRAM OF A  SOIL SYSTEM SUBMODEL

-------
GJ
     Input
    Variables
Surface
 Water
 System
Submodel
                         Soil
                       System
                       Submodel
                                                                I
                                                                1.
Conveyance
  System
 Submodel
                        Ground
                         Water
                        System
                       Submodel
Variables
                                      FIGURE 6.  CONCEPTUAL DIAGRAM OF AN IRRIGATION SYSTEM MODEL

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the soil system submodel  given  in  Figure 5  as. well  as  other  system sub-
models which are associated with irrigation systems.   Each of  these
submodels are composed of individual  process models which simulate the
system in question.

Systematic development of a model  in  this manner  facilitates the study
and solution of complex problems which are  concerned with controlling
and abating salinity  levels in  irrigation return  flows.   Since the system
model contains individual process  models, the sensitivity of the pro-
cesses to changes in  input variables  to the model can  be  assessed.  In
managing a system for a desired output, the behavior of an individual
process may need to be identified  and altered in  order to obtain the
desired output.

Field research has long been  the fount of technology development for im-
proved irrigation management  practices.  Methods  have  been developed for
increasing water use  efficiency yet maintaining a desirable  salt balance
in the soil profile.  Depth and spacing of  drain  tiles for proper drain-
age has been extensively  studied and  the theory of  drainage  ±s well
defined.  Movement of water in  unsaturated  soils  has also been well char-
acterized.  While the technology of water management in irrigation systems
has been investigated in  depth, salinity in the return flow  water has not
been studied so thoroughly.

Only recently has field research been directed  toward  improving the quality
of drainage or return flow waters. These studies have shown that control
and improvement of salinity levels in irrigation  return flows is techno-
logically feasible.   Subsurface application, scientific irrigation sched-
uling, and proper drainage offer means of reducing  salinity  levels while
maximizing yields.  Growers are not likely  to use these techniques, how-
ever, unless they can be  shown  that the improved  methods  are indeed
advantageous to them. Demonstration  projects have  been designed with
this aim, but the time and expense involved and the variable conditions
from one agricultural area to another prevent widespread  education by
this means.  A rapid, economical means of examining alternatives to pre-
sent management practices is  urgently needed to facilitate implementation
of improved management practices in widespread  areas.

Prediction modeling can provide the means of examining alternative
approaches for control of salinity levels.   Application of systems analysis,
sensitivity analysis, and optimization procedures to irrigation return
flow problems can greatly enhance  understanding the ramification of the
problems as well as provide alternative irrigation  management schemes.
Freedom from the real time frame and  resource outlay of field demonstra-
tion projects allows  rapid, economical evaluation of proposed management
schemes.

On-the-farm water management  has been cited (Skogerboe and Law, 1971)
as perhaps the area of greatest potential for improving salinity levels
                                  37

-------
in return flow waters.  Since changes in current management practices
may not be reflected as immediate changes in the quality of the return
water, expected long term improvements and benefits must be assessed by
prediction techniques.  Knowledge of the manner in which water behaves in
soils has permitted development of prediction techniques for water move-
ment in soil.  These techniques can then be used to estimate the amount
and timing of irrigation applications resulting in increased water use
efficiencies.  Such increases in efficiency lead to better management of
salinity in return flows since excessive leaching can be avoided.

Models which include optimization procedures can predict the best manage-
ment schemes for reducing salinity levels and improving crop yields as
well as simulating water and salinity flow in the system.  Optimization
procedures allow the system to be simulated with constraints on salinity
levels while maximizing crop yields.

The effectiveness of recent developments in methods of application of
irrigation water in reducing or controlling salinity in drainage waters
should be evaluated before they are recommended for widespread use.  The
high cost of installation of subsurface and trickle irrigation systems
may make their use restrictive unless comparable benefits can be shown to
accrue as a result of their installation.  Prediction modeling can be
used to evaluate their usefulness both in reducing salinity in the drain-
age waters and in improving yields as a result of better water management
and increased efficiencies.  Likewise, the effects of irrigation scheduling
on both yield increases and drainage water quality can be assessed.

