General Quantification ofCatchment-Scale Nutrient andPollutant Transport through theSubsurface to Surface and CoastalWatersG E O R G I A D E S T O U N I , * K L A S P E R S S O N ,C A R M E N P R I E T O , A N D J E R K E R J A R S J ODepartment of Physical Geography and Quaternary Geology,Stockholm University, SE-106 91, Stockholm, Sweden

Received August 1, 2009. Revised manuscript receivedJanuary 4, 2010. Accepted January 25, 2010.

This study develops a general quantification framework forconsistent intermodel and intercatchment comparison of thenutrient and pollutant mass loading from multiple sources in acatchment area to downstream surface and coastal waters.The framework accounts for the wide spectrum of differenttransport pathways and travel times through the subsurface (soil,groundwater, sediment) and the linked surface (streams,lakes, wetlands) water systems of a catchment. The accountis based on key flow partitioning and mass delivery fractions,which can be quantified differently by different flow andtransport and reaction models. The framework application isexemplified for two Swedish catchment cases with regard to thetransport of phosphorus and of a generic attenuating solute.The results show essential differences in model quantificationsof transport pathways and temporal spreading, with importantimplications for our understanding of cause and effect inthe catchment-scale nutrient and pollutant loading to downstreamwaters.

1. IntroductionMuch of the nutrient and pollutant loading that threatensthe quality and ecosystems of inland and coastal waters istransported through the subsurface (soil, groundwater,sediment) part of the terrestrial water cycle. The nutrientand pollutant loads originate from a variety of sources at andbelow the land surface such as heavy metal loading frommining wastes and abandoned mine voids (1-3), organicpollutant loading from contaminated land areas (4, 5), andnutrient loading from agricultural land, private sewagesystems, and pools that remain in the subsurface from earlieranthropogenic inputs (6-8). Potential chemical accidentson land (9) and failure of subsurface nuclear waste reposi-tories (10), for instance, also involve subsurface transport ofchemicals and radionuclides to surface and coastal waters.

However, models of catchment-scale solute transport,which have so far mainly focused on nutrients, often neglectthe spatio-temporally diffuse and variable nature of sub-surface mass transport and loading into surface waters, asfound in the model reviews and classifications by Darracqand Destouni (11) and Destouni et al. (12). In order to clarifydifferent model assumptions that are often adopted, and

their effects on the quantification of catchment-scale nutrientand pollutant transport, we have developed a general, model-independent conceptualization and mathematical repre-sentation framework. The framework can be used forintermodel and intercatchment comparison of the masstransport from different sources in a catchment area throughits different subsurface and surface transport pathways tothe resulting total load into downstream surface or coastalwaters.

The application of the framework is exemplified bycomparative analysis of different model results for the totalphosphorus (P) loading to the Baltic Sea from the SwedishWater Management District (WMD) Northern Baltic Proper(13) and the main Norrstrom Drainage Basin (NDB) (8) withinit. This application example identifies and quantifies essentialdifferences in different model accounts of the transportpathways, processes and time scales that determine thecatchment-scale mass transport, and loading to downstreamwaters. An additional application example for the coastalcatchment area of Forsmark (14-21) further clarifies thewhole spectrum of physical transport (advection) pathwaysand travel times through a catchment and analyzes howdifferent model handling of this spectrum affects thequantification of total mass loading to downstream waters.

2. General Problem Formulation and QuantificationFrameworkThis section outlines the development of the generalframework for consistent intermodel and intercatchmentcomparison of catchment-scale nutrient and pollutanttransport. The need for such comparison has been empha-sized by previous studies (11, 12, 22, 23), showing thatdifferent process assumptions and parametrizations used indifferent models have quite different implications for ourunderstanding of catchment-scale transport. Consistentintermodel comparison across various catchment conditionsis needed to discriminate among different models andunderstand the limits of their applicability. Consistentintercatchment comparison can clarify the general versusthe site-specific aspects of the catchment-scale nutrient andpollutant transport.

