modelling pesticide run-off to surface waters. part i: model theory and development

Pestic. Sci. 1998, 54, 113È120

Modelling Pesticide Run-Oþ to Surface Waters.Part I: Model Theory and DevelopmentRichard J. Williams

Institute of Hydrology, Wallingford, OXON OX10 8BB, UK

(Received 2 March 1998 ; revised version received 4 June 1998 ; accepted 3 July 1998)

Abstract : A conceptual model is presented to estimate the concentrations ofpesticides appearing in surface waters following their application as part of agri-cultural production. The model has been formulated particularly to deal withsoils that are prone to bypass Ñow and require artiÐcial sub-surface drainage.Pesticide concentrations and loads can be calculated at Ðeld drainage outlets orfor whole headwater catchments. The data required to run the model are gener-ally readily available from published sources (within the UK) and these datahave been detailed. The assumptions made in the model are stated and the limi-tations with respect to the general applicability of the model are discussed.

1998 Society of Chemical Industry(

Pestic. Sci., 54, 113È120 (1998)

Key words : mathematical model ; pesticide ; surface water ; bypass Ñow; agricul-ture

1 INTRODUCTION

It has been reported that in water samples taken forpesticide analysis from 3500 sites within England andWales during 1992 and 1993, 100 of the 120 pesticidestargeted were detected.1 Generally, detections were atsmall concentrations and in the cases of the 25 pesti-cides for which environmental quality standards havebeen set,1 the latter were exceeded in less than 4% ofsamples. This same report goes on to highlight Ðve her-bicides (atrazine, diuron, bentazone, isoproturon andmecoprop) which regularly exceeded the EC DrinkingWater Directive limit of 0É1 lg litre~1. More important-ly, these exceedances are likely to have arisen fromdi†use sources following their approved use. Many plot,edge of Ðeld and small catchment experiments havebeen carried out in the UK2h4 and in the USA5 whichsupport this assessment. However, it should be notedthat in the case of atrazine (until 1992) and diuron,run-o† may have resulted from approved non-

Contract/grant sponsor : National Rivers Authority(Environment Agency).Contract/grant sponsor : Natural Environment ResearchCouncil.

agricultural use and that some run-o† in agriculturalareas may have resulted from chemical spills.4 There isa need, however, for methods of estimating likely pesti-cide concentrations in surface waters resulting from theapplication of chemicals in the normal course of agri-cultural production.

Mathematical modelling is becoming a more widelyused tool in estimating pesticide run-o†. Perhaps thebest-known model is GLEAMS (Ground waterLoading E†ects of Agricultural Systems6) which isintended to be used to compare the edge-of-Ðeld e†ectsresulting from di†erent agricultural management prac-tices. While the pesticide concentrations predicted byGLEAMS are realistic, it is not a predictive model but acomparative tool. In common with many pesticide fatemodels, GLEAMS originally took no account of thepossibility of bypass Ñow, lateral subsurface Ñow orÑow through sub-surface drainage systems. All of theseprocesses can contribute signiÐcantly to pesticide run-o†.3,4 However, recently GLEAMS has been modiÐedto include crack Ñow through clay soils.7 This has beenachieved through considering the shrinkage character-istics of the soil, i.e. the interaction between watercontent and soil volume. If rainfall is sufficient toproduce surface ponding and overland Ñow, crack Ñow

1131998 Society of Chemical Industry. Pestic. Sci. 0031È613X/98/$17.50. Printed in Great Britain(

114 Richard J. W illiams

may be initiated when cracks are predicted to bepresent. Water in the cracks moves straight through thesoil proÐle until it reaches a model layer where nocracks are present. This modiÐcation is reported to giveimproved simulations in cracking clay soils.7 The modi-Ðed GLEAMS still does not consider lateral sub-surfaceÑow or sub-surface drainage systems. Three recentlydeveloped models have demonstrated an ability topredict pesticide concentrations in soils where bypassÑow, lateral sub-surface Ñow or Ñow through sub-surface drainage systems might be expected to occur ;they are the models of Brooke, SoilFug and SWAT.8h11