When the quality of applied irrigation water is marginal with respect to
specific ions or total dissolved solids, models which simulate the quality
changes resulting from ion exchange reactions and ion precipitation-
dissolution reactions in the soil can be of considerable aid in managing
such waters since the probable effects can be determined before their use.
This is especially helpful in managing high sodium and/or high bicarbonate
waters where precipitation of CaCO,. may give rise to increased "sodium
hazard."                          J

Drainage studies have long been made using simulation techniques, how-
ever, only recently have quality aspects been considered from the stand-
point of minimizing salinity in the return flow water.  The salinity
level of drainage water which results from consumptive use, ion exchange,
salt pickup, and mixing phenomena which occur as a result of irrigation
practices can be predicted by models.  In areas where poor drainage has
resulted in high salt levels in the soil profile, planning for subsurface
drains can be enhanced by use of prediction techniques which not only
handle the hydraulics but also the quality aspects of the proposed drain-
age system.  Development of adequate drainage facilities is necessary in
many irrigated areas to maintain a viable agricultural industry.
                                 38

-------
Irrigation return flows often constitute a major portion of summer stream
flows in many western rivers, thus  their management may greatly affect
the river basin system in which they  are located.  In river basins such
as the Colorado where salinity levels  are of prime importance in the
development of new areas and maintenance of present project areas, pre-
diction modeling is a useful tool in  managing  the total water resource
system.  The benefits of salinity control measures implemented in a given
area may accrue to some downstream  users.  If  an equitable sharing of the
expense of upstream improvements in control measures is to be found, then
some mechanism for identifying the  benefits accruing to both areas must
be developed.  Prediction modeling  can be used to assess these quality
improvements and arrive at  an adequate estimate of benefits accrued to
each area.

In the management of a river basin, irrigation may be only one of several
resource uses which are considered  in water resource planning.  The re-
lative importance of quality degradation caused by irrigation return flows
may dictate a shift in water resource uses to  comply with salinity stan-
dards.  To date, most planning of this nature  has relied on seat-of-the-
pants estimates of the salinity contribution that can be attributed to
agriculture.  Definitive prediction models are needed to impact this
level of planning.

In some states, water laws  and water  duties are structured such that they
may be the chief deterrent  to establishing salinity control measures in
those areas.  If institutional changes must be brought about to ensure
success of salinity control measures,  prediction models can be very help-
ful in generating possible  alternatives to present practices.  Subjecting
these potential alternatives to economic analysis by optimization pro-
cedures can result in better insight  to the probable success of the pro-
posed changes.  Changes in  water laws are not  likely to occur unless the
quality benefits of doing so are considerable.  Prediction models used
for this purpose must necessarily be  comprehensive and reliable in
projecting the benefits of  suggested  changes.

Prediction modeling will play an increasingly  important role in water
resource management, especially in  examining alternative approaches to
irrigation management practices and to improved control of salinity in
irrigation return  flows.  These predictive models will impact the legal
and economic  constraints  to improved  management practices.
                                    39

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                           SECTION VII

                        REFERENCES CITED

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     of Leaching," Transactions ASAE 13. pp 362-368  (1970).

 2.   Bear, J.,  Zaslavsky, D., and Irmay, S., Physical Principles of Water
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 3.   Bhuiyan, S. I., Hiler, E. A., van Bavel, C. H. M., and Aston, A. R.,
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11.   Dutt, G. R., "Prediction of the Concentration of Solutes in Soil
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                                  41

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12.  Dutt, G. R., "Effect of Small Amounts of Gypsum in Soils on  the
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13.  Dutt, G. R., and Anderson, W. D., "Effect of Ca-Saturated  Soils on
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14.  Dutt, G. R., and Doneen, L. D.,, "Predicting the Solute Composition
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15.  Dutt, G. R., and Tanji, K. K., "Predicting Concentrations  of Solutes
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16.  Eldridge, E. F., Return Irrigation Water—Characteristics  and  Effects.
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18.  Freeze, R. A.,  and Banner, J., "The Mechanism of Natural Groundwater
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24.  Hyatt, M. L., Riley, J. P., McKee, M. L., and Israelsen, E. L.,
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                                 42

