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c

c

H

X u

C

U >

H'CaoSu>

HPd4IM

OCU

uc03.HIMC O U03en

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to Fick, the rate of transfer of diffusing substance through a unit area of section isproportional to the concentration gradient measured normal to the section, i.e.

dcF* = - D; b F (3 - 3)

where F^ is the amount of substance diffusing p er unit area of a section per unit ti me, C isthe concentration of the diffusing substance, x is the distance measured normal to the sectionand D is the diffusion coefficient. The minus (-) sign is due to the fact that the transferof substance takes place in a direction along the decreasing concentration of the diffusingsubstance.

The molecular diffusion process plays a significant role in laminar flows to spreadpollutants; but in the case of turbulent flows its effects are negligible in comparison to the'turbulent diffusion proces s' which will be described in the next sub-section. Since, in almostall the natural streams the flows is turbulent, the molecular diffusion process is not adominant one in considering the spreading of pollutants in natural streams.

3.2.2.2 Turbulent diffusionThe spreading of pollutant s due to the random motion of the fluid 'particles' in a turbulentflow is termed turbulent diffusion. Turbulent diffusion i s, in fact, a characteristic featureof turbulent flows. Indeed, in the classic experiment of Reynolds this characteristicbehaviour indicated the onset of turbulence in a flow field. In the case of molecular diffusionprocess, the molecules of the diffusing substances are performing the random moti ons, whereas inthe case.of turbulent diffusion pr oces s, the 'fluid particl es' are performing random motions .By 'fluid partic le', we mean the volume of fluid which is so small th at, within the framework ofthe theory of continuum, it can be identified with a point which is displaced together with thesurrounding fluid. In order to trace the motion of the fluid particles , we assume the presenceof some admixtures in the flow field which behave in exactly the same way as the fluid particlesbut have special properties to permit the tracing of their motions.

The analogy between the motion of the molecules and that of the fluid particles enables aquantitative formulation of the turbulent diffusion process. Indeed, the amount of substance(F t ) diffusing per unit area of a section per unit time due to turbulent diffusion is expressedin terms of a (turbulent) diffusion coefficient and the concentration gradient of thediffusing substance as:

3CF t = - E 3 ( 3 - 4 )

Spreading of a substance due to turbulent diffusion is much more rapid than that due tomolecular diffusio n. In other words , the numerical values of E are far greater than those of

D.3.2.2.3 Secondary circulationIn addition to spreading due to the random motion of molecules and fluid particles, thepollutant s are also carried by the time averaged convective velociti es. Theref ore, anaccurate knowledge of the time average velocity field is a prerequisite to determining the fateof the pollutant introduced into the flow field. In non-circular flow cross-sections, typicalof natural streams, it has been observed that there is a mean current in a plane perpendicularto the direction of the flow even for a straight channel. Such curre nts, called the secondarycurrent of the second kind by Prandtl (1952), can carry the pollutants in the transverseplane of the flow cross-section.

At present, the knowledge of this secondary current is limited. The usual practice indispersion studies is to lump the effects of secondary currents with the other diffusionprocesses and measure an overall dispersion coefficient. Recent investigations of the spreading

of pollutants in the transverse direction in channels with secondary circulation have revealedthat the effects of secondary circulations on the spreading of pollutants are far greater thanthose of the turbulent and molecular diffusion processes and hence have demonstrated a need forfurther research on this type of secondary circulation.

3.2.2.4 Settling and transport with sedimentsIf the pollutant contains particulate matter or if it coats the sediment particles present inthe alluvial streams as a result of the physico-chemical processes such as adsorption, then thetransport and spreading of the pollutant are governed by the mechanisms controlling the motionof the sediment particles (Unesco, in press) .

The motion of sediment particles h as been studied extensively in the field of sedimenttransport and a brief account is given here. The strength of the flow needed to initiate themotion of the sediment particles forming the bed of the alluvial stream depends on the size and

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the specific weight of the particles and can be predicted with a reasonable accuracy using thewell-known Shields Curve shown in Figure 3.6. In.this figure, the critical mobility number Y c ris plotted against the critical grain size Reynolds Number X c r . The mobility number Y expressesthe balance between the shear stress (T ) exerted by the flow on the bed and the weight of asolid particle per unit surface area and hence can be written as:

2O.V* = y f - (3.5)

s /T.where p is the density of the fluid, v* (=/ ) is the shear velocity of the flow, y s is thesubmerged specific weigh t of the solid particle and P is the size of the particles.

The grain size Reynolds Number X expresses the balance between the inertia and the frictionforces and can be given by:

X = ^i=- (3.6)y

where \1 is the dynamic viscosity of the fluid.The values of Yc r and X c r are those resulting from the use of critical values of v* (i.e.

v* cr ) is equations (3.5) and (3.6). When the mobility number Y for a flow is less than thecritical mobility number Y c r then the particles will not be moved by the flow and under thesecircumstances the bed of the stream can be treated as a rigid one. If the strength of the flowincreases, increasing the shear stress at the bottom and consequently the mobility number Y, theparticles begin to move. If the ratio Y/ Y c r is between 1 and 15, the particles move in thevicinity of the bed by rolling and performing short jumps. During this stage of the flow, sanddunes begin to develop at the bottom and the particles advance along the bed in a series ofalternate rest and transport perio ds. Experiments indicate that the rest and the transportperiods are random in nature and hence the sediment particles are dispersed as they move withthe flow. Shen and Cheong (1973) have formulated the dispersion of the contaminated "Bedload"particles using the experimental evidence that the rest periods are exponentially distributedand the step lengths (the length of travel of particles bet ween rest periods) are gammadistributed.

For values of Y / Yc r greater than 15, the dunes begin to disappear and the particles areentrained into the main body of the flow, moving in suspension in irregular and random pathslike the fluid particles. Dispersion of the sediment particle s during this stage of motion canbe formulated in the same way as for the fluid particles, taking into account the negativebuoyancy of the sediment particles.

So far in this section various hydrodynamical processes which are responsible for thespreading of the pollutants have been considered in a descriptive manner. In the following, aquantitative treatment of the transport of pollutants in a natural stream, where all theseprocesses can interact, will be considered.

3.2.3 Mass-balance equations

3.2.3.1 General mass-balance equationMathematical treatment of the transport of pollutants in streams is based on the principle ofconservation of mass. In the following derivation of the mass-balance equation for a pollutant,it is considered for simplicity that the pollutant is a conservative substance. By the term1 conservative substance' we mean those substances which do not undergo any process other thandilution. In other word s, the processes such as decay, chemical reactions and production orremoval are not considered. Consideration of the non-conservative substances will be taken uplater on in this chapter.

Consider a closed volume V as shown in Figure 3.7 and let F be the rate of transfer of adiffusing substance per unit area through the surface S enclosing the volume V. The conservationof the mass of the diffusing substance entering and leaving the volume V per unit time must beequal to the rate of change of the concentration C of the diffusing substance in V at time t.

This mass conservation principle leads to the commonly used mass balance equation which fora neutrally buoyant and conservative substance, can be expressed as:

8c 8c 8c 8c + u ^ + u y ? + U z =

88x (D+ex)^-8x *%>ff ( D+e z ) g (3.7)

8_8y

It is assumed that the molecular diffusion coefficient D is constant in all directions whereasthe turbulent diffusion coefficient, , depends on the co-ordinate direction and can beexpressed by three scalars, e x , e v and e z .

For the case of sediment particles whi ch are heavier than water and which have a fall

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1 I I I I I I I I I I I

0.0011000

Figure 3.6 Shields Curve for sediment transport

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(Unit n o r m a l )

Figure 3.7 Control volume in a flow field

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velocity of w in the y direction, the mass balance equation can be Written as:

(3.8)C3t s c , 3 c 3cd v.- .se i 8 r,-.zc] s r,~

+ u* 3+ < Vw ) By"+ u- 9 7 = 8L( D + e* >3J + 8y" L^^^J + " L'"^ '

8C'3

For reasons indicated earlier, if the effect of the molecular diffusion is negligible incomparison to that of turbulent diffusion, then the molecular diffusion coefficient D can beleft out of both equatio ns (3.7) and (3.8).

In order to solve the mass balance equation (i.e. equation (3.7) for neutrally buoyantpollut ants and equation (3.8) for negatively buoyan t pollutants ) to pred ict the concentration ofthe pollutant as a function of space (x, y and z) and time t, the velocity components u x , u v andu z and the diffusion coefficients at every point in the flow field have to be known with theappropriat e initial boundary conditions for concentration distribution. Such a detaileddescription of the velocity field and the diffusion coefficients is usually not available forthe natural streams and therefore, the mass balance equation is often simplified by makingcertain assumptions regarding the flow field and the diffusion processe s. Some of the commonlymade simplifications will be considered here.

3.2.3.2 Longitudinal dispersion: cross-sectional average mass-balance equationTaylor (1954) described the spreading of a neutrally buoy ant, conservative pollutant in aunidirectional shear flow (i.e. flow in pipes) by making the following assumptions:1. The motion is predominantly in one direction, i.e. u v and u z are zero;2. The turbulent diffusion in the y and z directions of motion is negligible, i.e. e v = 0,

e z = 0;3. The molecular diffusion is negligible, i.e. D = 0.By averaging over the entire cross-section and writing

ux - u + u 1

C = C + C(3.9)

where the overbar denotes averages over the cross-section and u' and C represent spatialvariations from the mean , equation (3.7) can be written as :

5- + u -5= E - (3.103t 3x 9 x 2

whic h is the well-known Taylor's one-dimensional dispersion equation. E is an apparentlongitudinal diffusion coefficient which will henceforth be referred to as the longitudinaldispersion coefficient. Theoretical approaches to the estimation of the dispersion coefficientare given by Elder (1959) and Fisher (1966, 1967).

