Vandenberghe Veronique*, Ann van Griensven**(***), Willy Bauwens** and Peter A. Vanrolleghem*

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1 PROPAGATION OF UNCERTAINTY IN DIFFUSE POLLUTION INTO WATER QUALITY PREDICTIONS: APPLICATION TO THE RIVER DENDER IN FLANDERS, BELGIUM. Vandenberghe Veronque*, Ann van Grensven**(***), Wlly Bauwens** and Peter A. Vanrolleghem* * Ghent Unversty, Department of Appled Mathematcs, Bometrcs and Process Control (BIOMATH) Coupure Lnks 653, B-9000 Ghent, Belgum (E-mal: veronque.vandenberghe@bomath.rug.ac.be) ** Unversty of Calforna Rversde, Dept. Envronmental Scences (Geology buldng), Rversde CA951, USA *** Free Unversty of Brussels, Laboratory of Hydrology and Hydraulc Engneerng, Plenlaan, B-1050 Brussels, Belgum ABSTRACT In ths paper the uncertanty of water qualty predctons caused by uncertanty on the nputs related to emssons of dffuse polluton s detected and analysed. An uncertanty analyss on the effects of dffuse polluton s essental to compare the cost and benefts of measures to lower those emssons. In ths research we focus on the effects of dffuse polluton due to fertlser use on ntrate n the rver water. Wth the use of an effcent Monte Carlo method based on Latn Hypercube samplng, the contrbuton to the overall uncertanty by each of the nputs s calculated. The modellng envronment used s ESWAT, an extenson of SWAT, the Sol and Water Assessment Tool, whch s developed at the Blackland Research Center, Texas. ESWAT was developed to allow for an ntegral modellng of the water quantty and qualty processes n rver basns. The dffuse polluton sources are assessed by consderng crop and sol processes. The crop smulatons nclude growth and growth lmtatons, uptake of water and nutrents and several land management practces. The nstream water qualty model s based on QUALE. The spatal varablty of the terran strongly affects the non-pont source polluton processes. GIS (Geographcal Informaton System(s)) s used to account for the spatal varablty. The methodology s appled to the Dender basn n Flanders, Belgum. A senstvty analyss showed eght nputs that have sgnfcant nfluence on the tme that the ntrate content n the rver s hgher than 3 mg/l. It s the start date of growth of pasture, the amount of fertlser appled on pasture, on farmng land and on corn dependng on the subbasn. The uncertanty analyss ndcated wde uncertanty bounds (95% percentle bounds dffers up to +/- 50 % from the average NO 3 predctons). It was seen that n perods of dry weather no uncertanty s propagated nto the results of ntrate n the rver water. Consequently those perods are useful calbraton perods for the pont polluton nputs. Keywords: Dffuse polluton, ntegrated rver basn modellng, rver water qualty, uncertanty analyss INTRODUCTION Recently the European Unon has approved the EU Water Framework Drectve (EU-WFD). Ths drectve clams that by the end of 015 a good status of surface water and a good status of groundwater should be acheved (EU, 000). To that end, the EU-WFD provdes several gudelnes for montorng the water bodes, leavng the practcal mplementaton to the local governments. To make sure that the new water polcy wll succeed, a profound analyss of the actual and future state of the water s necessary. In ths context, the evaluaton of emssons nto rver water wll be mportant. The effects of a polluton load nto the rver can be evaluated usng models. However, for several reasons those model outputs are uncertan (Beck, 1987). Model outcome uncertantes can become very large due to: nput uncertanty, model uncertanty, uncertanty n the estmated model parameter values and mathematcal uncertanty. Pollutants dscharged nto the rver at certan ponts can be measured by montorng the dscharge and the water qualty. Dffuse polluton sources on the other hand are dstrbuted along the rver and are very dffcult to montor. Therefore, estmatng and calculatng the dffuse polluton to a rver can be subject to large nput uncertantes. To optmally allocate the efforts necessary to reduce those nput uncertantes, t s useful to evaluate the senstvty of the outputs to the dfferent nputs. In ths study we focus on the dffuse polluton of ntrate n the water due to fertlser use. Wth the use of an effcent Monte Carlo method based on Latn Hypercube samplng (McKay, 1988), the contrbuton to the uncertanty by each of the nputs s calculated. The methodology s appled to the Dender basn n Flanders, Belgum. Ths paper s structured as follows: frst we dscuss the model envronment and gve a descrpton of the rver basn for the case study. Then the appled methodology, whch conssts of a senstvty and uncertanty analyss, s explaned. The next secton gves and dscusses the results and fnally conclusons are formulated. THE MODELLING ENVIRONMENT ESWAT ESWAT s an extenson of SWAT (van Grensven and Bauwens, 000), the Sol and Water Assessment Tool developed by the USDA (Arnold et al., 1998). ESWAT was developed to allow for an ntegral modellng of the water quantty and qualty processes n rver basns. The dffuse polluton sources are assessed by consderng crop and sol processes. The 10-91