The proposed quantification framework for such com-parisons considers the releases of nutrient or pollutant massinto the subsurface water system of a catchment area, whichdischarges its water and waterborne mass loading into arecipient surface water system (Figure 1). The recipient maybe a downstream river stretch, lake, wetland, or coastal zone,and the catchment area may include several adjacent streamand groundwater (sub)catchments. There is no need toassume that surface water catchments coincide with ground-water catchments.

On the basis of the experiences and insights from previousconceptualizations and classifications of catchment-scalemass transport (11, 12, 22, 24, 25), we express the totalresulting mass load (Sr

tot) into the recipient (r) from thedifferent source inputs within the catchment area as the sum

where Sini is the mass input from source i, and Sin

i !gw-si Rgw-s

i

and Sini (1 - !gw-s

i )Rgwi are the corresponding mass load

components delivered to the recipient through the linkedsoil-to-groundwater-to-stream network pathways (orangeand green pathway lines in Figure 1) and the direct

* Corresponding author phone: +46 8 16 47 85; fax: +46 8 16 4794; e-mail: georgia.destouni@natgeo.su.se.

Srtot ) !

i

Sini [!gw-s

i Rgw-si + (1 - !gw-s

i )Rgwi ] (1)

Environ. Sci. Technol. 2010, 44, 2048–2055

2048 9 ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 44, NO. 6, 2010 10.1021/es902338y " 2010 American Chemical SocietyPublished on Web 02/16/2010

groundwater pathways (red pathway lines in Figure 1),respectively. The term !gw-s is the groundwater flow fractionthat contributes to the streamflow in the catchment area,and (1 - !gw-s) is the complementary groundwater flowfraction that flows directly into the recipient (flow fraction-ation terms in Figure 1). The terms Rgw-s and Rgw are thefractions of the mass input components !gw-sSin

i and (1 -!gw-s)Sin

i for the soil-to-groundwater-to-stream pathway andthe direct groundwater pathway, respectively, which aredelivered to the recipient after irreversible biogeochemicalattenuation along each pathway (transport-attenuationfractionation terms in Figure 1). The complementary terms(1 - Rgw-s) and (1 - Rgw) quantify the mass input fractionsthat are attenuated along each transport pathway. All fractions!gw-s, Rgw-s, and Rgw range between 0 and 1 and arespatiotemporally variable functions, which may under someconditions and by some models be approximated as constantin space and/or time.

The present inclusion of the flow partitioning fractions!gw-s and (1 - !gw-s) in the general eq 1 represents animportant extension from previous catchment-scale transportconceptualizations and models. This extension accounts forthe possibility that only the fraction !gw-s of the groundwatercontributes a mass load component into the stream network,while the remaining fraction (1 - !gw-s) yields a direct massload into the recipient. The (1 - !gw-s) flow fraction iscommonly neglected in nutrient-focused catchment-scaletransport models, which tacitly assume !gw-s)1 for all inlandsources. In reality, however, !gw-s may vary, depending onthe flow conditions and source locations and extents.

For coastal recipients, the (1 - !gw-s) fraction quantifiesthe submarine groundwater discharge (SGD), which maycarry significant mass loading to the sea. For example, theSGD to the South Atlantic Bight has been estimated to bemore than 30% of the monitored river flow and to carry anabout 15 times greater inland tracer (226Ra) mass load thanthat of river flow due to disproportionally large near-coastalsubsurface tracer concentrations (26, 27). Large near-coastalpopulation pressures have further been quantified for theSwedish catchment areas to the Baltic Sea (28). As aconsequence, a 5 times greater anthropogenic pollutantconcentration is expected to prevail in the about 20% (0.2Qtot) unmonitored near-coastal water flow than in the 80%(0.8 Qtot) monitored river flow from the Swedish catchmentareas to the sea (with Qtot being the total water flow to thesea) (27). If SGD constitutes a mere 20% of the total

unmonitored near-coastal water flow of 0.2 Qtot (i.e., just0.04 Qtot) (27), (1 - !gw-s) will on average be as high as 0.2for the source inputs in the near-coastal areas with 5 timesgreater concentration than that of the rest of the coastalcatchment. If the source inputs in the latter catchment areapart have on average !gw-s ! 1 (i.e., all groundwater in thisarea feeds into the monitored river flow of 0.8 Qtot), the smallSGD of 0.04 Qtot may carry a mass load of more than 25% ofthe monitored river mass load. This is expressed in the termsof eq 1 as

where the superscripts SGD-i and mon-riv-i denote the sourceinputs that feed into the SGD and into the monitored rivers,respectively. The last inequality is expected because thetransport distances and travel times to the sea from the near-coastal source inputs are relatively short, implying a relativelylarge mass delivery fractionRgw