The Brooke and SoilFug models are very similar,both being developments of the fugacity models ofMacKay.12,13 The models are essentially non-steady-state but equilibrium event models. They take intoaccount the disappearance of the chemical according todi†erent phenomena (degradation, volatilization, run-o†) but then calculate the partition among the di†erentphases of the soil using a level one fugacity model.SoilFug seeks to estimate the Ñow-weighted averageconcentration that occurs as the result of a whole rain-fall event while the Brooke model looks at changes at ashorter (hourly) time step to predict variations throughstorm events. The Ñow mechanisms described above arenot modelled explicitly in either model, but the hydro-logical response of the system is accounted for by usingactual measured (or estimated) run-o† amounts gener-ated during each rainfall event. Indeed, the originalmodel of Brooke assumed that all rainfall during anevent entered the stream and this gave rise to poor pre-dictions. A modiÐed version allowing for only a per-centage of rainfall to contribute to stream Ñow gavemuch better estimates, although the partially disso-ciated molecule, mecoprop, was still poorly simulated.14

The hydrological basis of SWAT is HOST(Hydrology of Soils Types15) which establishes a linkbetween UK soil types and the amount of water movingrapidly to streams in response to rainfall. Attenuationfactors, based on easily measurable physicochemicalparameters, describe the decrease in concentrations ofpesticide between Ðeld application and loss in run-o†water. The objective is to predict maximum concentra-tions in transient peaks of pesticide reaching surfacewaters as a result of individual rainfall events.

A more physically based, deterministic approach tomodelling solute transport through macroporous soilsis taken by two other leaching models, CRACK andMACRO.16,17 Both of these models estimate verticalleaching, but also estimate potential run-o† to surfacewaters at the Ðeld scale through simulation of surfacerun-o† and export through sub-surface drainagesystems.18 While both models explicitly model macro-pores and allow for exchange of water between macro-pores and the soil matrix, CRACK assumes that Ñowoccurs mainly in the macropores and that matrix Ñow isinsigniÐcant, while MACRO allows Ñow in both

domains. A full comparison of the two models is givenelsewhere.19

The model presented here seeks to include explicitly,at the small catchment scale, the hydrological pathwaysthat represent bypass Ñow, sub-surface lateral Ñow andÑow to sub-surface drains. These are the dominant pro-cesses in many UK agricultural soils. The Ñow paths forwater are treated as the main control on the arrival of apesticide at surface waters, while the physicochemicalproperties of sorption and half-life exert control overthe amount of pesticide available for transport. Themodel is based on a conceptualization of a drained soiland simulates Ñow rates and pesticide concentrationsover the main drainage season. The objective of thismodelling approach is to be able to simulate changes, atan hourly time step, in pesticide concentrations inwaters receiving run-o† through the course of individ-ual rainfall events. This allows both the peak and dura-tion of events to be estimated, thus allowing a betterestimate of any potential environmental impacts.

2 MODEL STRUCTURE

The model structure presented here was derived fromdetailed measurements of the soil water movement anddistribution in a drained Ðeld over successivewinters.20,21 Broadly, the study showed that an under-drained Ðeld consists of two types of soil proÐle whichare characterized by the rate at which they allow down-ward water movement. The bulk of the soil in the inter-drain position has a very small hydraulic conductivitywhich approaches zero when the soil is saturated ;downward water movement through the soil matrix istherefore very slow. The soil above the drains has amuch greater hydraulic conductivity and thus watermovement through the soil matrix in this part of theÐeld is much quicker. Thus, once the soil below thedrains is saturated and the drains begin to Ñow, thehydrological response of the drain is controlled by thesoil immediately above and adjacent to the drains.

A diagrammatic representation of the model is shownin Fig. 1. The model considers the top 2 m of the soilproÐle, which is divided into three layers above the levelof the drains and one below. Above the drain the layersare subdivided into two, representing the fast and slowparts of the soil proÐle described above. AgriculturalÐelds are generally sloping, and, in this conceptualiza-tion, the drain zone is considered to be down slope ofthe inter-drain zone. The consequent possible directionsof water movement are shown by the arrows in Fig. 1,where dotted arrows indicate the possibility of watermoving directly to lower layers (via macropores)without interacting with intervening layers. Thus, themodel allows explicitly for bypass Ñow to occur withinthe soil proÐle.

Modelling pesticide run-o†: theory and development 115

Fig. 1. Representation of the conceptual pesticide modelshowing the Ñow pathways between the soil boxes. Dotted

lines indicate the possibility of bypass Ñow.