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25.  Knisel, W. G., Jr., Baird, R. W., and Har-tman,M.-A,, "Runoff Volume
     Prediction From Daily Climatic Data," Water Resour. Res. 5, pp 84-94
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26.  Lai, S. H., "Cation Exchange and Transport in Soil Columns Undergoing
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27.  Leeds, J. V,, Jr., "Mathematical Model or "Curve Fit"—Tell It Like
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28.  Maaaland, D. E. L., "Rate of Quality Change of Drain Effluent From
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29.  Margheim, G. A., "Predicting the Quality of Irrigation Return Flows,"
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30.  Nielsen, D. R., Davidson, J. M., Biggar, J. W., and Miller, R. J.,
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31.  Nielsen, D. R., Jackson, R. D., Gary, J. W., and Evans, D. D., (eds.),
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32.  Nielsen, D. R., Kirkham, D., and van Wijk, W. R., "Diffusion
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34.  Oster, J. D., and  McNeal, B. L., "Computation of Soil Solution
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                                  43

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38.  Rubin, J., "Theoretical Analysis of Two-Dimensional, Transient
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     (1971).
                                44

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     Sci. Soc. Amer. Proc. 32, pp 329-334 (1968).

55.  Warrick,  A. W., Biggar, J. W., and Nielsen, D. R., "Simultaneous
     Solute  and Water TRansfer for an  Unsaturated  Soil," Water Resour.
     Res.  7, pp 1216-1225  (1971).
                                 45

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                            SECTION VIII

                        SELECTED BIBLIOGRAPEY

 1.  Alfaro,  J.  F.,  "Distribution of Salts in a Verticle Soil  Profile
    During Leaching," Ph.D. Dissertation, Utah State University Library
    Logan, Utah,  132 pp (1968).

 2.  Biggar,  J.  W.,  and Nielsen, D. R.,  "Diffusion Effects  in  Miscible
    Displacement  Occurring in Saturated and Unsaturated Porous Materials,"
    Jour.  Geophys.  Res. 65, pp 2887-2895 (I960).

 3.  Biggar,  J.  W.,  and Nielsen, D. R,,  "Miscible  Displacement in Porous
    Materials," Jour, of Soil Sci. 12,  pp 188-197 (1961).

 4.  Biggar,  J.  W.,  and Nielsen^ D. R.,  "Miscible  Displacement:  II.
    Behavior of Tracers," Soil Sci. Soc. Amer. Proc. 26, pp 125-128 (1962).

 5.  Biggar,  J.  W.,  and Nielsen, D. R.,  "Some Comments on Molecular
    Diffusion and Hydrodynamic Dispersion in Porous  Media," Jour. Geophys.
    Res. 67, pp 3636-3637 (1962) .                             ~~

 6.  Biggar,  J.  W.,  and Nielsen, D. R.,  "Improved  Leaching  Practices,"
    California Agriculture 16,  5 pp (1962).

 7.  Biggar,  J.  W.,  and Nielsen, D. R.,  "Miscible  Displacement:  V.
    Exchange Processes," Soil Sci. SOC. Amer. Proc.  27,  pp 623-627 (1963).

 8.  Biggar,  J.  W.,  and Nielsen, D. R.,  "Chloride  36  Diffusion During
    Stable and Unstable Flow Through Glass Beads," Soil Sci.  Soc. Amer.
    Proc.  28, pp  591-595 (1964).

 9.  Bondurant,  J. A., "Quality of Surface Irrigation Runoff Water," ASAE
    Paper No. 71-247 presented at the 1971 annual meeting  of  the ASAE,
    Chicago, Illinois (1971).

10.  Bouwer,  H., "Theoretical Aspects of Flow Above the Water  Table in
    Tile Drainage of Shallow Homogeneous Soils,"  Soil Sci. Soc. Amer.
    Proc.  23, pp  260-263 (1959).

11.  Bouwer,  H., "Salt Balance, Irrigation Efficiency, and  Drainage Design,"
    JOur.  Irrigation and Drainage Div.  ASCE 95 (IRl), pp 153-170  (1969).