SGD-i; this implication is furtherdiscussed in and supported by the application example insection 4. Note also that the SGD mass load contribution willbe even greater if !gw-s < 1 in the catchment area of themonitored rivers.

In general, the functions and values of the mass deliveryfractions Rgw-s and Rgw depend on the physical and bio-geochemical processes of transport, mass transfer, sorption,and reactive transformation, which may spatio-temporallyspread out and delay in addition to irreversibly attenuate thetransported mass. Various functional expressions and nu-merical quantifications have been reported in the literature,which can be used to quantify the mass delivery fractions Rfor combined transport and reaction processes. Differentexpressions and parametrizations are then valid for differentclasses of pollutants and nutrients in different water envi-ronments, including subsurface water (refs2, 29-37), surfacewater (refs 22, 23, 38, 39), and whole catchments (refs 24,40-42). These cited studies and many other studies in theliterature have used a transport modeling approach that asa first step quantifies the solute-independent, purely physicaladvective travel times and their distributions in the transportdomain. To represent reactive transport, these physicaldistributions are further convoluted with relevant solute-specific models of physical and biogeochemical mass transfer,sorption-desorption, attenuation, and other processes thatcan be expected to prevail along the physical transportpathways. This approach is used because the advective traveltimes and their distributions combine and express in acompact, mechanistic, and consistent way the basic physicalrelations between transport velocities, transport lengths, andtransport times, and are, together with the biogeochemicalprocess rates, key factors in determining the fate of tracers,nutrients, and pollutants (2, 24, 30, 31, 34, 40). Furthermore,the advective travel times constitute lower bounds in thewhole spectrum of transport time scales that spans the totaltemporal spreading of reactive nutrients and pollutants.

The advective travel times from any mass input locationagw_ (Figure 1) in the subsurface water system along thesoil-groundwater pathway direction xgw (orange or redpathlines in Figure 1) to a control plane location at xgw ) xCP

(end of the orange or the red pathlines in Figure 1) and frommass input location xs (Figure 1) in the stream network systemalong the stream pathway direction xs (green pathlines inFigure 1) to the outlet at xs ) xout (end of the green pathlines

FIGURE 1. Illustration of different solute sources (orange) andtransport pathways (dotted lines) through a catchment area to adownstream surface water recipient. The recipient may be adownstream stream or river stretch, lake, wetland, or coastalzone. Dotted red lines are pathways through the groundwater(gw) system, and dotted orange and green lines are pathwaysthrough the coupled groundwater-surface water (gw-s)system. The transport pathway notation is explained inconnection with eq 1 in the text.

!SGD-i

SinSGD-i(1 - !gw-s

SGD-i)RgwSGD-i#

!mon-riv-i

(0.2Qtot

5Sinmon-riv-i

0.8Qtot) $ 0.2 $ Rgw

SGD-i

>0.25 $ !mon-riv-i

Sinmon-riv-i $ 1$

Rgw-smon-riv-i for Rgw

SGD-i > Rgw-smon-riv-i

(2)

VOL. 44, NO. 6, 2010 / ENVIRONMENTAL SCIENCE & TECHNOLOGY 9 2049

at the recipient in Figure 1) are quantified as "gw ) "agw_xCP [dXgw/

vgw(Xgw)] and "s ) "xsxout[dXs/vs(Xs)], with vgw(Xgw) and vs(Xs)

being the local transport velocity in the xgw and xs directionat any advective solute transport position Xgw and Xs alongthe xgw and xs direction, respectively. The groundwater controlplane represents the groundwater-stream network interface(between the orange and the green pathlines in Figure 1) orthe groundwater-recipient interface (between the red path-ways and the recipient in Figure 1), depending on whetherit is the groundwater transport into the stream network orthat directly into the recipient that is being quantified.