2 crop smulatons nclude growth and growth lmtatons, uptake of water and nutrents and several land management practces. The n-stream water qualty model s based on QUALE (Brown and Barnwell, 1987). The spatal varablty of the terran strongly affects the non-pont source polluton processes. GIS (Geographcal Informaton System(s)) s used to account for the spatal varablty. Based on sol type and land use a number of Hydrologcal Response Unts (HRU s) can be defned. For each HRU, the ESWAT model smulates the processes nvolved n the land phase of the hydrologcal cycle, and computes runoff, sedment and chemcal loadng. Based on the areas of each HRU, the results are then summed for each subbasn. Atmospherc N fxaton (lghtnng and dscharge) Harvest fertlser fertlser Symbotc fxaton Manures, N wastes, N O and sludge NO 3 Dentrfcaton Ammona volatlsaton NO 3 - mmoblsaton Sol organc matter 95% total N Mneralsaton Immoblsaton NH 4 + Leachng NO - clay Fgure 1. The ntrogen cycle n ESWAT In terms of the ntrogen cycle, the three major forms n mneral sols are organc ntrogen assocated wth humus, mneral forms of ntrogen held by sol collods and mneral forms of ntrogen n soluton. Ntrogen may be added to the sol by fertlser, manure or resdue applcaton, fxaton by symbotc or nonsymbotc bactera and ran. Ntrogen s removed from the sol by plant uptake, leachng, volatlzaton, dentrfcaton and eroson. Fgure 1 shows the major components of the ntrogen cycle. Ntrate s an anon and s not attracted to or sorbed by sol partcles. Because retenton of ntrate by sols s mnmal, ntrate s very susceptble to leachng. In SWAT the algorthms to calculate ntrate leachng smultaneously solve for loss of ntrate n surface runoff and lateral flow. Fnally ntrate ends n the rver. THE DENDER IN FLANDERS, BELGIUM The catchment of the rver Dender has a total area of 1384 km and has an average dscharge of 10 m 3 /s at ts mouth. Fgure shows how the Dender basn s stuated n the Flanders. As about 90% of the flow results from storm runoff and the pont sources make very lttle contrbuton, the flow of the rver s very rregular wth hgh peak dscharges durng ntensve ran events and very low flows durng dry perods (Bervoets et al., 1989). The rver Dender s heavly polluted. Part comes from pont-polluton (e.g. ndustry) but also from dffuse sources of polluton orgnatng manly from agrcultural actvty. Although there s an unmstakable relaton between ntensve agrcultural actvty and the occurrence of hgh nutrent concentratons n the envronment, few precse data are avalable about the contrbuton of agrcultural actvty to the total nutrent concentratons. The data needed for the model mplemented n ESWAT were also very sparse and conversons had to be made to make the data useful for the model (Smets, 1999). To buld the model, the total catchment was subdvded nto 16 subbasns (Fgure 3). Input nformaton for each subbasn s grouped nto categores for unque areas of landcover, sol and management wthn the subbasns. Man sol classes are sand, loamsand, slty loam and mpervous areas. For landuse, 5 classes are mportant: mpervous areas, forests, pasture, corn (maze and corn) and land for common agrcultural use (crop culture, not corn). About 30% of the landuse s pasture, whle crop farmng represents ca. 50% of the landuse. METHODOLOGY A prevous study for the same knd of ntrogen leachng model (mplemented n SWIM) from arable land n large rver basns (Krysanova and Haberlandt, 001) showed that the relatve mportance of natural and antropogenc factors affectng ntrogen leachng n the Saale rver basn was as follows: (1) sol, () clmate (3) fertlsaton rate and (4) crop rotaton. Reducng the uncertanty on nputs for sol and clmate depends on better equpment to measure the dfferent varables and proper use of sophstcated mathematcal technques to nterpolate for places that are not measured. A lot of studes on that 10-9