In a uniform channel with constant stream velocity, the dispersion coefficient may becalculated from a tracer curve as

E = < ^

where L is the distance travelled, u is the velocity and a 2 is the variance of the concentrationcurve of the type shown in Figure 3.3.

It should be pointed out that Taylor's one-dimensional approach does not apply in regionsclose to the location where the pollutants are injected. Fisher (1966) demonstrates that theone-dimensi onal approach of Taylor is valid only when C is much smaller than C and identifiestwo distinct periods in the transport of the pollutants from a point source in a naturalstream. These two periods are:

1. The convective period, during which the movement of the pollutants is dependent on theinitial convective velocity and the concentration distribution is highly skewed;2. The diffusive period, during which the bulk motion of the pollutants can be described byTaylor's one-dimensional equation.Based on his experimental results, Fisher found that the time T at which the diffusive periodbegan was about 0.4 times the Eulerian time scale for the flow, i.e.

a 2T = 0.4 (3.12)e z

where a is the distance between the point of maximum velocity to the most distant bank.In terms of distance L downstream from the source of polluti on, the criterion for the use

of Taylor's equation becomes:> ij|_G 3

c Rv *

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where R is the hydraulic radius.

3.2.3.3 Transverse dispersion: depth-average mass-balance equationSince in most natural streams, width is considerably larger than the depth, the pollutantsbecome uniformly spread over the depth much faster than they are spread uniformly across thewidth and hence it is customary to treat the motion of the pollutants in terms of the depthaverage version of the mass balance equation. E. R. Holley (1971) integrated equation (3.7)with zero molecular diffusion over the depth and obtained the following equation:

T. /3C , dC , dC. 3 ., dC v . d ., 3C. , n .. ..h -5 + u 3 + u_ 3) = 3 (h e -5- +-5 (h e_ 3) (3.14)

dt x dx z dz dx x dx dz z dzwhere the overbar now denotes the average over the depth and the dispersion coefficients e x ande z are defined by the following expressions:

r - 3c. _ 3c.x " e x 3 X -

e x dx

- 8C 3cu' C - , 3 = e_ 3

z z dz z dz

(3.15)

e x and e 2 , therefore, include the effects of both the turbulent diffusion and those of thedifferential convection.

For a continuous injection of the pollutant when the concentration distribution becomesindependent of time t, the longitudinal dispersion of pollutants is often neglected because of

negligible concentration gradient in the longitudinal direction and hence the equation representing such a case becomes:

3c - 3c. _ 3 ., 3c,^ 3x" + U z 3 ? - 3z (h e z 3z'ux - 7 + u z 377) = (h e 7 -577) (3.16)

If the channel reach is straight, u z becomes zero and if h is constant equation (3.16) takes theform:

u x 3 = 3 (e 3) (3.17)x dx 3z z dz

3C 3 , 3z 3z'

_z .^ .,4.., ^ . , includes the effects of turbulent diffusion in the z direction and the effectsof the secondary currents of the second kind which result from the non-circular geometry. If thechannel reach is a meandering one, then u z becomes the secondary current resulting from thecurvature (secondary currents of the first kind in Prandtl's terminology) and does not vanish.

u z can be computed from the depth average continuity equation for incompressible flows at:

uz = - h 4~ fc zhdz (3.18)z h 3x ' 0 z

in terms of the depth average longitudinal velocity u x and the flow depth h. The depth h alsovaries across the channel either due to superelevation in the case of rigid bottom channels ordue to the scour and deposition of sediments in alluvial channels. The dispersion coefficiente z for this case includes the effects of turbulent diffusion and the differential convectionresulting from the secondary current of the first kind. Therefore, the full form of equation(3.16) is necessary to describe the transport of the pollutants in meandering reaches of the

stream. The dispersion coefficient e in both cases has to be measured experimentally sincethere is no theoretical means to predict it at the present time.

Several investigators have measured e z under different channel geometry and flowconditions and a summary of all the existing measurements can be found in a paper byKrishnappan and Lau (1974).

It should be remembered that the depth average mass-balance equation (i.e. equation (3.16))is not valid in regions where the pollutants are not mixed completely over the depth. Sayre(1973) has established from a theoretical solution of the mass-balance equation in2-dimensional flow that the distance (L ) from the point of injection where equation (3.16) isnot valid is:

T . ^ 0 - 5 ( h / 2 ) 2 x (3.19)

Swhere e y is an average turbulent diffusion coefficient in the vertical direction. Equation(3.19) is applicable for the case when the pollutant is injected at the mid-depth.

The vertical turbulent diffusion coefficient e v is obtained by assuming that theturbulent transfer of mass and momentum are equivalent, that the shear stress in the vertical is

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linearly distributed and that the velocity distribution is logarithmic. The expression for e vunder the above assumption becomes :

i y = 0.07 h.v^ (3.20)

With this value of , equation (3.19) reduces to:Ld x- e = 1.8 (3.21)h v *

Within the region between the section where the pollutant is injected and the section which isat a distance L downstrea m, one ha s to treat the transport of the pollutants in terms of thefull mass balance equation, i.e. equation (3.7).3.2.3.4 Non-conservative pollutantsIn the case of non-conservative po lluta nts, the mass-balance equation (3.7) has to be correctedfor the production or the removal of the pollutants due to chemical reactions, change of stateor transfer across the boundaries by adding an appropriate source or sink term S which is , ingeneral, a function of space, time and the concentration of the polluta nt itself. In otherwords, the mass-balance equation for a non-conservative pollutant becomes:

3c 3c 3c 3c 3 _ , 3c 3 ln . 3c 3 , , 3c ,_ ,3 Ux 3 ^ + ^ 3y- u z 31 = ^ < D + x ) ^ + ay" (D + Ey) ay" + a 7 (D + e z>. + S(x;y;z;t;C)

(3.22)

The term S (x;y,-z;t;C)

depends on the nature of the production or the removal processes but inall cases it expresses the rate at which a pollutant is added or removed from the controlvolume. Some of the common examples of the non-conservative substances are dissolved oxygenand biochemical oxygen demand, which will be considered in detail in the next section on theprocesses affecting biological self-purification.

3.3 SELF-PURIFICATION AND THE OXYGEN BALANCE

Biological self-purification is the process in which organic wastes are broken down by therespiration of micro-organisms into stable end products. It is a biochemical oxidation processthrough which organic wastes are consumed leaving behind end products such as carbon dioxide,water, phosphates and nitrates. The water is 'purified 1 in the sense that the concentration ofwaste material has been reduced. Organic materials which can be broken down (i.e. are biodegradable) include natural materials such as simple sugars, starch, fats, proteins as well as

more complex natural or synthetic compounds which are found in sewage or other wast es. Thistype of respiration, in which biochemical oxidation takes place using the free dissolved oxygenin the wate r, is called aerobic respiration. The micro-organisms involved are called aerobes .

There is another type of respiration which can take place when free oxygen is notavailable. Certain mic ro-organisms known as anaerobes and some known as 'facultative aerobes'can still break down simple sugars without the use of oxygen. This is called anaerobicrespiration. Howeve r, when anaerobic respiration takes pla ce, end products such as hydrogensulphide, ammonia and methane which may be toxic as well as foul smelling are often produced.

Thus, through the biochemical respiration, self-purification of the river takes place butin the same process oxygen is being removed from the aquatic environment. If the supply ofoxygen into the system is exceeded by the demand from respiration, an undesirable anaerobicstate will occur. There fore , the self-purification process is very closely tied with thedissolved oxygen content and indeed with all the sources and sinks of oxygen in a river. Sincedissolved oxygen is such a critical water quality parameter, the various processes affecting

the dissolved oxygen will be discussed.One of the first studies of the DO balance was by Streeter and Phelps (1925), who developed

the classic oxygen balance equations by considering biochemical oxidation as the only sink andatmospheric reaeration as the only source of oxygen. These equations express the effects of BODsatisfaction or deoxygenation and reaeration through the water surface, the rates of which areexpressed by rate coefficients K-_ and K2-

The equations of Streeter and Phelps were found to be adequate to give a schematizedrepresentation of the variation of dissolved oxygen concentration downstream of the point ofdischarge. If the water's oxygen content is examined along the river, downstream from anassumed constant waste discharge, we notice what is known as a sag curve (see Figure 3. 8).Firstly, the oxygen content decreases rapidly, reaches a minimum, then increases toreach asymptotically the saturation point. From a practical point of view, what matters is theminimum content value.