The transport of pesticide in the system is assumed tobe associated with the water movement, with pesticidebeing re-partitioned between the soil and water phasesat the end of each time step (1 h). The model keepsaccount of the amounts of water and the dissolved andadsorbed pesticide in each box and calculates changesto these, depending on a mass balance of inputs,outputs and internal sources and sinks.

2.1 Water movement

To explain the details of water and pesticide movementit is best to consider a single box from the model (Fig.2). Let the subscript i be used to refer to one of theseven boxes in Fig. 1 above. The change in soil watercontent of box i, is given byS

i

dSi

dt\ q

i~1 [ qbpi] d

u[ q

i[ dl

i] qbm

i~1 (1)

where is the Ñow per unit area (mm) from box i ;qi

qbpi

is the Ñow from box i [ 1 that bypasses box i in cracksor macropores ; is the Ñow per unit area (mm) fromd

uan up-slope box, is the Ñow to a down-slope box ordl

i

Fig. 2. Flow paths contributing to the mass balance around asoil box.

stream and is the Ñow that was in bypass routesqbmi~1

in box i [ 1 that return to the soil matrix in box i ; t istime (hours). For the top two model boxes, 1 and 5, theinÑow to the box is rainfall minus evaporation. Flowmay only occur from box i, either vertically or later-(q

i)

ally when where is the Ðeld capac-(dli) S

i[ SFC

i, SFC

iity of box i. Flow from box i depends on the watercontent of box 1 and is given by

qi\ kv

i(S

i[ SFC

i)(1[ tan(a)) (2)

where (h~1) is a measure of the vertical conductivitykvi

of box i, and a is the average slope of the Ðeld (degrees).Similarly the down-slope drainage is given bydl

i

dli\ kh

i(S

i[ SFC

i)tan(a) (3)

where is a measure of the horizontal conductivity ofkhi

box i. Both the horizontal and vertical conductivitiesare assumed to vary with water content in a similarmanner,

kvi\ (S

i/SMAX

i)3SAT kv

i(4)

where is the horizontal conductivity when theSAT kvi

soil in box i is saturated. It is possible to set a minimumvalue for the conductivity which is used until such atime as it is exceeded by the value calculated by eqn (4).

A fraction of water may bypass a given layer throughmacropores and cracks. Some clay soils swell when wetand shrink on drying, resulting in di†ering macroporedensities through the season. Under rainfall conditionsthat result in ponding and overland Ñow, summercracks can result in increased bypass Ñow to depth. Themodel presented here is only for use in the drainageperiod when soil moisture levels will be sufficiently highto reduce cracking to a minimum and large macroporeswill be limited to those that occur due to old root chan-nels and earthworm burrows. Therefore,

qbpi\ CF

iqi

(5)

where is the macropore Ñow fraction in the ith box.CFi

The continuity of cracks through layers is given by theratio, to a maximum of unity. Thus, once inCF

i/CF

i~1a crack, water is assumed to remain there until thecrack ends. Hence,

qbmi\A1 [ CF

iCF

i~1

Bqbp

i~1 (6)

In general the number of bypass Ñow routes willdecrease with depth, thus some proportion of the crackswill end in various of the model boxes. As bypass Ñowroutes terminate, the water they are carrying is assumedto remix with the water in the soil matrix of the box inwhich they terminate.


Water may only enter a box if it is not saturated (ieis given by ;S

i\ SMAX

i) ; SMAX

i

SMAXi\ /

iVi

(7)

where and are respectively the porosity and/i

Vi

volume per unit area (mm) of box i. This is not the casefor water draining from boxes 3 and 7 into box 4 whenit is saturated. In this case water will displace thatalready in box 4 into the drainage system and thus gen-erate drainÑow.

2.2 Pesticide movement

Pesticide is added to the model by assuming that theamount applied is well mixed into the top layer of themodel (boxes 1 and 5, Fig. 1) and partitioned betweenthe soil and the soil water following a reversible instan-taneous linear sorption isotherm

PSi\ PW

i* k

di(8)

and

kdi

\ koc

OCi

(9)

where is the pesticide concentration in the soilPSi

phase (lg kg~1), is the concentration of the pesti-PWi*

cide in the dissolved phase (lg litre~1), is the parti-kdi

tion coefficient (litre kg~1) and is the partitionkOC

coefficient (litre kg~1) normalized for fractional contentof organic carbon, OC

i.