For example, the combined delivery fraction Rgw-si for

continuous, temporally constant mass input and output ofa hypothetical solute that undergoes first-order attenuationmay be expressed as the simple product Rgw

i Rsi between

delivery fractions Rgwi for the soil-groundwater system to

the stream network and Rsi for the stream network to the

recipient. The latter fractions can in turn be quantified as(22)

where #gw and #s are the first-order mass attenuation rate inthe soil-groundwater system and stream network, respec-tively, ggw("gw;agw_,xCP) is the probability density function (pdf)of "gw in the soil-groundwater system and fs("s;xs,xout) is thepdf of "s in the stream network. Furthermore, eqs 3 and 4include integration over the source extent Vgw

i in thesubsurface system and mass input extent Ls

i along the streamnetwork.

The term Vgwi may represent the whole volumetric extent

of the source i, or for negligible source depth (extent normalto the land surface) just the lateral source area (extent parallelto the land surface). The term Ls

i represents the length extentof the mass input from the groundwater system into andalong the stream network. If the source input is not uniformover Vgw

i and Lsi, a nonuniformity weighting must be included

in eqs 3 and 4. The spatial integration accounts for how thetravel times, "gw and "s, and their statistics depend on themass input locations, agw_ over Vgw

i and xs along Lsi, and their

associated transport distances, xCP to the groundwater-streamnetwork or the groundwater-recipient interface, and xout tothe stream network outlet. The deterministic integrationsover Vgw

i and Lsi in eqs 3 and 4 represent an extension from

the purely stochastic mass delivery fraction expressionsderived by Lindgren and Destouni (22), which includedintegration only over a statistical population of travel times.Stochastic quantifications have also been proposed for morecomplex, transient flow and/or mass input conditions(12, 22, 31, 40-43) and could be used instead of or to extendeqs 3 and 4.

The total delivered mass fraction from any source i to therecipient is quantified by the whole term !gw-s

i Rgw-si + (1 -

!gw-si )Rgw

i in eq 1. Previous studies, which have linkedcatchment-scale nutrient and pollutant transport modelingwith abatement optimization modeling, have shown theessential importance of the total mass delivery fractions forfinding efficient solutions to the abatement of the catchment-scale nutrient and pollutant loading (12, 25, 44-46). Thedelivery fraction terms !gw-s

i Rgw-si + (1 - !gw-s

i )Rgwi can be

used directly in such catchment-scale abatement optimiza-tion modeling, as outlined in these earlier studies, afterrelevant flow, transport, and biogeochemical process quan-

tification. However, this process quantification may differwidely between different model interpretations of the sameflow and mass load data (11, 12, 21-23). Such differencesmay be essential and can be identified and quantified byapplication of the general framework (1) to different modelresults for the same catchment-scale solute transport prob-lem, as exemplified in the following section for transport oftotal phosphorus (P) to the coast.

3. Phosphorus Transport ExampleFigure 2 shows the Swedish WMD Northern Baltic Proper andthe main drainage basin NDB within it. Figure 3a further showsthe reported model results (8, 13) of P loading to the Baltic Seacoast from these nested catchment areas. We have extracted,area-normalized, and expressed these results in the generalterms of eq 1 for direct comparison. In this way, the essentialsimilarities and differences between the two modeling ap-proaches that underlie the reported WMD (13) and NDB (8)results could be clearly identified and quantified.