12.  Bower, C. A., "Prediction of the Effects of Irrigation Waters on
    Soils,"  Proc. UNESCO Arid Zone Symposium, Salinity Problems in Arid
    Zones, Teheran, Iran, pp 215-222 (1961).
                                 47

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13.  Bower, C. A., Ogata, G.,  and Tucker,  J. M., "Sodium Hazard of
     Irrigation Waters as Influenced by Leaching Fraction and by
     Precipitation or Solution of Calcium Carbonate," Soil Sci. 106,
     pp 29-34 (1968).

14.  Bower, C. A., Spencer, J. R., and Weeks, L, 0,,  "Salt and Water
     Balance, Coachella Valley, California," Jour .  of the Irrigation and
     Drainage Div. ASCE 95 (m) , pp 55-64 (1969).
15.  Brady, N. C., Agriculture arid the Quality of Our Environment, AAAS
     Publication 85, Washington, B.C. (1967).

16.  Bresler, E., Kemper, W. D., and Hanks,  R. J., "Infiltration, Redistri-
     bution, and Subsequent Evaporation of Water from Soil as Affected by
     Wetting Rate and Hysteresis," Soil Sci. SOc. Arar^  Proc. 33, pp 832-
     840 (1969).

17.  Brooks, R. H., Goertzen, J. 0., and Bower,  C. A., "Prediction of
     Changes in the Cationic Composition of  the  Soil Solution Upon
     Irrigation with High-Sodium Waters," Soil Sci. Soc. Amer. Proc. 22,
     pp 122-124 (1958).

18.  Carter, D. L., Bondurant, J. A., and Robbins, C. W., "Water-Soluble
     N03~nitrogen, P04 -phosphorus, and Total Salt Balances on a Large
     Irrigation Tract," Soil Sci. Soc. Amer. ;Pfoc. 35, pp 331-335 (1971).

19.  Cunningham, M. B., Haney, P. D., Bendixen,  T. W., and Howard, C. S.,
     "Effect of Irrigation Runoff on Surface Water Supplies,  a Panel
     Discussion," Jour. Amer. Water Works Ass. 45, pp 1159-1178 (1953).

20.  Davidson, J. M., Nielsen, D. R., and Biggar, J. W., "Measurements
     and Description of Water Flow Through Columbia Silt Loam and Hesperia
     Sandy Loam," Hilgardia 34, pp 601-617 (1963).

21.  Day, P. R., and Forsythe, W. M., "Hydrodynamic Dispersion of Solutes
     in the Soil Moisture Stream," Soil Sci. Soc. Amer.  Proc. 21,
     pp 477-480 (1957).

22.  DeCoursey, D. G., "Application of Computer Technology to Hydrologic
     Model Building," In The Use of Analog and Digital Computers in
     Hydrology, IASH/AIHS, UNESCO, Paris, pp 233-239 (1969).

23.  Desai, H., and Raphael, D. L., "A Water Shed Flow Model of Stochastic
     Structure," Proc. Third Annual Amer. Water Resour. Conference,
     November 8-10, pp 59-73 (1967) .   ~~
                                  48

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24.  Dixon, N. P., Hendricks, D. W., Huber, A. L, and Bagley, J. M.,
     Developing a Hydro-Quality Simulation Mcidel. PRWG 67-1, Utah Water
     Research Laboratory, Utah State University, Logan, Utah, 193 pp (1970)

25.  Doneen, L. D., "Salination of  Soil by Salts in the Irrigation Water,"
     Trans. Amer. Geophys. Union 35, pp 943-950  (1954).

26.  Doneen, L. D., (ed.), Proceedings, Symposium on Agricultural Waste
     Waters, Report No.  10, Water Resources Center, University of Cali-
     fornia, Davis (1966).

27.  Doneen, L. D., Effect of Soil  Salinity and Nitrates on Tile Drainage
     in the San Joaquin  Valley of California, Water Science and Engineer-
     ing Papers 4002,  Dept. of Water Science and Engineering, University
     of California, Davis  (1966).