Assuming that each of the boxes in Fig. 1 is wellmixed, then the rate of change of mass of dissolvedpesticide in the ith box, is given by(S

iPW

i)

dSiPW

idt

\ (qi~1[ qbp

i)PW

i~1 ] duiPW

u

[ (qi] dl

i)PW

i] qbm

i~1PWbm

[ RdSiPW

i(10)

where is the dissolved pesticide concentration perPWi

unit area of the ith box, is the pesticide concentra-PWu

tion of water draining from an up-slope box, isPWbm

the concentration of pesticide in the bypass Ñow and Rd

is the Ðrst-order rate coefficient describing degradationof the pesticide. Water moving through bypass routes isassumed to have the same concentration as the soilwater in the box with which it was last in contact. Therate of change of mass of pesticide adsorbed onto thesoil is given by ;

dPSi

dt\ [R

dPS

i(11)

where is the soil-adsorbed pesticide concentrationPSi

per unit area in the ith box (lg kg~1). New concentra-tions of the pesticide are thus calculated for the end of

each model time step. These concentrations may not,however, be in equilibrium. Therefore, the total pesti-cide in each of the boxes is calculated from the dis-solved and solid-phase concentrations and thenpartitioned using eqn (8). These new equilibrium valuesare then taken to be the starting points for the nextmodel time step.

2.3 Drain Ñow

The model only allows drain Ñow when the deep soilbox, (box 4, Fig. 1) is at saturation. When this occurs,drain Ñow is the sum of the vertically draining waterfrom boxes 3 and 7 plus any water from rainfall andboxes 5 and 6 moving via bypass routes that are con-nected to the drain. Thus, for any time step in whichdrain Ñow occurs,

Df\ (q7] qbp7] qbp6] qbp5) f ] q3(1 [ f ) (12)

where is the drain Ñow (mm h~1) and f is the ratio ofDf

the enhanced conductivity area to the total area of arepresentative drainage element (see Fig. 1). Watermoving from boxes 3 and 7 is assumed to produce drainÑow by displacement of water from box 4, while waterin bypass routes is directly intercepted by the drain. Ifthe amount of water arriving at box 4 during a timestep is in excess of the saturation deÐcit in that box,then drain Ñow will occur but will be reduced by theamount necessary to satisfy the deÐcit. The pesticideconcentration of the drain Ñow, is given by a massD

p,

balance of the contributions from the various Ñowpaths. Note that it is possible for part of the rainfall tobypass the top box and proceed directly to the nextlayer. In practice however, the thin top layer is used inthe model as a mixing zone for incoming rainfall andapplied pesticide and therefore is assigned few macro-pores. This is very likely to be the case after the cultiva-tion of a new seed bed. Water with a potentially largeconcentration of pesticide may then bypass lower boxesto reach the drain directly. Water behaving in thismanner will, in the model, have a concentration equalto that of any overland Ñow that might be generated(see below).

Dp\

((q7PW 4] qbp7 PW 6] qbp6PW 5] qbp5PW

r) f ] q3PW 4(1 [ f ))

Df

(13)

where is the concentration of the pesticide in thePWr

rainfall (usually zero).

2.4 Stream Ñow

Stream Ñow is the sum of the lateral drainage fromboxes 5È7, drain Ñow and a base Ñow term, B

f


(mm h~1). is the value of the minimum stream ÑowBf

which occurs when all the soil boxes are dry. The modelassumes the dynamic response of the catchment is con-trolled by the upper soil layers and there is little or noconnection with the ground water. However manystreams from surface-water-dominated catchments areperennial, being sustained by springs resulting fromrecharge external to the surface water catchment, hencethe term The stream Ñow (mm h~1) during a modelB

f.

time step is given by

Sf\ D

f] (dl5] dl6] dl7] dl

r) f ] dl4] B

f(14)

Again the concentration of pesticide in the stream, isSo ,calculated from a mass balance of the contributionsfrom all the Ñow paths, thus,