The total coastal loading Srtot reported for 2005 conditions

in the NDB (8) includes an anthropogenic component {intotal !anthr-iSin

anthr-i[!gw-santhr-iRgw-s

anthr-i+ (1-!gw-santhr-i)Rgw

anthr-i], black andlight gray parts in Figure 3a} and a natural component {intotal !nat-iSin

nat-i[!gw-snat-i Rgw-s

nat-i + (1-!gw-snat-i )Rgw

nat-i], dark gray in Figure3a}. The NDB model results (8) further imply that theobservable anthropogenic P load in 2005 includes only arelatively fast-delivered part {!anthr-iSin

anthr-i[!gw-santhr-iRgw-ssfast

anthr-i +(1 - !gw-s

anthr-i)Rgwsfastanthr-i ], black in Figure 3a} of the total anthro-

pogenic P mass load {!anthr-iSinanthr-i[!gw-s

anthr-iRgw-santhr-i +

(1 - !gw-santhr-i)Rgw

anthr-i]} that will, sooner or later, reach the coastfrom the contemporary inland P source inputs. With the totaldelivery fractions expressed as Rgw-s

anthr-i )Rgw-ssfastanthr-i +Rgw-ssslow

anthr-i

and Rgwanthr-i )Rgwsfast

anthr-i +Rgwsslowanthr-i , the currently observable load

part is determined by their fast delivery componentsRgw-ssfastanthr-i

and Rgwsfastanthr-i . The remaining, slow delivery components

Rgw-ssslowanthr-i andRgwsslow

anthr-i yield a delayed transport contribution{!anthr-iSin

anthr-i[!gw-santhr-iRgw-ssslow

anthr-i + (1 - !gw-santhr-i)Rgwsslow

anthr-i ], lightgray in Figure 3a}, which has been modeled to continueto add a slow load component to the total anthropogeniccoastal P load long after 2005 (8).

The report (13) for the WMD Northern Baltic Properconstitutes part of the formal Swedish implementation ofthe EU Water Framework Directive (2000/60/EC; http://ec.europa.eu/environment/water/water-framework/index_en.html). The reported anthropogenic P loading to the sea from

Rgwi (xCP) ) 1

Vgwi "0

% "Vgwi

exp[-#gw"gw(agw, xCP)] $

ggw("gw;agw, xCP)d"gwdagw (3)

Rsi(xout) ) 1

Lsi "0

% "Lsiexp[-#s"s(xs, xout)]fs("s;xs, xout)d"sdxs

(4)

FIGURE 2. Location and extent of the Water ManagementDistrict (WMD) Northern Baltic Proper and the NorrstromDrainage Basin (NDB) within it.

2050 9 ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 44, NO. 6, 2010

the WMD includes also direct point discharges from wastewatertreatment plants and industries into the coastal water; such directcoastal discharges were not part of the NDB modeling (8), whichregarded only the nutrient transport from source inputs in thecatchment itself. The WMD report (13), however, does notdistinguish between inland and direct discharge contributions tothe total P loading. We have in this study estimated the latter(!anthr-coastal-iSin

anthr-coastal-i, white in Figure 3a, with coastal deliveryfractions equal to 1 because these discharges do not involve anyinlandtransportandattenuation)fromotherreporteddata(47,48)for such discharges into the Baltic Proper marine basin, thecatchment area of which includes the WMD Northern BalticProper. The currently observable total load of about 7 kg km-2

year-1 from the catchment area (excluding the direct coastaldischarges)anditscomponentsofabout3-4kgkm-2 year-1 eachfrom both the anthropogenic sources (light gray in Figure 3a) andnatural sources (black in Figure 3a) are thus consistent betweenthe NDB and the WMD modeling.

However, the NDB model result for the total load fromthe contemporary anthropogenic sources in the catchment!anthr-iSin

anthr-i(!gw-santhr-iRgw-s

anthr-i + (1 - !gw-santhr-i)Rgw

anthr-i) is greaterthan just the presently observable, fast-delivered anthro-pogenic load component !anthr-iSin

anthr-i(!gw-santhr-iRgw-ssfast

anthr-i +(1 - !gw-s

anthr-i)Rgwsfastanthr-i ) ! 3 kg km-2 year-1 (light gray in Figure

3a) because it also anticipates a delayed anthropogenicload component from the same sources !anthr-iSin