28.  Dyer, K. L., "Unsaturated Flow Phenomena in Panoche Sandy Clay Loam
     as Indicated by  Leaching of Chloride and Nitrate Ions," Soil Sci.
     Soc. Amer. Proc.  29, pp 121-126  (1965).

29.  Dyer, K. L., "Interpretation of Chloride and Nitrate Ion Distribution
     Patterns in Adjacent  Irrigated and Nonirrigated Panoche Soils,"
     Soil Sci. Soc. Amer. Proc.  29, pp 170-176  (1965).

30.  Eldridge, E. F.,  "Irrigation as a Source of Water Pollution," Jour.
     of the Water Poll.  Cont. Fed.  35, pp 614-625  (1963).

31.  El-Swaify,  S. A., and  Swindale, L. D.,  "Effects of Saline Water on
     the Chemical Properties of  Some Tropical Soils," Soil Sci. Soc.
     Amer. Proc.  34,  pp  207-211  (1970).

32.  Franzoy,  C.  E.,  and Tankersley, E. L.,  "Predicting Irrigations
     from  Climatic Data and Soil Parameters," Transactions ASAE 13,
     pp 814-816  (1970).

33.  Gardner, H.  R.,  and Gardner, W.  R.,  "Relation of Water Application
     to Evaporation  and Storage  of  Soil Water,"  Soil  Sci. Soc. Amer.
     Proc.  33, pp 192-196 (1969).

34.  Green, R. E., Hanks,  R.  J.,  and  Larson, W.  E.,  "Estimates of Field
     Infiltration by Numerical  Solutions  of the Moisture  Flow Equation,"
     Soil  Sci.  Soc.  Amer.  Proc.  28, pp 15-19 (1964).

35.  Green, D. W., Dabiri,  H., Weinaug,  C.  F.,  and Prill, R.,  "Numerical
     Modeling of Unsaturated Groundwater  Flow and Comparison of  the Model
     to a.  Field  Experiment," Water Resour.  Res.  6, pp  862-874  (1970).
                                 49

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36.  Grover, B. L.f Campbell,  C. B., and Campbell, M. D., "A Prediction
     Equation for Vegetative.Effects on Water Yield from Watersheds in
     Arid Areas." Soil Sci. Soc. Amer. Proc. 34. pp 669-673 0-970.

37.  Hall, F. R., "Dissolved Solids—Discharge Relationships 1.  Mixing
     Models." Water Resquf. Res. 6,  pp 845-850 G-97Q),

38.  Hargreaves, G. H., "Consumptive Use Derived from Evaporation Pan
     Data," Jour, bf the Irrigation and Drainage Div. ASCE 94 (IRl),
     pp 97-105 (1968).

39.  Hartman, M. A., "Soil Moisture Recounting Under a Permanent Grass
     Cover," Jour. Geophys. Res. 65, pp 355-357 (I960).

40.  Hill, R. A,, "Future Quantity and Quality of Colorado River Water,"
     Jour, irrigation and Drainage Div. ASCE 91 (IRl), pp 17-30 (1965).

41.  Holtman, J. B., "Linear and Non^Linear Application of Mathematical
     Programming," Transactions ASAE 13, pp 854-858 (1970).

42,  Howells, D. H., "Land Use Function in Water Quality Management,"
     Water Resout. Bulliten 7, pp 162-170 (1971).

43.  Hyatt, M. L., Hiley, J. P., and Israelsen, E. K., "Utilization of
     the Analog Computer for Simulating the Salinity Flow System of the
     Upper Colorado River Basin," In the Use of Analog and Digital
     Computers in Hydrology, IASH/AIHS, UNESCO, Paris, pp 101-111 (1969).

44.  Jensen, M. E., Robb, D. C. N.,  and Franzoy, C. E., "Scheduling
     Irrigations Using Climate-Crop-Soil Data," Jour. Irrigation and
     Drainage Div. ASCE 96 (IR1), pp 25-38 (1970).

45.  Johnson, W. R., Ittihadieh, F.  I., and Pillsbury, A. F., "Nitrogen
     and Phosphorous in Tile Drainage Effluent," Soil Sci. Soc. Amer.
     Proc. 29, pp 287-289 (1965).