3 subject already exst (Sevruk, 1986). Untl recently reducng the nput uncertanty relatng to fertlsaton rate was not studed. In Flanders new legslaton concernng fertlsaton applcaton was made n the late nnetes. Campagns to lst the fertlser use were then started and t s known that stll a large amount of nformaton s wrong or mssng. A lot of effort s stll needed to complete the nformaton. The evaluaton and quantfcaton of the mpacts of land management practces on ntrogen wash-off to surface water s therefore very mportant. Fgure. The rver Dender basn n Flanders Fgure 3. The rver Dender Basn, Denderbelle (o) and the subbasns) In ths study we focus on fertlsaton rate and tme of fertlser applcaton on the most mportant crops for the Dender rver basn. For the applcaton of fertlser for the dfferent land uses three applcaton dates were assumed; 1 st of March, 1 st of Aprl and 1 st of May. Also operatons as plantng and harvestng dates can be defned. Day and months were used to specfy the plantng and harvestng dates. Of course, those dates depend on clmate, crop and farmer. So assumptons had to be made concernng those dates. The output that was focussed upon was the tme that ntrate concentratons n the rver Dender at Denderbelle (near the mouth) were hgher than 3 mg/l. Data on fertlser and manure use are provded by The Flemsh Insttute for Land Use (Vlaamse Landmaatschappj,VLM). They provded data on the nutrent use and producton for each muncpalty n Flanders. In SWAT, one has to specfy for each subbasn the total amount of fertlser and the detaled composton of the fertlser. Some conversons of the suppled data had to be made so that they could be used n ESWAT. It conssted of recalculatons of the applcaton rates for each muncpalty to applcaton rates per subbasn (Smets, 1999). Further the same amount of fertlser on all crops was assumed for ths model. Ths s clearly dfferent from practce, but at ths stage, nsuffcent detals are avalable to specfy ths more realstcally. Frst, a global senstvty analyss s used to show what the most mportant factors are. Then the nfluence of uncertan data on the rver NO 3 concentratons tme seres s evaluated wth an uncertanty analyss. For both the same Monte Carlo sampled nputs could be used. The senstvty analyss focuses on the nputs, to rank ther mportance whle the uncertanty analyss assumes uncertan nputs and only consders and evaluates the outputs. Senstvty analyss The senstvty analyss (SA) technque used here s based on a mult-lnear regresson of the nputs on a specfc output. A Monte Carlo technque, Latn Hypercube samplng makes sure that the total range of nputs s covered. When the number of samples equals 4/3 tmes the number of nputs such a samplng s suffcent to perform a relable SA (McKay, 1988). For the samplng of the nputs and the analyss of the outputs, a program was wrtten to couple UNCSAM, the program used for the SA (Janssen, 199) wth the management nput fles of ESWAT. We used the standardsed regresson coeffcent (SRC) as an ndcaton of the relatve mportance of the dfferent nputs. SRC = y / S x / S y x wth y / x = change n output due to a change n an nput factor and S y, S x the standard devaton of respectvely the output and the nput. The nput standard devaton S x s specfed by the user. The orderng of mportance of the nput factors based on that statstc s as good as the assocated model coeffcent of determnaton R of the whole mult-lnear regresson. The closer R s to 1, the better the results. When the nput varables are lnearly related, the applcaton of a lnear regresson can lead to an accuracy problem, the collnearty problem (Hockng, 1983). The Varance Inflaton Factor (VIF) s consdered to be a useful measure to detect collneartes. The VIF s defned as: 10-93

4 [ C ] = ( 1 R ) 1 VIF where = x R = the R value that results from regressng y on only x. For every subbasn the total amount of fertlser and the tme of plantng and harvestng of crops have to be gven to the model. A senstvty analyss can now be performed to evaluate the nfluence of those nputs on the model results for NO 3 n the rver water. We evaluate the senstvty of the model on the followng result: the tme that NO 3 s hgher than 3 mg/l. The fractons of mneral N, organc N, and NH 3 -N n the fertlsers are consdered to be known and fxed. Hence, we only analyse the total amount of fertlser used (Table 1). As there are a lot of dfferences n management practces between the dfferent farmers and the tme of plantng and harvestng s dfferent from year to year, the plant date and harvest date for the crops are also consdered n the analyss. For a global senstvty analyss