Subsequent studies have pointed out that other sources and sinks have to be taken into

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0ocCO

+w fQ

E(O0trS oQ

0>MDO Ddtnt0D>10Ta>H0m

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account (Dobbins, 1964; Camp, 19 63; Owens and Edwar ds, 1963; Edwards and Owen s, 1965). Alist of these processes is as follows:- the removal of BOD by sedimentation or adsorption;- the addition of BOD by the scour of bottom deposits or by the diffusion of partly decomposed

organic products from the benthal layer into the water above;- the addition of BOD by local runoff;- the removal of oxygen from the water by diffusion into the benthal layer to satisfy the

oxygen demand in the aerobic zone of this layer; 1

- the removal of oxygen from the water by- the purging action of gases rising from the benthallayer;

- the addition of oxygen by the photosynthetic action of plankton and fixed plan ts;- the removal of oxygen by the respiration of plankton and fixed plants;- the continuous redistribution of both the BOD and the oxygen by the effect of longitudinal

dispersion, particularly when the waste loads vary suddenly (e.g. as a result of an accident).- the addition of oxygen by reaeration proce sses.

Bennett and Rathbun (1971) have written a very good summary describing the methodsavailable to measure or evaluate the various source-sink terms. In gener al, the dominantprocesses which ought to be considered in the oxygen balance of a river are the following:1. The BOD (biochemical oxygen demand) of the carbonaceous and nitrogeneous wastes in thewater;2. Oxygen demand of the bottom deposits;3. Immediate chemical oxygen demand;4. Oxygen required for plant respiration;5. Oxygen produced by plant photosyn thesis;6. Oxygen gained from atmospheric reaeration.

Referring to equation (3.22) for the mass-balance of a non-conservative substance, theequation for the dissolved oxygen (DO) distribution for the case of a straight uniform reach andnegligible molecular diffusion is:

3 c - 3c 3 3(5 0 ,. ,.ir- + u__ -5 = -5e v + . SJ 3.23)9t x 3x 3x x 3x 1 1

where C is the depth average concentration and Sj_ represents the individual source and sinkterms which will be described below.

3.3.1 Biochem ical oxygen demand (BOD)

The BOD is the oxygen required by the micro-organisms for the respiration process describedpreviously. The amount of the organic waste is measured by its demand on the oxygen resource.The value for the BOD concentration is not consta nt but changes with time and distance along ariver because a s oxygen is used up to oxidize the waste, the amount of waste material decreasesand the oxygen demand drops. When all of the waste has been oxidized the BOD then becomes zero.BOD can also be removed from the water by sedimentation or it can be added to the water by thescouring and resuspension of bottom deposits. These factors have to be considered in order tosolve for the BOD distribution along the river.

It is usually assumed that the rate of biochemical oxidation is a first order process, i.e.the oxidation rate is proportional to the amount of waste remaining in the water. The net rateof sedimentation and scour is also generally assumed to be proportional to the amount of BODpresent . Therefo re, referring to equation (3.22) again, the equation for the distribution ofBOD can be written as:

! + v -jr = # - - K,L - K3E (3.24)3t x 3x 3x x 3x J- J

where L = average BOD concentration in the water ; K-j_ = rate constant for the biochemicaloxidation; K3 = rate constant for the net rate of settling and resuspension of BOD.

The oxygen sink term in equation (3.23) represe nting the biochemica l oxida tion is -Kj_L andhas to be obtained from the solution of equation (3.24). The amount of BOD in a sample ofwater has to be determined from a BOD test. The standard procedures for the test are describedby the American Public Health Association (1971). In principle, this test consists of takingtwo samples of the same water, determining the DO concentration of one sample, incubating theother sample in darkness for five days and then determining its DO concentration. The differencein DO is the 5-day BOD of the sample. However, it is not known how well this laboratory value

Especially important in shallow streams with a depth of say below 2 m (Edwards and Rolley, 1965).

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of BOD represents the true BOD value in the stream because the conditions of temperature,turbulence and biological activity are all different. Hull (1969) and Camp (1965) haverecommended using a dark bottle suspended in the river for the BOD test. The rateconstant K]_ is determined by measurements of the BOD at successive stations on a river. Valuesfor K]_ can var y from 0.01 da y - 1 to 0.3 day - 1 depending on the type of waste and the degree ofstabilization (Camp, 1963). Therefor e, K]_ values m ust be determined' for a particula r reach forthe particular type of waste under consideration.

The coefficient K3 for the settling and resuspension of BOD has to be determined from BODprofile measurements. Even though these are physical processe s, governed by the flow conditionsand particle size, it has been shown by Kranck (1974) that particulate matter from a Kraft milleffluent flocculates into different sizes depending on the particle population in the receivingmedia. Theref ore, it is very difficult to predict the settling rate which can conceivably varyin the downstream direction. Under steady state conditions, with no sediment build-up, theamount of settling and scour should be equal. However, the material settling and that beingscoured may not have the same BOD concentration. Because of these factors , the coefficient K3is usually just an average for the river reach being studied. Dobbins (1964) has indicated howK3 can be calculated from the measured BOD profi le, provided that K]_ has bee n determined fromlaboratory measurement s.

3.3.2 Immediate chemical oxygen demand

Many types of industrial effluents contain substances which are fairly quickly oxidized by molecular oxygen. These substances such as ferrous iron, sulphite, sulphide and aldehyde all exerta load on the DO content and the amount of oxygen required for the oxidation is called theimmediate chemical oxygen demand. The test for this demand is given by the American PublicHealth Association (1971).

3.3.3 Plant respiration and photosynthesis

Aquatic plan ts, benthic algae and phytoplankton all consume oxygen for their respiration proc esswhich takes place continuously. At the same time, if sunlight is pres ent, the plants combinecarbon dioxide and water in the process of photosynthesis to produce a simple sugar and r eleasefree molecular oxygen into the environment. In genera l, in the daylight hou rs, the amount ofoxygen produced by photosynthesis exceeds the amount consumed by respiration. However, duringhours of darkness , photosynthesis does not take place and plants then act solely as a sink foroxygen. Therefore, dissolved oxygen levels tend to be highest in mid-afternoon and lowestduring the early hours of the morning.

The photosynthesis production of oxygen depends on several factors including the lightintensity, the optical density of the water and the quantity of plants (Edwards and Owens , 1965).Pescod (1969) conducted oxygen studies in a tropical alluvial river and found that even thoughenvironmental conditions were suitable for algal growth and a high level of photosyn thesis, theturbidity reduced light transmission so that the actual oxygen production was very low. Nevertheless, the processes of photosynthesis and respiration can be very important factors and shouldbe included in the DO balance.

The photosynthesis and respiration rate can be measured in one of two ways. In the lightand dark bottle technique, samples of water are placed in opaque and transparent bottles andsuspended in the stream for a period of time. From the initial sample, DO concentration and thefinal concentrations in the bottles, the photosynthesis and respiration rates can be calculated.From a DO balance of the reach and assuming reaeration and other factors to be indep endent oftime, the photosynthesis and respiration rates can be calculated.

3.3.4 Atmosph eric reaerati on

Reaeration is the process of absorption of atmospheric oxygen into the water. It is one of themost important factors controlling the waste assimilative capacity of a river 'because phot osynthesis and reaeration are the only two sources of oxygen repleni shment, and photosy nthesiscan take place only when there is sunlight.

It can be shown from molecular theory that the water surface which is in contact with theatmosphere becomes saturated with oxygen in a very short time. However, once the surface issaturated the dissolved oxygen has to find its way into the body of the fluid before moreoxygen can be absorbed. In the region very close to the surface, viscosity dominates and

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oxygen is transferred into the liquid below it by molecular diffusion which as we know, is avery slow proce ss. Below this surface region oxygen is quickly dispersed throughout the rest ofthe depth by turbulent diffusion which occurs in most natural flows. There fore, the dissolvedoxygen concentration throughout most of the flow is generally quite uniform. Althoug h,strictly spea king, fluid elements are continuously moving in and out of the surface region, inthe time average sense one can consider that there is a very thin region close to the surface inwhich the DO concentration drops very sharply from saturation to that for the bulk of the flow.This region is termed the turbulent surface film or oxygen boundary layer by Holley (1973) andis in many respects analogous to the viscous sublayer in the flow over a solid boundary.

It is generally agreed that the rate of oxygen absorption is proportional to the oxygendeficit, i.e. the difference between the saturation concentration and the actual DOconcentration. The proportionality constant is called the reaeration coefficient K2. Therefore,the source term for the right side of equation (3.23) representing reaeration is K2(C s -C) whereCs is the saturation DO concentration. C s is a function of temperature and may be calculatedapproximately from the following empirical equation:

Cs = 14.541233 - 0.3928026T + 0.00732326T 2 - 0.00006629T 3 (3.25)

where T is stream temperature (C). The reaeration coefficient K2 is naturally not a constantfor all flows . It depends on many variables including channel slope, bottom roughn ess, flowvelocity and wind conditi ons. All these factors affect the turbulence near the water surfacewhich, as we have seen, controls the rate of oxygen absorption.