anthr-i(!gw-santhr-i

Rgw-santhr-i + (1 - !gw-s

anthr-i)Rgwanthr-i) ! 6 kg km-2 year-1 (dark gray

in Figure 3a). In contrast, the WMD model assumes that thetotal anthropogenic equals the presently observable, fast-delivered anthropogenic load component, neglecting anypossible delayed, slow load component. In other words, theWMD modeling (13) assumes the P transport times throughthe catchment area to be so small that the coastal loads fromall contemporary sources are essentially directly observable,while the NDB modeling yields a transport time spectrumthat includes a large fraction of much greater transport times.The latter is due to slow advection and reversible P masstransfer and sorption-desorption and implies that an evenlarger anthropogenic load component than the currently

observable one is still in transport through the catchmentarea and will reach the coast at later times (8).

Furthermore, even the consistent quantification of thecurrently observable anthropogenic load is achieved by quitedifferent underlying assumptions in and results from theWMD and the NDB modeling. This is illustrated in panels band c of Figure 3 with regard to the anthropogenic sourceinputs Sin

anthr-i and in Figure 3d with regard to the assumedor modeled delivery fractions Rgw-s

anthr-i ) Rgw-ssfastanthr-i + Rgw-ssslow

anthr-i .Figure 3b shows the source inputs that are associated withthe different coastal load components in Figure 3a. For theNDB, the anthropogenic source inputs (light gray in Figure3b) yield fast-delivered (light gray in Figure 3a) and slow-delivered (dark gray in Figure 3a) coastal load components.For the WMD, the catchment source inputs are smaller forpoint sources and larger for diffuse sources than thosereported from the NDB modeling in absolute (Figure 3b)and relative (Figure 3c) terms.

Figure 3d further shows that the WMD modeling yieldsa smaller average delivery fraction Rgw-s

anthr-i for the catchmentpoint sources than that of the NDB modeling. Yet the WMDmodeling upholds a similar currently observable coastalloading as the NDB by use of a much greater average fastdelivery fraction componentRgw-ssfast

anthr-i for the diffuse sources.With regard to the total P loading that will ultimately reachthe coastal waters from the diffuse sources, however, theNDB modeling yields a large average slow delivery fractioncomponentRgw-ssslow

anthr-i . In total, considering all anthropogenicsources and the fast-delivered and delayed coastal loadcomponents, the NDB modeling yields a greater total deliveryfraction (71%) than that of the WMD modeling (52%) (whitebars in Figure 3d).

With regard to the direct groundwater-to-recipient de-livery fractionRgw

anthr-i and the flow partitioning fractions !gw-s

and (1 - !gw-s) in the general eq 1, the NDB and WMDmodeling assume !gw-s ) 1. This assumption may bereasonable for the NDB, a drainage basin defined by a singlesurface water outlet to the coast. The WMD, however, includesmany small near-coastal catchment areas in addition to the

FIGURE 3. Results for total phosphorus (P) transport from the Northern Baltic Proper Water Management District (WMD) (13) and theNorrstrom Drainage Basin (NDB) (8) in terms of (a) coastal P mass loads to the Baltic Sea coast, (b) total source inputs of P mass,except for the natural inputs for the WMD, which were not reported (13), (c) relative distribution of anthropogenic mass inputs of Pbetween diffuse and point sources, and (d) delivered mass fraction to the coast of anthropogenic point and diffuse source inputs ofP.

VOL. 44, NO. 6, 2010 / ENVIRONMENTAL SCIENCE & TECHNOLOGY 9 2051

NDB (Figure 2). The nutrient and pollutant mass loadingfrom such areas to the sea may be large (27), and the followingsection exemplifies how the source inputs and mass transportin these areas affect the coastal loading. Furthermore, thefollowing section exemplifies the whole spectrum of differenttransport pathways and travel times through a catchment,and shows how various model assumptions about thisspectrum affect the quantification of total mass loading todownstream waters.