we take the unform dstrbuton wth standard devaton S. The ranges of the unform dstrbutons are gven n Table. We assumed no correlaton. To x supply the nformaton on those ranges a few farmers lvng n Maarkedal (stuated n the Dender basn) were ntervewed about ther land management practces. Table 1. Composton of the manure as nput n SWAT Chemcal Percentage of total fertlser (100*kg/kg) HNO3 8.5% Mneral P 7.5 % Organc N 8% Organc P 7.5% Ammona 8.5 % Table. Ranges for global senstvty analyss of management practce nputs for Ntrogen Input Uncertanty Plant date for the crops +/- 1 month Harvest date of the crops +/- 1 month Amount of fertlser appled per +/-5% subbasn and per crop (kg/ha) Uncertanty analyss The Flemsh Insttute for Land Use provded nput data for the model. Due to unregstrated manure and fertlser use t s very lkely that those data are underestmated. The amount of fertlser was the same for all crops whch s unrealstc and t s very lkely that the composton of the fertlser used s not always the same as was assumed here. The uncertanty of the latter two generalsatons s caught by the uncertanty n the amount of fertlser used on the crops. Such an uncertanty s propagated through the model and gves a fnal uncertanty on the model results of the water qualty near the mouth of the rver. An uncertanty analyss n whch all of the uncertan sources are vared at the same tme s performed to see the effects of the uncertanty of the nputs. For ths analyss we calculate the uncertanty bands.e. the 5% and 95% percentles for the results of the tme seres obtaned after samplng the nputs as also done n the senstvty analyss. RESULTS AND DISCUSSION Senstvty analyss As the used senstvty analyss technque s based on lnear regresson, two measures are calculated to see whether a lnear regresson s acceptable. The frst measure s the Regresson Coeffcent (RC) whch was for the whole multlnear regresson. Because ths value s close to 1 and the F-statstc showed that the regresson s sgnfcant, a lnear regresson s adequate. The value of means that there s a fracton of the output varance, 15.5%, that s left unaccounted for. The second measure s the Varance Inflaton Factor (VIF). The largest VIF for ths analyss was A VIF smaller than 5 means that the correlaton between the nputs s small enough to allow applcaton of a lnear regresson (Janssen et al, 199). The standardsed regresson coeffcent s sgnfcant on the 10% level for eght parameters. In table 3 the parameters are ranked Table 3. The eght most mportant nputs, ther SRC and ther senstvty rankng. Input SRC Rank Amount of fertlsaton on pasture n subbasn Amount of fertlsaton on farmng land n subbasn growth date of pasture Plant date on farmng land Amount of fertlsaton on corn n subbasn Amount of fertlsaton on corn n subbasn Amount of fertlsaton on pasture n subbasn Amount of fertlsaton on corn n subbasn

5 For rver ntrate concentratons the amount of fertlser used n the subbasns that are layng upstream are especally mportant. Ths SA also shows that t s more mportant to focus on the amount of fertlser than on the management practces. Uncertanty analyss Fgure 4 llustrates the contrbuton of an uncertanty up to 5% to the amount of fertlser appled on the crops and an uncertanty of one month for the plant and harvest dates. The 95 % bound shows much hgher peaks than the mean concentratons tme seres. Ths means that some peak values of ntrate n the rver water at Denderbelle may not be predcted properly due to an underestmaton of the amount of fertlser used. Those peaks (eg. day 156 and 60) are above levels of ntrate concentratons for basc water qualty. Only a few measurements were avalable for the calbraton of the model. As can be seen, some of the measurng ponts are avalable at tme nstants were the uncertanty on the nputs s not propagated. Fortunately, the model calbraton was successful. The data around day 340 are wthn the uncertanty bound, but the ones on day 40 are clearly not predcted well. ranfall (mm) ranfall tme (days) flow flow (m 3 /s) Ntrate (mg/l) mean 5% percentle 95% percentle measurng ponts tme (days) Fgure 4. The smulaton of ntrate and flow n the Dender rver wth measurements of ntrate (bottom) and ranfall (top) at Denderbelle and the 5 and 95% confdence ntervals. The nputs we consdered uncertan n ths study are only a fracton of all the nputs that cause uncertanty, but t s shown that the nputs related to fertlser use already gve a large uncertanty n certan perods of the year (95% percentle bounds dffers up to +/- 50 % from the average NO 3 predctons). Those are perods wth ranfall and hgh flows. Knowng that there are more sources of uncertanty related to dffuse polluton, the nput uncertanty s expected to be even hgher. Therefor t s clear that care has to be taken durng the gatherng of data needed to run a dynamc process-based model for the predcton of effects of dffuse polluton