Numerous studies have been made and many prediction equations have been presented for thereaeration coefficient K2- These equations are either strictly empirical, based on experimentalreaeration r ates , or are derived from some conceptual model of the process with coefficientswhich also have to be determined experimentally. The proposed models and prediction equationshave been reviewed by Lau (1972) and by Bennett and Rathbun (1971). Many of the empiricalprediction equations appeared to give a good fit only to the few sets of data from which theywere derived. The conceptual models suffer from the fact that they all contain two or morecoefficients which again depend on various flow variables and are difficult to evaluate.Reliable experimental data, especially field data, are very difficult to obtain because manyfactors affect the DO balance and it is difficult to account correctly for all of them. Lau(1975) found from his laboratory experiments that the dimensionless variable K2h/u is a function

of both the friction factor f and the Reynolds number uh/v where V is the kinematic viscosity ofwater. This shows that simple prediction equations which try to relate K2 to u and h can not, ingeneral be satisfactory. Wilson and McLeod (1974) tested sixteen prediction equations againstpublished data covering a wide range of hydraulic variables and found that even the ones withthe best correlations gave very unreliable prediction rates. They suggested that the poorperformance of these equations may be attributable to the omission of one or more significantvariables. Of the equations tested, those of Dobbins (1964) and of Parkhurst and Pomeroy (1972)gave the best fit to all the data investigated. The latter equation is the simpler of the twoand is given in terms of the mass transfer coefficient K L at 20C. The equation is :

KL20C = - 9 6 ( 1 + - 1 7 F r 2 > ( S u ) 0 " 3 7 5 (3.26)where K L = I^h (m pe r h r ) ; F r = Froude number (u/Vgh); S = slope of energy line; u = flow velocity(m per se c) ; h = flow depth (m).

It is clear that not one of the existing equations can satisfactorily predict thereaeration rate over a wide range of flow conditions. Based on the results of Lau (1975) itappears that the variation of K2 cannot be covered by a single equation. Therefor e, the usermust exercise judgement in selecting an equation for K9.

3.4 PREDICTION OF WATER QUALITY CONDITIONSSo far, in the last two sections the equations governing the transport of both the conservativeand non-conservative substances have been formulated and some of the commonly made simplificationsof these equations considered. In this section dealing with the prediction of water qualityunder steady state flow condition s, some of the available solutions to these equations will bereviewed.

3.4.1 Longitudinal spreading of a conservative pollutant

Consider the longitudinal spreading of a slug of a conservative pollutant injected instantaneouslyin a natural stream. After the convective period, the transport of this slug of pollutant canbe described by the cross-sectional average mass balance equation (i.e. equation (3.10). Th e

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Solution o f this equation c a n b e expressed a s :

(3.27)(x;t) = l / 4 i i t e X p(x-t) 2"

4E t

where M i s t h e mass o f t h e pol lu tan ts a n d A i s t h e cross-sect ional area o f t h e channel .In order t o u s e equation (3.27) t o predic t t h e concentrat ion distr ibution o f t h e p o l l u t a n t

and consequently t h e qual i ty o f w a t e r, t h e dispers ion coeff ic ien t E h a s t o b e known.The dispersion coefficient E c a n b e evaluated from tracer experiments o r derived from t h e

theoret ical equations, Fisher (1968).

3.4.2 Long itud inal spreadi ng o f a non-conserva t ive po l lu tan t

Cons ider t h e longitudinal spreading o f a slug o f a non-conservative pollutant injected instantaneously i n a s t ra igh t channel . T h e pol lu tan t i s assumed t o undergo a f irs t order react ion s othat t he rate o f removal c a n b e represented b y k C where k i s a react ion rate constant . I n thiscase t he t ranspor t o f t h e pollutant beyond t h e ' convective period' c a n b e represented b y t h e o n e -dimensional dispersion equation with a sink term which i s :

3C - 8C 3 2 C"57" u ' 5 = E ~^~23t 3x 3x

A solution of equatio n (3.28) is

.. + u -~ - = E r-r - k C (3.28)dt dx dx

5 ( x ; t )

= A 7 4 i E 7e x p

*_ , (x-ut) 2 + 4Ekt-i~

4E t '(3.29)

where M is the mass o f t h e non-conservative pollutant introduced into t h e stream.The value o f t h e longitudinal dispersion coefficient E c a n b e evaluated i n t h e same manner

as i n t h e previous case.

3.4.3 Oxygen balance

The solut ion o f t h e D O concentrat ion i s a l i t t le more complicated because o f t h e B O D term a n danalyt ical solut ions a r e obtained only f o r t h e one-dimensional case, considering t h e wholecross-sect ion o f t h e r iver t o b e well mixed. A s a n examp le, Dobbins (1964) considered remov al o fBO D b y sed imenta t ion o r absorp t ion , t h e addi t ion o f B O D along t he reach a s wel l a s t h e B O Dreact ion ra te . T h e B O D profi le equation i s :

U

x S= E

& -(K

1+ K

3) L + L

a where L a i s t h e rate o f addit ion o f B O D along t h e reach a n d K 3 i s t h e rate o f sed imenta t ion o rabsorption.

The solut ion i s given b y :L a

L = L exp(mx) + - (l-exp(mx)) (3.31)IXT + IS.3

where :

u x - M ux 2 + 4 ( K i + K 3 ) E )m = 2i

and, L 0 = L at x = 0 . This value fo r L i s then used i n t h e D O balance equation given b y :

dc d 2 rU x

dx"= E

d ^+ K

2C

s -C )

-K

1L

-D

B( 3

-3 2 )

where DB stands f o r t h e n e t effect o f plan t photosynthes i s a n d respirat ion a n d bentha l demand.The solut ion, subject t o the boundary condit ions that C = C 0 a t x = 0 an d equi l ib r ium

between atmospheric reaerat ion a n d photosynthes i s a n d benthal demand a t x = , i s given b y :L aKl ( Lo - y . , + K ) (exp(mx)-exp(rx)) D K L

(C s -C) = f lL_3 + (C s -C 0)exp(rx) + (-f- + L a ) (l-exp(rx))K9 - ( K , + K , ) K 2 K 2 ( K 1 + K3 > (3.33)

Uv- (uv Z+rK?E)15where : r

Ux-(ux 2+rK2E)ij2E

Equation (3.33) i s valid f o r describing t h e cross-sect ional average concentrat ion o f D Owhen t h e B O D i s reasonably well mixed throughout. Howeve r, outfal l dischar ges a r e genera l ly

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located at one bank or at some location in the stream and are not initially well mixed acrossthe section. Therefor e, a cross-sectional variation in BOD exists across the river and until itis well mixed there will be a cross-sectional variations in DO concentration as well. In thiscase the two-dimensional equations have to be solved. Holley (1973) compared the one-dimensionaland two-dimensional distributions and found that, except in cases of relatively fast transversemixing, the two-dimensional solution gave smaller minimum DO concentrations and the minimumconcentrations were as low as one-fourth of those calculated by the one-dimensional solution.Thus if the stretch of river under consideration includes ecologically sensitive areas such asspawning g rounds, a two-dimensional DO balance should be used.

3.4.4 Management applications of flow and water quality models

3.4.4.1 IntroductionThe application of the solutions described in the previous section to many water pollutionproblems is often of limited value because the solutions assume constant flow conditions. Thesteady state water quality solutions are mainly used for long-term planning problems wheregenera l in formation o n the likely resp onse of the sys.tem is required (Newsome et al., 1971).Howeve r, many problems in water quality management derive from transient violations of waterquality standards which are governed as much by the hydrological behaviour of a jsystem as thedischarge of pollutants at points within it. Recently, Warn and Brew (1980) have drawnattention to the limitations of steady-state models in setting consent conditions for effluentdischarges and attribute these limitations to the inability of steady-state models to accountfor the short-term interactions between flow and quality.

In applying a model to a management problem, it is important to recognise that the model isat best an imperfect representation of 'real-world' behaviour, that model simulations andforecasts are subject to error, and that decisions based on the model will be subject touncertainty. A model which explicitly recognises the presence of this error is termed astochastic model; models which also represent the time variant interaction between flow andquality are termed dynamic-stochastic water quality models.

3.4.4.2 Dynamic model structureFor application to design and operational management probl ems, a dynamic water quality modelshould have the following attributes :1. the model should be capable of using time-varying input (upstream) measures of waterquality to compute time varying output (downstream) responses;2. the model should be simple, yet characterise adequately those dynamic aspects of system

behaviour of particular importance for the problem at hand;3. the model should provide a reasonable mathematical approximation to the physico-chemicalchanges occurring in the river system and should be calibrated using measurements collected fromthe river at a sufficiently high frequency and for a sufficiently long period of time;4. the model should account for the inevitable errors associated with laboratory analysis andsampling, as well as the uncertainty associated wi th imprecise knowledge of the pertinentphysical, chemical and biological mechanisms.

As indicated in Figure 3.9, the function of the dynamic model is to link the water qualitymodel with the hydrological model such that interactions are incorporated directly. The dynamicwater quality models employed in several major water quality studies (for example , The BedfordOuse Study - Whitehead et al , 1979, 1981) are based on a transportation delay/continuouslystirred tank reactor (CSTR) idealisati on of a river (see Figure 3.10). The mathematicalformulation of this model is in terms of lumped parameter ordinary differential equations anddraws upon standard elements of chemical engineering reactor analysis, e.g. Himmelblau and

Bischoff (1968).The principal advantages of this lumped-parameter model over the corresponding partialdifferential equation model are the following:1. the computational effort associated with the solution of the equations is greatly reduced;2. statistically efficient algorithms for model structure identification and parameterestimation can be readily utilized.While the parameters of steady-state models have traditionally been estimated either fromlaboratory experiments or through reference to the literature, the parameters of dynamic modelscan be estimated directly from field data, thus ensuring that the model behaviour will berepresentative of processes occurring at the field scale.