Sp\

DfD

p] (dl5PW 5 ] dl6PW 6] dl7PW 7

] dlrPW 5) f ] dl4 PW 4] B

fB

pSf

(15)

where is the water entering the stream as overlanddlr

Ñow and is the pesticide concentration of the streamBp

base Ñow (often zero). Overland Ñow is generated whenthe water content of either box 1 or box 5 is calculatedto be in excess of the saturated value. This condition ischecked at each hourly time step and the amount ofoverland Ñow in that hour is set to the di†erencebetween the saturated and calculated values. The watercontent of the box is reset to the saturated value. Thewater content of box 1 or box 5 will be in excess of thesaturated value if, in any one time step, the amount ofrainfall less the evaporation exceeds the amount ofwater draining from the box plus any unÐlled porositybelow the saturated value. Water Ñowing overland frombox 1 will inÐltrate into box 5 if this box is not saturat-ed and overland Ñow from box 5 will enter the streamdirectly. The concentration of pesticide in the overlandÑow is assumed to be equal to the concentration of thebox from which it was generated.

3 MODEL ASSUMPTIONS AND LIMITATIONS

All models are based on a number of assumptionswhich will have a bearing on the circumstances in whichthe model can be applied. The assumptions implied inthis conceptualization are considered below. The limi-tations arising from these are then discussed.

(i) The model has been developed using data fromonly one Ðeld study and only this data set hasbeen used to test the performance of themodel.22 There is always a concern in such

cases that the conceptualization of the modelmay be speciÐc to a particular site. Further-more, the data required to run the model maynot be generally available and thus its usebecomes restricted. This last point is con-sidered below.

(ii) The model assumes that the soil proÐle can bemodelled as a series of linked, well-mixedboxes. In reality the concentration through thelength of the soil proÐle represented by a boxwill vary. For this reason the approach sug-gested here will not predict leaching depths forpesticides accurately. However, the approachshould give a good estimation of the pesticidethat is available to be removed from the proÐleat any given time after application.

(iii) The model is a lumped model, i.e. parametersare given a single value to represent an entirecompartment. There is no spatial variability inthe rate of movement of water and pesticide tothe catchment outlet, other than that allowedby the separation of the elements above andbetween the drains. Thus the size of catchmentthat can be modelled using this approach islimited.

(iv) The model assumes that the movement ofwater through the soil proÐle is predominantlydownward and should only be run for singledrainage seasons.

(v) Implied in the model conceptualization is theassumption that all, or at least an extensiveproportion, of the catchment is artiÐciallydrained. This further implies that the modelwould not be suitable to be used in situationswhere overland Ñow is the predominant sourceof entry into stream Ñow.

(vi) The conceptualization is based around acracking soil with macropores.

(vii) The model assumes that the pesticide sorbsreversibly onto the solid phase and thatchanges in pesticide concentrations can be re-equilibrated at the end of each model timestep.

(viii) The degradation of the pesticide, by whatevermeans, is assumed to be adequately describedusing a Ðrst-order decay rate. It is furtherassumed that degradation rates are constantthrough the drainage season.

(ix) The crop density is assumed to be sufficientlylow not to intercept a signiÐcant proportion ofeither rainfall or the applied pesticide.

(x) The hydrological year starts on 1 September,and it is assumed that soil water stores are attheir minimum at this time.

Of all the model limitations outlined above, the Ðrstthree are the most important ; (ii) and (iii) are basic


assumptions in the conceptualization of the model and(i) emphasizes the limited testing to which the model hasbeen subjected. The conceptualization can be con-sidered to be independent of location and will not a†ectthe general applicability of the model, other than in thesize of catchment that can be modelled as a singleentity.

Assumptions (vii) and (viii) are commonly used inpesticide modelling and reÑect the general availability ofdata to describe these processes. Assumption (iv) isagain a critical restraint on the use of the model. Themodel allows only for the downward movement ofwater and can thus be applied only to a soil proÐlewhich is draining. Therefore, any redistribution of pesti-cide that might occur due to the reversal of the waterpotentials caused by high evaporation cannot be model-led. In the UK, this means that the model should onlybe applied from late autumn to early spring. However,this time frame covers the hydrological conditions mostlikely to lead to pesticide run-o† and should not proveto be a practical limitation. The starting date for themodel is Ðxed assuming that 1 September is the start ofthe hydrological year ; in most years (and most locationswithin the UK) this assumption will hold. This assump-tion is made only in order to give a Ðxed starting pointfor the amounts of water held in the model boxes. If the

water contents of the seven boxes were known at agiven time in the year, these could be input as the initialconditions in the model and the simulation carried outas normal.