6 Ths uncertanty analyss shows also some mportant results for future measurement campagns. Ths study learns that we could obtan a better calbraton for the dffuse polluton part of the model wth data that were taken durng perods wth ranfall and hgh flows, because the model output ntrate s more senstve towards nputs of dffuse polluton n those perods. If you want to focus on calbratng the n-stream behavour and pont polluton then measurements durng dry perods are needed as the model s then not senstve towards nput of dffuse polluton. CONCLUSIONS The model output ntrate n the rver water s senstve towards eght nputs related to fertlser use. It are the start date of the growth of pasture, the amount of fertlser appled on pasture n subbasn 16 and 1, on farmng land n subbasn 4 and on corn n subbasn 5, 11 and 1. The dates of plantng and harvestng the crops appear not to be mportant. To reduce the output uncertanty t s best to focus on data about fertlser amounts appled on crops. In the uncertanty analyss, the effects of uncertan nput of fertlser use and land management on ntrate concentratons n the rver are shown. In certan perods of the year the uncertanty bounds are very wde. Because there are more sources of uncertanty, not consdered n ths study, t becomes clear that t s very mportant to gather accurate data to run a dynamc process-based model for the predcton of effects of dffuse polluton. The uncertanty analyss s also of great use for expermental desgn. Measurements durng dry perods can be used to better calbrate the model for pont source polluton because the nputs of dffuse polluton are not mportant then. On the other hand, perods wth ranfall and hgh flows are needed for the calbraton of the model wth dffuse polluton because the model output ntrate s then very senstve towards the nputs related to farmer s practces. More detaled studes are needed to see the exact contrbuton of the nput uncertantes to the output uncertanty but we can already conclude on the bass of ths study that uncertanty analyss s an essental part of dffuse polluton modellng to evaluate and draw conclusons from model predctons. ACKNOWLEDGEMENTS The authors gves specal thanks to the fnancal support of the EU Harmon-Ca project ( EVKI-CT ). LITERATURE Arnold J.G., Wllams J.R., Srvnvasan R. and Kng K.W. (1996). SWAT manual. USDA, Agrcultural Research Servce and Blackland Research Center, Texas. Beck, M.B. (1987). Uncertanty n water qualty models. Wat. Res. Res., 3(8), Bervoets L., Schneders A. and Verheyen R.F. (1989). Onderzoek naar de verspredng en de typologe van ecologsch waardevolle waterlopen n het Vlaams gewest. Deel 1 - Het Denderbekken, Unverstare Instellng Antwerpen, 76p. Brown, L.C. and Barnwell T.O. (1987). The Enhanced Stream Water Qualty Models QUALE and QUALE-UNCAS: Documentaton and User Model, EPA/600/3-87/007, USA. Janssen P.H.M., Heuberger, P.S.C. and Sanders S. (199). Manual Uncsam 1.1., a software package for senstvty and uncertanty analyss. Blthoven, The Netherlands. Krysanova V. and Haberlandt U. (001). Assessment of ntrogen leachng from arable land n large rver basns. Part I. Smulaton experments usng a process-based model. Ecol. Modellng,150, McKay M.D. (1988). Senstvty and uncertanty analyss usng a statstcal sample of nput values. In: Uncertanty analyss, Y. Ronen, ed., CRC Press, Inc., Boca Raton, Florda, Sevruk, B. (1986). Correcton of precptaton measurements. Proceedngs ETH, IAHS Internatonal Workshop on the Correcton of Precptaton Measurements, 1-3 Aprl 1985, ETH Zürch, Zürcher Geographsche Schrften, 3. Smets S. (1999). Modellng of nutrent losses n the Dender catchment usng SWAT. Masters dssertaton. Katholeke Uunverstet Leuven Vrje Unverstet Brussel, Belgum Vandenberghe V., van Grensven A., Bauwens W. (00). Detecton of the most optmal measurng ponts for water qualty varables: Applcaton to the rver water qualty model of the rver Dender n ESWAT. Wat.Sc.Tech., 46(3). Van Grensven A. and Bauwens W. (000). Integral modellng of catchments. Wat.Sc.Tech,, 43(7), Wllems P.(000). Probablstc mmsson modellng of recevng surface waters. PhD thess, Katholeke Unverstet Leuven, Faculty of Appled Scences, Leuven, Belgum 10-96