3.4.4.3 Applications of dynamic water quality modelThere are two principal uses for dynamic water quality models :1. to supplement the use of steady-state models at the planning/design stage in carrying out

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EFFLUENTINPUTSBO DD O

UPSTREAMINPUTS

- O HCHLOROPHYLL aBO DDO

SUNLIGHTTEMPERATUREMODEL

PARAMETERS

PHYSICO-CHEMICALM O D E L

EFFLUENT FLOW

RIVER FLOWi

SYSTEM

NOISE

SUNLIGHTTEMPERATUREMODEL

PARAMETERS

OPHYSICO-CHEMICALMODEL

SYSTEM

NOISE

O

SUNLIGHTTEMPERATUREMODEL

PARAMETERS

PHYSICO-CHEMICALMODEL

D O W N S T R E A MBODDO

MULTI REACH CHANNEL FLOW MODEL

RUNOFF FLOW

D O W N S T R E A MFLOW

B

A

RAINFALL STOCHASTIC "WHITE" NOISE INPUT

Figure 3.9 Integrated flow and quality model (Whitehead et al, 1981)

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INPUTSDO.i lt]^

BOD,u 2lt|

INPUTINCIDENTSUNLIGHT,

IV O L U M EV

T EMPE RATU RE

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more detailed investigations of alternative system designs, where a system, in the presentcontext, is a configuration of storage reservoirs (surface and groundwater), sewage and watertreatment plants linked through a network of natural and artificial water courses. Specificall y,dynamic models can be used to evaluate the efficacy (ultimately measured in terms of cost-effectiveness) of different designs in maintaining standards at critical points in a system andof exploring some of the subtle effects which can occur over time (e.g. the build-up of apolluta nt in a pumped storage reservoir through continued recycling of water). A typical timeunit for such models would be one day and water quantity simulation models on this time scalehave been used for several years in evaluating the reliability of systems for water supply;2. to assist in the operational control of river systems. The increasing use of automaticwater quality monitors and telemetry affords considerable scope for hour-to-hour decision-makingthrough the use of short-term forecasts of water quality. Such forecasts are particularlyuseful when abstracted water is to be blended with waters of different quality from othersources such as reservoirs or aquifers.

3.5 MAJOR TYPES OF BIOTIC CHANGES CAUSED BY SELECTED POLLUTANTS

3.5.1 Introduction

Aquatic ecosystems react to pollutants by changing their structure and dynamics in respect ofquality and quantity. The effects of pollutants depend on type and actual condition of theaquatic ecosystems under consideration, and on the dose/effect relation between the pollutantand the organisms concerned. Generally, the ecological consequences of the inflow of pollutantscan be classified as follows:1. Acute consequences

1.1 Inhibition of biological activity and changes in the aquatic ecosystems.1.2 Impoverishment of the aquatic ecosystems.1.3 Depop ulati ons and fish kill.

2. Chronic effects.2.1 Bioaccumulation of persistent pollutants in organism s.2.2 Concentration and effects of pollutants in the nutrient chain, reduction in the quality

and quantity of aquatic organisms, e.g. fish.It is proposed here to consider two groups of pollutants classified according to their primaryeffects:1. Substances which settle or cause turbidity; and2. Oxygen-consuming substances.

3.5.2 Substances which settle or cause turbidity

Turbidity due to suspended matter and its sedimentation is a natural phenomenon encountered inmany streams , particularly in large rivers where it occurs continuously or periodically. Onlyorganisms adapted to such conditions live in these surface waters. Their nutrient base is , toa large extent, of allochthonous origin. Many other medium and small watercourses carrynaturally clear water with turbidity occurring only temporarily during flood perio ds. Henceturbidity and sedimentation remain ineffective, or have only a moderate effect, mostly in theform of a strictly local deposition of fine material which permi ts the development of avariety of minor biotopes on the bottom of the watercourse.

Inorganic suspended sediments enter the watercourses in the form of coal particles, ironoxide or china clay, mostly from the ore and stone industry. Organ ic, poorly degradablesubstances such as those from the wood and paper industry reach the rivers mainly through wastewater. The primary effect of substances causing turbidity and settling when the tractive forceof the water decreases is a deterioration in light intensity. Activity and growth of aquaticplants (aquatic macrop hytes, moss and algae) are inhibited even to the extent of completeelimination.

Thus, the food base of the animals dependent on these plants is also destroyed. Suspendedsolids quickly clog the filter apparatus of certain insect larvae (e.g. caddis larvae), whichnormally use their apparatus to trap organic particles for nutrition. With increasingdeposition of fine material on stones, gravel and wood in the wate r, the food source oforganisms living on solid substrate (algae, moss, snails, caddis larvae, etc.) is destroyed.This also affects the mobile organisms which depend on the substratum as a physical base, suchas stone, ephemeral and caddis fly larvae, or those which graze on it, such as snails. Othermobile aquatic animals like Gammarus (a very important fish-food in the salmonid region ofstreams and rivers) can no longer develop and fish production will be reduced.

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Fine-grained sediments, usually considered as silt deposits, are inhabited by worm-shapedorganisms (sludge worms and some chironomid larvae) which are specially adapted to this biotope,provided that sediment accretion is slight and that the material itself (e.g. iron oxidesediment) is not hostile to colonization. Generally, sedimentation of fine particles destroysthe diversity of the habitat. In addition to these purely physical effects of the substancescausing turbidity, it must be realized that, simultaneously with these substances, otherpollutants and toxic agents reach the water intensifying the effects of the suspendedsubstances on the aquatic organisms. Detailed information of this matter is compiled by Hynes(1960).

3.5.3 Oxygen-consuming substances

Changes in the oxygen content of surface waters may have natural causes or result from humaninfluence. Natural fluctuations of the oxygen concentration in surface waters result from theactivity of autotrophic plants which produce and consume oxygen in a day-and-night rhythm.

Changes in the oxygen budget which are caused by waste water are of much graver consequencefor aquatic life. Oxygen-consuming substances in waste water may be substances which reactchemically with the dissolved oxygen in the water. The best-known example is water with a highcontent of iron II salts which are oxidized in the water by the dissolved oxygen to form iron IIIoxide. In this case, the effect on the oxygen content and the organisms in the water is limitedto a smaller or larger part of the surface water and will persist until the oxygen loss iscompensated for by surface reaeration. Iron polluted water usually is acidic and enters thewatercourses from mines. Ferrous iron salts together with the.acidity of the water lead to anexcessive development of filamentous iron-bacteria and reduction in most of the other organisms(Klein, 1962).

The main problem is created by substances which are degraded biochemically with oxygenbeing consumed in the process, i.e. substances mineralized by bacterial activity. This appliesequally to domestic, agricultural and industrial waste waters. Actual effects depend on quantityand concentration of the biologically degradable substances and on their dilution in the water.Physiographic conditions are also involved because part of the biochemical oxygen consumption iscompensated for as a result of physical aeration as effected, for example, by turbulent flow.

Biochemical oxygen consumption in water results from the activity of heterotrophicbacteria which use organic substances for nutrition. The first change in aquatic life is,therefore, an increase in the number of bacteria and an intensification of bacterial activity.At the same time, other changes take place which, with increasing pollution, lead to ever newbiological structures as, in addition to the oxygen content, a variety of other rivercharacteristics also change. These include: turbidity and the resulting reduction in lightintensity; increased food supply for filtering organisms and a rise in the concentration ofmineral nutrients which stimulate the growth of algae and aquatic macrophytes. This isfollowed by further changes in the ecological system which manifest themselves visibly in thestructure and dynamics of the aquatic biotopes. This dependence of the colonization on theeffects of the biologically degradable, oxygen-consuming substances is the basis of biologicalwater quality monitoring and assessment (cf. Guidebook on Water Quality Surveys, Unesco/WHO,1978, and Hynes, 1960). With water pollution increasing, the following seven stages can beobserved:

3.5.4 Stages of biotic change

Stage 1Clean waters with a naturally limited supply of plant nutrients. Flow is rapid and turbulent.

The water is clear and always in a state approaching oxygen saturation. The water is cool, evenin summer, especially in temperate latitudes and altitudes. Colonization is sparse, ormoderately dense at best. It includes long-living algae, in particular red and blue-green algae(e.g. Batrachospermum, Hildenbrandia, Lemanea, Calothrix parietina and Phormidium inundatum).

Various diatoms and moss species, as well as animals such as Planaria alpina, and insects (stonefly and caddis fly larvae) may be found. The larvae have external gills and their cycle ofdevelopment may last from one to several years.

The nutritional basis of the animals consists primarily of washed-in plant material that isrich in cellulose content. These waters are spawning grounds for salmonids whose survivaldepends particularly on the availability of an adequate oxygen supply.

Stage 2The same basic characteristics as those of stage 1, i.e. rapid and turbulent flow and cool waterin summer. Slightly increased inflow of inorganic nutrients and small quantities of organic,

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biologically degradable substances leads to denser colonization and greater species variety.This occurs, e.g. with the inflow of small volumes of domestic sewage which do not causesignificant reductions in the oxygen content. At this low concentration, the influence ofputrescible organic substances manifests itself after a short distance of self-purificationprimarily as a fertilizing effect. The presence of filamentous green algae (e.g. Ulothrixzonata) and of certain diatoms (e.g. Meridion circulare) in the community is particularlyevident. Insect larvae with external gills but small gill surfaces, such as mphinemoura, Perlamarginata, some caddis, stone and ephemeral fly larvae, predominate. The development cycle ofthe animals is usually one year. The nutritional base of the animals consists of autochthonousmaterial (algae and moss) .

