VELOCIDAD DEL PROCESAMIENTO DE INFORMACIÓN

4.1 INTRODUCTION

In this chapter we derive and test a model for the transport of salt along a one-dimensional stream connected to an aquifer containing highly saline w aters. As mentioned in the previous chapter, the tran sp o rt of a conservative solute such as salt along a one-dimensional stream can be modelled by the following advection-diffusion equation

where

c is the stream salinity;

u is the averaged cross-sectional velocity; D is a diffusion coefficient;

r denotes the source of salt coming from the groundwater; and r represents all sources or sinks of salt other than r .

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One of the main reasons for developing the solute transport model has been to provide resource management bodies with a mathematical tool that is easy to implement and that can be used to

1) provide a daily estimate of stream salinity c at a fixed downstream location during periods of low to medium flows in response to upstream flows and upstream salt concentration as well as to lateral inflows from

salty aquifers; and

2) quantify the salt load discharged from the aquifer into the stream via an estimation of r in response to stream flow levels.

dc_

dt + u — dc

= -ä-(D (x)A - fr + r (4.1.1)

dx dx gu/

levels of sa lt concentration which if too h ig h are dam aging to irrig atio n activities. Such events usually occur during periods of low to m edium flows since in such cases dilution is low and groundw ater g rad ien ts tow ard th e stream can be high. The second objective re su lts from th e need to assess m an ag em en t strateg ies aim ed a t reducing th e influx of aq u ifer salin ity into the stream .

The sta n d a rd approach for solving a p a rtia l differential equation, such as th e advection-diffusion equation (4.1.1), is to discretize its dom ain of definition and solve the associated set of algebraic equations. In th is thesis, we have chosen to attack the problem from a different angle to deal w ith practical situations where the d a ta base m ay not be sufficient to confidently calibrate a finite difference or finite elem ent discretization scheme.

A first step in our approach is to sim plify eq u atio n (4.1.1) from its d ifferen tial form to a more global re p re se n ta tio n t h a t re ta in s enough stru ctu re to achieve the m odelling objectives. To do so, we will focus our a tten tio n on stream -aquifer system s where

1) the salt concentration in the aquifer is high in com parison w ith th a t of the stream ; and

2) advection dom inates diffusion.

An exam ple of a stream -aquifer system ch aracterized by high aquifer salinity and little diffusion along th e stream is th e stre tc h of th e River M urray betw een E uston and Redcliffs. This stretch illu strated in Figure 4.1 is p a rt of the study area to which th e solute tra n s p o rt model developed in this chapter is to be applied. There, highly saline w aters discharge into the stream resu ltin g in a significant increase in dow nstream salin ity during low to m edium flows. This is illu s tra te d in F ig u re 4.2 w here plots of salinity a t E uston are routed dow nstream and compared to those m easured a t Redcliffs.

Moreover, M aunsell et al (1984) have suggested th a t diffusion processes along the River M urray are generally sm all com pared w ith advection. This is supported by a recent study by Joy et al (1988) w here diffusive fluxes along several stretches of the River M urray were found to be up to th ree orders of m agnitude sm aller th a n advective fluxes. To illu stra te th is point qualitatively, Figure 4.3 provides salinity profiles a t B oundary Bend and Euston.

N E W S O U T H W A L E S S O U T H V I C T O R I A f A D E L A I D E [M u rra y Bridg e DARTMOUTH \ D A M A U S T R A L I A \ R I V E R M U R R A Y A N D I TS T R I B U T A R I E S V//A Study k ilo m e tre s

F ig u re 4.1 M ap o f the R ive r M u rra y and its trib u ta rie s show ing th e stu d y area (shaded) between Euston and Redcliffs.

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accession

discharge

JAN I FEBI MAR | APR | MAY | JUN | JUL | AUG | SEP | OCT | NOV | DEC

TIM E (MONTHS) 1 9 7 8

F ig u re 4.2 S a lin ity p ro file s ro u te d from E u sto n to R e d cliffs (co n tin u o u s) to g e th e r w ith s a lin ity p ro file s m easured a t R e d cliffs (dash). The p lo t o f th e ir difference in d ica te s a s ig n ific a n t increase (or accession) o f s a lin ity a long th e stre tc h p a rtic u la rly d u rin g lo w to m e d iu m flow s. T he stre a m discharge a t C olignan is also plotted.

F ig u re 4.3 shows th a t sh arp spikes u p stre a m a t B oundary B end are tra n s la te d w ith o u t any obvious dam ping to th e dow nstream location a t E u sto n following variable trav el tim es of a couple of days to two weeks depending on stream discharge levels.

discharge