Only assumptions (v) and (vi) make speciÐc demandson the soil type and drainage within a catchment onwhich the model is to be run. The model containsparameters that may be used to alter the macroporosityof the soil and the extent of the drainage network so asto minimize the limitations of these assumptions.However, if the fraction of the catchment drained andthe macroporosity were to be set to zero, then careshould be taken to ensure that the model produces sens-ible results. One approach would be to compare thehydrographs produced by the model with observed data(these data are generally more readily available thanpesticide data).

4 DATA REQUIREMENTS

The data required to run the model are summarized inTable 1. The majority of these data are relatively easyto Ðnd, particularly within the UK. Soils data, forexample, are available from a personal computer basedsystem called SEISMIC at a resolution of 5 km2 and

TABLE 1Data Required to Run the Pesticide Run-O† Model

Data type Description Extent

Catchment Catchment area (ha)Area drained (ha)Slope (degrees) Catchment average to

surface waterBase Ñow (mm h~1) Single value for the stream

Meteorological Rainfall (ha) Hourly time seriesPotential Evaporation (mm) As above

Soil physical Depth of boxes representing soil For each soil layerproperties proÐle (mm)

Minimum water content (mm) For each of the seven modelboxes

Field Capacity (mm) As abovePorosity (%) As aboveBulk Density (kg litre~1) As aboveOrganic carbon content (%) As aboveMacropore volume (%) As above

Soil hydraulic Vertical Ñow rate parameter (h~1) As aboveproperties

Horizontal Ñow rate parameter (h~1) As aboveFraction of hydrological unit with Single value for the

enhanced conductivity catchmentPesticide Date For each application

application dataRate (kg AI ha~1) As aboveArea treated (ha) As above

Pesticide properties kd

or koc

(litre kg~1) For each pesticideHalf-life (days) As above


the data required for this model could be found fromwithin this system.23 The exceptions to this are theparameters describing the abundance of macropores inthe model boxes. A measure of this value, however,might be found from study of the low tension end of thewater release curve. Water tensions can be equated toapproximate pore sizes that will be holding water atthat tension ; macropores hold water only at low ten-sions.24 Choosing a suitably low tension to representmacropores of an appropriate size will enable the frac-tion of the porosity associated with macropores to becalculated from the area of the water release curve withtensions lower than the selected value. Pesticide physi-cochemical properties are readily available from anumber of reference works.22,26 It is noted, however,that caution should be exercised in using data derivedfrom Ðeld experiments conducted under conditions thatdi†er from the intended model application. It is invari-ably best to obtain Ðeld measurements of degradationrates from the catchment to be modelled.

Rainfall data and estimates of potential evaporationshould be available from local meteorological stations.These data are the driving variables for the model andthe frequency of their measurement will control themodel time step. Hourly data for rainfall and dailyvalues for evaporation are the shortest time step atwhich these data are readily available, hence the use ofan hourly time step in this model. In theory othermodel time steps could be used but this has not beentested. Often, however, model runs are used to estimatethe likelihood of leaching at speciÐc sites. In these casessynthetic time series of data can be used that reÑect thelocal meterorological conditions. Data about the catch-ment size and pesticide applications should be knownfor the particular model application.

The most difficult parameters to specify are those thatcontrol the horizontal and vertical movement betweenboxes. Because the model approach described here isconceptual in design, it is not possible to take the valuesof these parameters directly from measurable soilhydraulic parameters. However, the relative magnitudesof these parameters should be related to the soilhydraulic conductivity values and this will give somelimits in deÐning these values.

5 CONCLUSIONS

This paper has represented a conceptual model of pesti-cide run-o† to surface waters that may help address theneed for improved tools to aid in the assessment of therisk posed by the approved use of pesticides in agricul-ture. The aim of the model is to estimate the peak con-centration and duration of pesticide losses to streamsduring rainfall events following application to land. Themodel has undergone only limited testing on one catch-ment and as this catchment also contributed to the con-

ceptualization of the model caution would be needed inapplying it elsewhere. The majority of the model param-eters can be estimated from readily available data and,within the limitations discussed, the possibility existsthat the mode could be applied more generally.

ACKNOWLEDGEMENTS

The funding for this work was provided by the NationalRivers Authority (now part of the Environment Agency)and the Natural Environment Research Council whosesupport is gratefully acknowledged.

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