These reaches are also of importance as spawning grounds for salmonids and other fishrequiring clean, well oxygenated water.

Stage 3The current in these streams ranges from rapid to slow. In summer, the water may be either coldor warm. The degree of pollution by oxygen-consuming substances occurs under natural conditionsif the drainage area offers a rich nutrient supply.

The higher temperatures cause more intensive biological activity. Moderate pollution byorganic, biologically degradable substances is quickly reduced by the self-purification process.

The degradation products have a stimulating effect on plant growth so that locally limiteddeposition of silt with autochthonous organic substances may occur at certain points. Oxygenconsumption during biological degradation is low but there are marked diurnal variations inoxygen content caused by photosynthesis and plant respiration. Aquatic plants may cover largeareas of the water surface, at least during' the main growing period. The biomass of the algaeis considerable; in slow-flowing streams, the water may be turbid as a result of the massdevelopment of planktonic algae.

All important groups of fresh water algae occur in this zone. The outstanding characteristics, however, are the great variety of species, and in temperate climates there is a changeof species during the year. Spring with cool water and low light intensity: diatoms; summerwith warm water and high light intensity: green algae; autumn with relatively warm water andlow light intensity: decrease in the number of green algae and renewed increase in the diatoms;winter with cool water and low light intensity: decrease in the number of all autotrophic plants.

The animals also reach maximum species variety in this zone, and it is characteristic thatmany kinds of snails, small crustaceans and insect larvae reach high population densities. Mostinsect larvae have exterior gills which offer a large surface area for gaseous exchange. Two ormore generations per year may be produced. Due to the rich supply of vegetable food (algae,macrophytes), grazers and filter-feeders predominate. Of the predatory animals present, mostare insects and their larvae, in particular dragon-flies.

As a result of the rich stock of fish food organisms and the good oxygen supply, this zoneis highly productive and used for spawning by salmonids and cyprinids.

Stage 4Continued increase in the pollution by oxygen-consuming substances leads to a condition of'critical pollution 1 . It is characterized by a wide amplitude between maximum and minimumoxygen concentration. These waters usually support a dense growth of algae and'aquaticmacrophytes. Among them, and on the solid substratum, live many filtering organisms, detrituseaters and grazers. Predacious species (leeches, beetles, water bugs) will occur. Stone flylarvae and other animals adapted to a permanently high oxygen content of the water are lacking.Generally speaking, there is less species diversity than in Stage 3. A few forms, on the otherhand, show a tendency towards mass development. As a rule, the cycle of development is short,

many species producing several generations in a year.The rich supply of organic substances leads to intensive bacterial activity and the highrate of self-purification is associated with a high rate of oxygen consumption. Mineralizationof organic substances leads, at the same time, to an increase in the nutrient supply so that theaforementioned mass development of algae and macrophytes can take place. Heavy oxygen super-saturation in daytime alternates with a marked reduction in oxygen concentration at night.Under unfavourable conditions, the oxygen content of the water may drop, especially in the earlyhours of the morning, to a point where fish may be killed even though surface waters of thisstage often are high yield fish waters.

To cope with the wide amplitude of oxygen concentrations many of the insect species (e.g.beetles and predatory bugs) have organs for extracting oxygen from the atmosphere and are airbreathers. Other characteristics are the occurrence of many ciliates which feed primarily onbacteria, and the development, already visible with the naked eye, of small colonies of the so-called sewage fungus (Sphaerotllus natans).

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Stage 5Further increase in pollution by waste water containing organic, biologically degradablesubstances usually results in milky turbidity. Bacterial activity is so intensive that lowoxygen concentrations predominate.

Aquatic macrophytes and algae may be present in sufficient numbers to influence the oxygenbudget, but they do not visually dominate. Extensive colonies of sewage fungus can be observedwith associated populations of bacteria and ciliate protozoans. Only a few species of animalscan tolerate the low oxygen content but these, as a rule, have a high population density. Theyare animals of little sensitivity to oxygen scarcity, such as isopods, leeches and sponges.Blood worms (Chironomus thummi) and sludge worms (Tubifex sp.) whose blood pigment allows themto store oxygen and to make optimum use of low oxygen concentrations, settle on the digestedsludge deposited in this zone.

The larger animals are mostly predatory (eg leeches and diving beetles).At this level of extreme adaptation, it is not only the oxygen concentration which plays a

dominating role in the selection of the species. A complex of diversified effects is alreadyapparent. With decreasing oxygen content, the concentration of intermediate products ofbiological degradation, such as ammonium, nitrite and hydrogen sulphide, increases. Thesesubstances can either consume oxygen by further oxidation or they can have toxic effects, atleast in higher concentrations (hydrogen sulphide), i.e. non-toxic ammonium (NH4) changes intotoxic ammonia (NH3) at high pH values.

While fish life is still possible under these conditions, the yield is poor and periodicfish kills occur.

Stage 6Heavier pollution leads to a high degree of turbidity and to increased concentrations of noxiousmetabolic products of microbial degradation, with the result that the living conditions of macro-organisms are severely limited. Autotrophic plants do not occur and the biogenous oxygen supplyis lacking. The bottom of the river is covered by digested sludge on which only a few speciesare living; these', however, occur frequently in large numbers. They feed almost exclusively ondetritus. Tolerance to low oxygen concentrations is ensured by possession of haemoglobin(eg blood worms, sludge worms), or else oxygen is taken from the atmosphere, eg the larvae of

Eristalls tenax which have a breathing tube that can be expanded to a length of 15 cm and bymeans of which they can reach the air above the water surface. The predacious macro-organismsrather frequently encountered in the preceding stage now occur only sporadically.

Fish cannot develop under these conditions, at best, they can briefly stay at favourablepoints.

Stage 7With even heavier excessive pollution by oxygen-consuming waste water constituents, putrefactionprocesses prevail. The water is very turbid and usually smells clearly of hydrogen sulphide.Life is reduced to bacteria, colourless flagellates and ciliates feeding on bacteria. A typicalfeature is the mass occurrence of sulphur bacteria which can assimilate sulphur compounds orhydrogen sulphide. Autotrophic organisms and fish are not present.

REFERENCES

American Public Health Association, 1971. Standard methods for the examination of water andwastewater, 13th ed., New York, 769 p.

Bennett, J. P. and Rathbun, R. E., 1972. Reaeratioh in open-channel flow, Geological SurveyProfessional Paper 737, United States Government Printing Office, Washington.

Camp, T. R., 1963. Water and its imparities, New York, Reinhold Book Corp., 355 p.

Dobbins, W. E., 1964. BOD and Oxygen Relationships in Streams, Proc. Am. Soc. Civil Engrs, J.Sanit. Eng. Div., 90, pp 53-78.

Edwards, R. W. and Owens, M., 1965. The oxygen balance of streams, Fifth Symposium BritishEcol. S o c , Oxford, Blackwell Sei. Pubs., p. 149-172.

Edwards, R. W. and Rolley, H. L. J., 1965. Oxygen consumption of river muds, Jour. Ecol.,v. 53, Mar., p. 1-19.

Elder, J. W., 1959, The dispersion of marked fluid in turbulent shear flow, Journal of FluidMech., vol. 5, p. 544-560.

Fick, A., 1855. Ann. Phys. hpz., vol. 170, no. 59.

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Fisher, H. B., 1966. Longitudinal dispersion in laboratory and natural streams, W. M. KeckLaboratory of Hydraulics and Water Resources, Report no. KH-R-1, California Institute ofTechnology.

Fisher, H. B., 1967. The mechanics of dispersion in natural streams, Journal of the HydraulicsDivision, vol. 53, no. HY6, p. 187-216.

Fisher, H. B., 1968. Dispersion predictions in natural streams, Journal of the SanitaryEngineering Division, ASCE, vol. 84, no. SA5, p. 927-943.

Fourier, J. B., 1822. Theorie analytique de la chaleur, Oeuvres de Fourier.

Himmelblau, P. M. and Bischoff, 1968. Process Analysis and Simulation, John Wiley, New York.

Holley, E. R., 1971. Transverse mixing in rivers, Part I, Delft Hydraulics Laboratory, S132.

Holley, E. R., 1973. Diffusion and boundary layer concepts in aeration through liquid surfaces.Water Res., T_, 559-573.

Hull, C. H. J., 1969. Discussion of management and measurement of DO in impoundments, Am. Soc.Civil Engineers Jour., v. 95, no. SA-1, p. 158-178.

Hynes, H. B. N., 1960. The Biology of Polluted Waters, Liverpool University Press, Liverpool.

Klein, L., 1962. River Pollution, Butterworth, London.

Kranck, K., 1974. The role of flocculation in the transport of particulate pollutants in the

marine environment, Proceedings of the International Conference on Transport of PersistantChemicas in Aquatic Ecosystems, Ottawa, Ontario, Canada.

Krishnappan, B. G., Lau, Y. L., 1974. Transverse dispersion in meandering channels, Proc.International Conference on Transport of Persistent Chemicals in Aquatic Ecosystems, Ottawa,Ontario, Canada, p. 1-17 - 1-23.

Lau, Y. L., 1972. A review of conceptual models and prediction equations for reaeration in openchannel flow, Tech. Bull. 61_, Inland Waters Branch, Department of the Environment, Ottawa,Ontario, Canada.