46.  Keller, J., and Alfaro, J. R.,  "Effect of Water Application Rate
     on Leaching," Soil Sci. 102, pp 107-114 (1966).

47.  Law, J. P., Jr.,  and Bernard, H., "Impact of Agricultural Pollutants
     on Water Users," Transactions ASAE 13, pp 474-478 (1970).

48.  Law, J. P., Jr.,  and Davidson, J. M., and Reed, L. W.,  Degradation
     of Water Quality in Irrigation Return Flow,  Oklahoma State University
     Agricultural Experiment Station, Bulletin B-684 (1970).
                                 50

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49.  Law, J. P., Jr., and Skogerboe,  G. V.,  "Potential  for  Controlling
     Quality of Irrigation Return Flows," Jour. of Environmental
     Quality 1, pp 140-145 (1972) .              ~~

50.  Law, J. P., Jr., and Witherow, J. L., (ed.), Water  Quality Manage-
     ment Problems in Arid Regions, Water Pollution Control Research
     Series 13030 DYY 6/69, USDI-FWQA, 105 pp  (1970).

51.  Law, J. P., Jr., and Witherow, J. L., "Irrigation  Residues," Jour.
     of Soil and Water Conservation 26, pp 54-56  (1971).

52.  Leonard, R. B., Variations  in the Chemical Quality of Groundwater
     Beneath an Irrigated Field,  Cedar Bluff Irrigation District, Kansas,
     Bulletin 1-11, Kansas State Department of Health,  Topeka, Kansas,
     20 pp  (1969).

53.  Leonard, R. B., and Morgan,  C. 0., Application of  Computer Techniques
     to Seepage-Salinity Surveys in Kansas, Special Distribution
     Publication 47, State Geological Survey, University of Kansas,
     Lawrence, Kansas, 44 pp  (1970).

54.  Leonard, R. B., Effect of Irrigation on the  Chemical Quality of
     Low Streamflow Adjacent  to  Cedar Bluff Irrigation  District, Kansas,
     Bulletin 1-10, Kansas State Department of Health,  Topeka, Kansas,
     17 pp  (1969) .

55.  Link,  D. A., and Splinter,  W. E., "Survey of Simulation Techniques
     and Applications to Agricultural Problems,"  Transactions ASAE 13,
     pp  837-843  (1970).

56.  Loeltz, 0. J., and McDonald, C.  C., "Water Consumption in the Lower
     Colorado River Valley,"  Jour, of the Irrigation  and Drainage Div.
     ASCE 95 (IR1), pp 65-78  (1969).

57.  Longenbaugh, R. A., "Mathematical Simulation of  a  Stream-Aquifer
     System," Proc. Third Annual Amer. Water Resour.  Conference, November
     8-10,  pp 74-83  (1967).

58.  Lunt,  0. R.,  (ed.), Proceedings, Agricultural Water Quality Conference
     Water  Resources Center,  University of California held  at Lake
     Arrowhead,  California, August 12-14, 66 pp  (1963).

59.  Meron, A.,  and Ludwig, H. F.,  "Salt Balances in  Groundwater," Jour.
     Sanitary Engineering Div. ASCE  89  (SA3),  pp  41-61  (1963).

60.  McGauhey, P. H., "Quality Changes Through Agricultural Use," In.
     Engineering Management of Water  Quality,  McGraw-Hill Book Co.,
     New York, pp  58-66  (1968).
                                 51

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61.  McGauhey, P. H., Krone, R. B., and Winneberger, J. H., Soil Mantle
     as a Wastewater Treatment System—Review of Literature, SERL
     Report No. 66-7, University of California, Berkeley, 119 pp (1966).

62.  McGauhey, P. H., and Krone, R. B., Soil Mantle as a Wastewater
     Treatment System, Final Report, SERL Report No. 67-11, University
     of California, Berkeley, 201 pp (1967).

63.  Nielsen, D. R., and Biggar, J. W., "Miscible Displacement in Soils:
     I.  Experimental Information," Soil Sci. Soc. Amer. Proc. 25,
     pp 1-5 (1961).