Lau, Y. L., 1975. An experimental investigation of reaeration in open-channel flow, Progress inWater Technology, vol. 7, nos. 3/4, pp 519-530.

Newsome, D. H., Bowden, K. and Green, J. A., 1971. A Mathematical Model of the Trent RiverSystem, Symposium on the Trent Research Programme, Inst, of Water Pollution Control, Nottingham.

Owens, M. and Edwards, R. W., 1963. Some oxygen studies in the River Lark, Soc. for WaterTreatment and Exam., P r o c , vol. 12, p. 126-145.

Parkhurst, J. D. and Pomeroy, R. D., 1972. Oxygen absorption in streams, J. Sanit. Engng. Div. ,Am. Soc. Civ. Engrs., 98, SAl, 101-124.

Pescod, M. B., 1969. Photo synthetic oxygen production in a polluted tropical estuary, Jour.Water Pollution Control Fed., v. 41, no. 8, p. R309-R321.

Prandtl, L., 1952. Essentials of fluid dynamics, Blackie and Son Ltd., Glasgow, Scotland.

Sayer, W. W., 1973. Natural Mixing Processes in Rivers. In: Shen, H. W. (ed.)., EnvironmentalImpact on Rivers, published by H. W. Shen, P.O. Box 606, Fort Collins, Colorado, USA.

Shen, H. W. and Cheong, H. F., 1973. Dispersion of contaminated sediment bed load, Journal ofthe Hydraulics Division, ASCE, vol. 99, no. HY11, p. 1947-1965.

Streeter, H. W. and Phelps, E. B., 1925. A study of the pollution and natural purification ofthe Ohio River, Public Health Bull. No. 146, Washington, US Public Health Service, 75 p.

Taylor, G. I., 1954. The dispersion of matter in turbulent flow through a pipe, Proc. R. S o c ,vol. A223, p. 446-468.

Thomann, R. V., 1972. Systems Analysis and Water Quality Management, McGraw Hill, New York.

Unesco/WHO, 1978. Water Quality Surveys. Unesco, Paris, and WHO, Geneva, Studies and reportsin hydrology, No. 23.

Unesco, 1981. (in press) . Relationship between water quality and sediment transport. Paris,Unesco, Technical Papers in Hydrology.

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Warn, A. E. and Brew, G. F., 1980. Mass Balance, Water Research, Vol. 12.

Whitehead, P. G., Young, P. C. and Hornberger, G. E. , 1979. A systems model of flow andwater quality in the Bedford Ouse River system, Part I Streamflow Modelling, Water Research,Vol. 13 , pp 1155-1169.

Whitehead, P. G., Beck, M. B. and O'Connor, P. E. , 1981. A systems model of flow and waterquality in the Bedford Ouse River system, Part II Water Quality Modelling, Water Research,Vol. 15, pp 1157-1171.

Whitehead, P. G., 1981. Operation Management of Water Quality in River Systems, Institute ofHydrology Report.

Wilson, G. T. and Macleod, N., 1974. A critical appraisal of empirical equations and models forthe prediction of the coefficient of reaeration of deoxygenated water, Water Res. 8, 341-366.

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4 Characteristicsof lakes a n d reservoirs

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4 .1 INTRODUCTION

To unders tand the e ffec t s o f po l lu tan t s on l akes and rese rvo i r s , some account has to be t akenof the i r genera l charac te r i s t i c s and p rop er t i e s . In the space permi t t ed here on ly the bas icfea tu res can be desc r ibed ; fo r de ta i l ed i n format ion the reader i s r e fe r red to more ex tens iv etex t s (Hutch inson 1957 , Rut tne r 1 962 , Dussa r t 19 66 , Lowe McConne l l 1 966 , Gol te r man 1 9 7 5 ) .

Lakes and rese rvo i r s a re typ ica l ly s t and i ng wat e r s , the fo rmer na tu ra l ly occur r ing and th ela t t e r man-m ade . They exh ib i t a vas t r ange o f su r face a re as , vo l umes , dep ths and wate rre ten t i on t imes . Many lakes have enormous ly long re ten t i on t imes , o f te n measu red in hund redsof years whi le mos t r ese rvo i r s have re ten t ion t imes cons iderab ly l e s s . M a n y r e s e r v o i r s w i t hvery shor t r e ten t ion t imes possess some of the charac te r i s t i c s o f r ive rs , e .g . hor izon ta lg rad ien t s in chemica l pa ramet e rs and wate r cur re n t s . Or lob (1969) dev i sed an index todesc r ibe how c lose a body of wa te r i s to the r ive r i ne o r l acus t r ine s i tua t ion . The h ighe r theva lue o f the index the c lose r the body of wa te r i s to behav i ng l i ke a r ive r and no t exh ib i t in gthermal s t ra t i f i ca t ion .

Fr --Mwhere Fr = S t ra t i f i ca t ion index

L = Leng th of wat er body (m)

d = Avera ge dep th (m)Q = Avera ge d i scharge f rom wate r body (m / s)V = Volume (m 3 )

Three examples o f the index a re g iven in Tab le 4 .1 .

Tab le 4 .1 Three examples o f the app l ica t i on o f Or lob ' s (1969) equa t ion fo r de te rmi n ing thes t ra t i f i ca t io n index Fr ( f rom M Markows ky - pe rson a l communic a t ion)

R e s e r v o i r

Hungry Horse

L a k e R o o s e v e l t

W e l l s ( 2 )

Length

m

4.7 x IO 1*

2.0 x I O 5

4.6 x 10 1*

Meandepth

m

70

70

26

Discharge tovolume ratio

sec"

1.2 x 10~_ 7

5.0 x 106.7 x 1 0 - 5

Fr

0.0026

0.46

3.8

Comments

Stratified

Weakly stratified

Completely mixed

(1) Montan a , USA(2) Columbia Ri ver, USA

Because o f c l imat ic cond i t ions , evapora t ive losses can have an in tens ive in f luence onsha l low lakes pa r t i cu la r ly so in a r id o r semi-a r id reg ions . I f the re a re no na tu ra l o u t f lo wsla rge changes in wa te r l eve l can occur. In con t r as t , man-m ade rese rvo i r s usua l ly have a

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regulated outflow and depending on their use and the climatic conditions may experience nodrawdown at all or a regular draw-down/refill regime. This leads to differences in thebehaviour of lakes and reservoirs, referred to later.

There are two main types of reservoirs:1. Those created by damming a river and flooding its valley.2. Those created by constructing an artificial basin and filled by pumping or gravitation.Both types of reservoir can be used for several purposes, e.g.1. Reservoirs primarily intended to store water in times of plenty for use for drinkingor irrigation during times of shortage. These reservoirs may be operated on a 'put and take"basis, i.e. being maintained at top water level by matching demand for supply with abstractionfrom the raw source or be filled during the wet season and drawn down during the dry season.2. Flood control reservoirs. These usually have a controlled falling water level duringthe major part of the year so that there is sufficient storage capacity to accommodate floods.In extreme cases, the reservoir may be filled in a few days .3. Pumped storage reservoirs are used for power generation and may be filled and emptiedon a 24-hour cycle.4. Power station reservoirs are usually kept at top water level so as to ensure constantpower generation or cooling.5. Reservoirs for recreation usually require a constant water level.

4.2 PHYSICAL AND HYDRAULIC CHARACTERISTICS

4.2.1 Thermal stratification

It is convenient to begin by considering a lake in a temperate region in spring when theentire body of water is at a uniform temperature, at or slightly above 4C, the temperature ofmaximum density. Increasing solar radiation warms the surface layers and currents set up bywind stress on the water surface generate turbulent motion leading to mixing and downwardtransport of heat. In all lakes of sufficient depth, heating in the spring from a lowtemperature, the water tends to become divided into an upper region of more or less uniformlywarm, circulating turbulent and illuminated water termed the epilimnion, and a deep, coldrelatively undisturbed and dark region termed the hypolimnion. The two layers are separatedby a relatively narrow layer of water of rapidly decreasing temperature with depth termed themetalimnion. This development reaches its peak in summer and is called the summer stratification.

During the autumn thereis no

gain in heat and the lake begins to cool. There is asteady increase in thickness of the epilimnion as its temperature falls and initially thedeeper layers of the hypolimnion may be hardly disturbed. As the cooling proceeds, theepilimnion finally includes the whole lake which is then in full autumnal circulation. Thisevent is called the autumnal or fall overturn. The lake may continue to circulate throughoutthe winter at low temperatures but if prolonged ice cover develops, it is possible to developan inverse stratification where colder, less dense water may overlie water at 4C. Thissituation may prevail until spring or ice-melt when the water is once again isothermal andfreely circulating. This event is called the spring overturn. The whole cycle is illustrateddiagrammatically in Figure 4.1.

Hutchinson and Loeffler (1956) have classified lakes according to their thermal behaviourand recognised six main categories:1. Cold Monomictic - usually polar, sub-polar or high mountain lakes with full circulationonly in summer usually being free from ice for only a short period.

2. Dimictic -temperate lakes with full circulation in spring

andautumn, stratified

insummer. (This type is described in detail above).3. Warm Monomictic - sub-tropical lakes, stratified for most of the year, full circulationin early winter.4. Oligomictic - small or very deep lakes where a very small temperature difference betweentop and bottom surfaces maintains stable stratification. The lake circulates only atrare, irregular intervals when abnormal cold spells occur.5. Warm Polymictic - tropical lakes receiving solar radiation during the day but back-radiating at night 'allowing nocturnal mixing.6. Cold Polymictic - lakes at great altitudes, no permanent stratification develops, mixingat night.

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caioo

idoH

PO

-H"O

(Ptu

a&

yo

O

oCD-

fNO o^

C

O cE

>.

.Q

.U

i

!

cn/o

\

6

\

Vi\

V

1

\

1i!

'

cocEO ti

.oo.yO

o

3

ooI-ida5tdarHaeH

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4.2.2 Water movement

In general, current systems in lakes are of two kinds. The first is periodic and generally dueto the disturbance of the lake by wind forces or atmospheric pressure causing an oscillationof the lake or part of it. If a wind that has piled up water at one end of the lake suddenlydies down, a current will flow momentarily restoring the lake to its former level. Thecurrent will not have lost its energy and will continue, piling up water at the oppositeend of the lake. This current or seiche constitutes an oscillation about a nodal line. Aswith other oscillating systems there is a tendency for harmonics to form and seiches maybe multi-nodal.

The second kind of current is non-periodic, generated by external forces namely theinfluent-effluent system of the lake, unequal heating, the entry of dissolved material fromthe sediments and variations in atmospheric pressure and winds. Special problems arise invery large lakes where the Coriolis force (an inertial current imposed by the earth'srotation) is of significant influence. One of the effects is the existence of a vertical'thermal bar' between warm, inshore waters and cold, offshore waters. For details see

Murthy and Blanton (1975) and Rodgers (1968). An example of the effect of the influent-effluent system of the lake has been described by Hutchinson (1957) for Lake Constance wherethe course of the River Rhine through the lake has been tracked (see Figure 4.2) .

Special problems with the behaviour of incoming water may also arise in reservoirsespecially but not exclusively in the narrow, elongated river impoundment type. If thereis a pronounced temperature (and density) difference between the influent and the reservoir,the incoming water may plume across the surface or flow along the bottom. In either caseshort-circuiting of the system will occur and many of the benefits of storage will be lost.Uhlmann (1975) gives a schematic view of the basic flow and stratification patterns ofreservoir water (Figure 4.3) . Flow phenomena influence retention time so there may be largedifferences between the theoretical and actual retention times in reservoirs.

Further problems due to temperature may arise depending on the position of the reservoiroutlet. The demand placed on a reservoir to provide water affects the water level, thedynamics of the impounded water and the conditions downstream of the reservoir. If thereservoir outlet is close to the surface, the river downstream will receive warm water insummer and cold in winter. From deep stratified reservoirs with outlets at the bottmm,cold hypolimnetic water may be released continuously thus providing a habitat downstream forcold "water adapted fish.

In pumped storage reservoirs, temperature regime and stratification depend to aconsiderable degree on the mode of operation. Conditions in shallow reservoirs for drinking

water supply correspond to those in natural lakes. In deep pumped storage reservoirs usedfor power generation, there may be no stratification because of the rapid flow through ofwater.

4.3 CHEMICAL AND BIOLOGICAL CHARACTERISTICS

Information on the general chemical composition of lakes and reservoirs can be obtained fromthe basic texts referred to in the introduction to this chapter. Although many elementshave been shown to be essential for aquatic life this chapter will concentrate on phosphorusand nitrogen as the main chemical factors influencing primary production. The complexityof the cycling of elements within aquatic ecosystems can be seen in Figure 4.4.

Thermal stratification in standing water-bodies strongly influences the biology andchemistry. The epilimnion is usually well illuminated (euphotic) and, given sufficientnutrients such as nitrogen and phosphorus, planktonic algae develop and grow. The epilimnion

can then also be said to be trophogenic. Where extensive growths of algae occur there maybe increases in the pH as the carbon dioxide and bicarbonate ions in solution are convertedto organic matter. Diurnal fluctuations in dissolved oxygen concentration may also occur.Most of the organic matter produced in the epilimnion falls into the dark, cool hypolimnion.Consumption and conversion of this rain of particulate matter is effected by animals andbacteria. This process can be likened to the self-purification system occurring in rivers.However, in the hypolimnion the supply of oxygen is strictly limited and it is possible forthe decomposition processes to use up the available oxygen, producing anaerobic conditions.Unless man intervenes to prevent or ameliorate this situation,there will be no replenishmentuntil next circulation or turnover.

The intensity of photosynthetic activity varies enormously as can be seen in Figure 4.5taken from Tailing (1965). An example of intense deoxygenation occurring in the hypolimnionis shown in Figure 4.6. The graphs show that for approximately 7 months the hypolimnion was

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Figure 4.2 Ordinary disposition of surface currents in Lake Constan ce. Dotted lineindicates typical course of the Rhine (from Hutchinson, 1957)

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Inflow

Spring

Outf low

S u m m e r

.JUL? Dispersion Stratification

Winter

Figure 4.3 Schematic diagram of flow and stratification patterns in a reservoir (fromUhlmann, 1975)

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DissolvedOrganic- N

biodgradationA m m o n i a - N

biodgradationexcretion.

Detritus - N

death and faecesdea th and faeces

Zooplankton- N

Zooplankton- P

death and faeces

grazing

oxidationNitrite - N

oxidationuptake

Nitrate - N

Phytoplankton- N

Phytoplankton- P

death and faeces,

Detritus - P biodgradation

uptake

Orthophosphate -P

Figure 4.4 Nitrogen and phosphorus cycles in aerobic aquatic ecosystems (from Watanabe, 1978)

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J_ * s s e

depth

depth

density ofalgal cropas chlorophyll g_

( m g / m3 )

photosyntheticactivity per

unit volume

( m g 02 / m ^ h )

50 0

W I N D E R M E R E

photosyntheticactivity per

unit area( m g 02 / m 2 h )

L. VICTORIA

Figure 4.5 Comparative measures for the seasonal diatum maxima in Windermere (14th May 1959)and Lake Victoria (3rd August 1961) of depth profiles, of population density,depth profiles of photosynthetic activity and of derived estimates of photosyntheticactivity per unit area (from Tailing, 1965)

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aLakeKariba Isotherms

Figure 4.6 Seasonal changes in water temperature and dissolved oxygen in Lake Kariba 1960-1963.The H2S zone in 4.6b indicates oxygen less than 1 mg 02/litre (from Lowe-McConne ll,1966)

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almost entirely anaerobic, allowing poisonous hydrogen sulphide to be formed.This interaction between lake morphology, hydrology, chemistry and biological activity

permits the construction of a lake classification (or typology) scheme. It is an acceptedfact that this is essentially a subjective classification without clear definitions ofborderlines of change.

In this system we have, on one hand, oligotrophia lakes which are usually clear anddeep with low concentrations of nutrients and little plankton activity. Bioproduction andother bioprocesses have little influence on ionic equilibrium and chemical concentrations.At the end of the stratification period the hypolimnion will still have well oxygenated conditions ( 70% of saturation).

On the other hand, eutrophic lakes may be turbid because of suspended plankton withsecchi disc visibility of less than 2m deep. High concentrations of nutrients stimulateintense activity of phytoplankton producing supersaturation of oxygen in the epilimnion.At the end of the stratification period the oxygen concentration in the hypolimnion mayvary from 0-30% of saturation.

Excessively eutrophic lakes have been described variously as polytrophic, hyper-eutrophicor hypertrophic. Some characteristics of hypertrophic lakes are the presence of hydrogensulphide in the totally anaerobic hypolimnion and massive developments or blooms of algaeat the surface.

The intermediate phase between oligotrophic and eutrophic may be termed mesotrophic.On the basis of data collected from a large number of lakes worldwide, Vollenweider, 1968,

1975) has produced a series of correlations aimed at defining and predicting the trophicstate of a body of water within certain limits or probability. One such prediction isshown in figure 4.7 which relates the average chlorophyll concentration in a body of waterto the phosphorus load imposed upon it taking due account of retention time and mean depth.

One of the outcomes of a worldwide research programme coordinated by OECD is thatdefinite limits have now been proposed for the trophic categories described above. Thelimits are based on average phosphorus concentration, mean and maximum chlorophyllconcentrations and mean and maximum secchi disc transparencies (Vollenweider& Kerebes, in press).

Any lake or reservoir can be divided into several zones or biotopes which differmarkedly in their biological characteristics.

The littoral zone (Figure 4.8) is shallow and illuminated and characteristicallyinhabited by aquatic plants if the substratum permits. Obviously sand, clay or silt marginswill support a richer flora than igneous rock. The littoral is often richly productivebeing inhabited by snails, insect larvae and worms. It is an important feeding ground forwater birds and an important spawning ground for fish. In a shallow lake or reservoir itmay play a dominant role.

Below the littoral lies the benthal zone which may well be illuminated and productivein its upper part and dark and non-productive in its lower. It is an important habitat foralgae and bacteria and protozoa, worms and insect larvae are often to be found in abundance.

The main water mass is termed the pelagial and in most lakes is the dominating biotope.The upper, illuminated trophogenic zone is the habitat of phytoplankton - microscopic algaeadapted to a floating life. Feeding upon them, or each other or any suspended particlematter are the floating animals or Zooplankton. The level of primary productivitydecreases with depth until a certain point is reached where destructive processes equalthe productive processes and this may be termed the compensation depth. Below this isthe tropholytic zone where the organic m