64.  Nielsen, D. R., and Biggar, J. W., "Experimental Consideration of
     Diffusion Analysis in Unsaturated Flow Problems," Soil Sci. Soc.
     Amer. Proc. 26, pp 107-111 (1962).

65.  Nielsen, D. R., and Biggar, J. W., "Miscible Displacement:  III.
     Theoretical Considerations," Soil Sci. Soc. Amer. Proc. 26, pp 216-
     221 (1962).

66.  Nielsen, D. R., and Biggar, J. W., "Miscible Displacement:  IV.
     Mixing in Glass Beads," Soil Sci. Soc. Amer. Proc. 27, pp 10-13
     (1963).

67.  Nielsen, D. R., Biggar, J. W., and Miller, R. J., "Soil Profile
     Studies and Water Management for Salinity Control," California
     Agriculture 18, pp 4-5 (1964).

68.  Nielsen, D. R., and Jackson, R. D., "Changes in Water Quality  During
     Seepage," In Proc., Second Seepage Symposium, Phoenix, Arizona, ARS-
     USDA, pp 41-147 (1968).

69.  Nielsen, D. R., and Vachaud, G., "Infiltration of Water into Vertical
     and Horizontal Soil Columns," J. Indian Soc. of Soil Sci. 13,  pp 15-
     23 (1965).

70.  Ortiz, J., and Luthin, J. N., "Movement of Salts in Ponded Aniso-
     tropic Soils," Jour, of the Irrigation and Drainage Div. ASCE  96
     (IR3), pp 257-264 (1970).

71.  Paul, J. L, Tanji, K. K., and Anderson, W. D., "Estimating Soil
     and Saturation Extract Composition by Computer Method," Soil Sci.
     Soc. Amer. Proc. 30, pp 15-17 (1966).
                                52

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72.  Peterson, H. B., Bishop, A. A., and Law, J. P., Jr., "Problems of
     Pollution of Irrigation Waters in Arid Regions," In Water Quality
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73.  Pillsbury, A. F., (ed.), Watet Resources Center—Annual Report,
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     California, 203 pp (1970).

74.  Pillsbury, A. F., and Blaney, H. F., "Salinity Problems and Manage-
     ment in River System," Jour. Irrigation and Drainage Div. ASCE 92
     (IR1), pp 77-90  (1966).

75.  Rasheed, H. R., King, L.  G., and Keller, J., "Sprinkler Irrigation
     Scheduling Based on Water and Salt Budgets," ASAE paper No. 70-736
     presented at the 1970 winter meeting of the ASAE, Chicago, Illinois,
     (1970) .

76.  Riley, J. P., Chadwick, D. G., and Israelsen, E. K., "Watershed
     Simulation by Electric Analog Computer," In the Use of Analog ancl
     Digital  Computers in Hydrology, IASH/A1HS, UNESCO, Paris, pp 25-37(1969)

77.  Sallam, A. W. M. H., "Leaching and Reclamation Equations for Saline
     Soils," Ph.D. Dissertation, Utah State University, Logan, Utah, (1966).

78.  Scotter, D. R.,  and Raats, P. A. C., "Movement of Salt and Water
     Near Crystalline Salt in  Relatively Dry Soil," Soil Sci. 109,
     pp 170-178  (1970).

79.  Sievers, D. M.,  Lentz, G. L., and Beasley, R. P., "Movement of
     Agricultural Fertilizers  and Organic Insecticides in Surface Runoff,"
     Transactions ASAE 13, pp  323-325  (1970).

80.  Srinilta, S. A., Nielsen, D. R., and Kirkham,  D., "Steady Flow of
     Water  Through a Two-Layer Soil," Water Resour. Res. 5, pp 1053-1063
      (1969) .

81.  Steele,  T.  D.,  "Digital-Computer Applications  in Chemical-Quality
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82.  Sylvester,  R. 0., and Seabloom, R. W., "A Study on the Character
     and Significance of  Irrigation  Return  Flows  in the Yakima River
     Basin,"  Department of Civil Engineering,  University of Washington,
     Pullman  (1962).
                                  53

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83.  Sylvester, R. 0., and Seabloom, R. W., "Quality and Significance
     of Irrigation Return Flow," Jour. Irrigation and Drainage Div.
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84.  Tanji K. K., Hydrochemistry and Computer Programming I.  Electrolytic
     Conductance, Sulfate Ion Association, Cation Activity, and Solubility
     of Gypsum in Aqueous Solutions, Water Science and Engineering Paper
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85.  Tanji, K. K., "Predicting Specific Conductance from Electrolytic
     Properties and Ion Association in Some Aqueous Solutions," Soil
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86.  Tenorio, P. A., Young, R. H. F., Burbank, N. C., Jr., and Lau, L. S.,
     Identification of Irrigation Return Water in the Sub-Surface,
     Phase III, Kahuka, Oahu, and Kahului, and Lahaina, Maui, Water
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87.  Tenorio, P. A., Young, R. H. F., and Whitehead, H. C., Identification
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88.  Terkeltoub, R. W., and Babcock, K. L., "A Simple Method for Predict-
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89.  Texas Water Development Board,  Systems Simulation for Management
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90.  Texas Water Development Board,  Simulation of Water Quality in
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                                 54

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94.  Van Denburgh, A.  S.,  and Feth,  J.  H.,  "Solute Erosion and Chloride
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99.  Willardson, L.  S., and Bishop, A. A., "Analysis of Surface Irrigation
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 * U. S. GOVERNMENT PRINTING OFFICE • 1 973 —514-1 53/232
                                 55

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  SELECTED WATER
  RESOURCES ABSTRACTS
  INPUT TRANSACTION FORM
                    t. .Report No.
               a -cession N
                                        W
  4, Title
  PREDICTION MODELING FOR SALINITY CONTROL IN IRRIGATION
  RETURN FLOWS,
                                        S,. R&pottBsie
                                        4.
                                        8. f.atfarmistg Orgatu&rifoa
  ".  Author(s)

  Hornsbv.  A. G.
  9.  Organization
  United States  Environmental Protection Agency
  Robert S. Kerr Environmental Research  Laboratory
  Ada, Oklahoma
                                        10,  Pro/ectNa.
                                           EPA 13030  GJS
                                        11.  Contract I Graat So.
                                       •it,  Type, ppO&pel* and
                                           Period Covered
  12. Sponsoring'

  15. Supplementary Notes
  Environmental Protection Technology  series
  EPA-R2-73-168
  16. Absttart

  A review of the current state-of-the-art of prediction modeling as applied
  to salinity control in irrigation  return flows is presented.  Prediction
  models  are needed to assess the effects of proposed changes in irrigation
  management practices on the quality  of return flows.  The processes which
  affect  salinity levels in return flows are enumerated and their interactions
  are  alluded to.  Models used  to predict the quantity and quality of return
  flows are  briefly discussed to show  the development of the current level  of
  technology.  The readers are  referred to the original documents for more
  rigid development of the models and  incumbent assumptions.  It was concluded
  that technology of water and  salt  flow in soil systems is sufficiently
  developed  to permit formulation of models using systems analysis to evaluate
  proposed changes in management practices.  Development of systems models  to
  study irrigation return flow  problems and conjunctive water resource  uses
  was  recommended.  A bibliography of  selected references is given in addition
  to the  references cited.
   J7a. Descriptors
   Irrigation systems, surface  flow,  subsurface flow, salt movement,  ion exchange,
   system analysis, water resource management, simulation, evapotranspiration,
   soil physical properties, soil  moisture-


   17b. Identifiers
   17'-. COWRR Field & Group   02 D, E,  F,  G;  04 A, B; 05 B
   IS.  Availability
fc
 t (Mepe^,
   Se'QntyC} «.  i *
                                              , Pages
Send To:
                                                       WATER RESOURCES SCIENTIFIC INFORMATION CENTER
                                                       U.S. DEPARTMENT OF THE INTERIOR
                                                       WASHINGTON. D. C. 2O24O
  Abstractor  A.  G.  Hornsbv
             Inttitutioi.  EPA - RSKERL
• WRSIC 102 (Rev. .(UN

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