4. Transport Pathway and Travel Time Effects on MassDelivery FractionsFor exemplification purposes, we have used reported modelresults for water flow (19, 21) and advective travel time (49, 50)for the coastal catchment area of Forsmark (Figure 4), incombination with eqs 3 and 4. For commensurate simplicitylevels in the physical transport and biogeochemical processrepresentations, we have neglected random travel timefluctuations, using ggw("gw;agw_,xCP))$("gw- "gw;agw_,xCP) andfs("s;xs,xout) ) $("s - "s;xs,xout) in eqs 3 and 4, where "gw and"s are the expected (mean) travel times from each mass inputlocation in the catchment, and $ is the Dirac delta function.The travel time calculations for these conditions are sum-marized in section SI-A of the Supporting Information. Thecalculations include all the different water subsystems thatare encountered by the mass transport along different source-to-recipient pathways through the catchment, includinggroundwater, streams, and wetlands and lakes as parts of a

whole stream network or separately if they are isolated(section SI-A of the Supporting Information).

With regard to the flow partitioning fraction !gw-s, landcover and flow direction maps that were available on a 10 mresolution for the Forsmark area were used to identify twomain subcatchment areas (Figure 4d): area A1, which is thetotal catchment area of all the connected stream networksthat drain into the sea (shown in Figure 4c), and area A2,which is the total area of all the small near-coastal sub-catchments without any surface water outlets to the sea. Theoutflow to the coast from the area A2 must thus be mainlygroundwater flow (i.e., SGD), implying that !gw-s ) 0 andconsequently (1 - !gw-s) ) 1 everywhere in this area. In areaA1, !gw-s may have different values between 0 and 1,depending on flow conditions and source locations, extents,and depths (Figure 1). For the present exemplificationpurposes, different example scenarios are considered for!gw-s

in area A1, along with different scenarios of characteristicbiogeochemical attenuation rates, representing differentclasses of nutrients and pollutants. For illustration simplicity,we show here results for attenuation rates #gw ) #s ) #, whichdoes not imply any general assumption of similar attenuationrates in the soil-groundwater system as in the stream networkbecause eqs 3 and 4 clearly account for different #gw and #s.

Section SI-B of the Supporting Information maps thewhole spectrum of advective travel times to the coast fromall the 10 m # 10 m grid cells in the Forsmark catchmentarea (Figure SI-1 of the Supporting Information) and

FIGURE 4. Forsmark coastal catchment area. (a) Location of the Forsmark catchment area within Sweden. (b) Forsmark catchmentarea (yellow) with elements of the surface water system in different colors: red for streams, green for lakes and sea, and blue forwetlands. (c) Stream network systems within Forsmark composed of connected streams, lakes, and wetlands (black) that dischargeinto the sea. (d) Total catchment area A1 of all stream networks that are connected with and discharge into the sea (gray area) andthe near-coastal area A2 of subcatchments with no surface water outflow into the sea (black area). The stream network area (blackin panel c) and areas A1 (gray in panel d) and A2 (black in panel d) constitute 15%, 89%, and 11% of the total Forsmark catchmentarea (about 30 km2), respectively.

2052 9 ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 44, NO. 6, 2010

summarizes the travel time statistics for the separate ground-water and stream network subsystems and the whole catch-ment area (Figure SI-2 and Table SI-1of the SupportingInformation) for different !gw-s and source extent-locationscenarios. From such quantifications, the relevant advectivetravel time distributions for different source scenarios canbe extracted and coupled (2, 22-24, 29-42) with the relevantcharacteristic rates for attenuation, mass transfer, sorption-desorption, and/or reactive transformation processes af-fecting different nutrients and pollutants. This coupling isillustrated in section SI-B and Figure SI-3 of the SupportingInformation for the transport and attenuation exampleexpressed by eqs 3 and 4, in terms of the total delivered massfraction !gw-sRgw-s+ (1 - !gw-s)Rgw to the coast for differentattenuation rate # scenarios, with the results mapped foreach grid cell in the Forsmark catchment area.

Figure 5 summarizes and illustrates the total mass deliveryfrom the whole Forsmark catchment area to the coast fordifferent scenarios of source location and extent, and !gw-s

and # values. Comparison between the results for a uniformsource over the whole catchment area (black bars in Figure5) and a concentrated source in the near-coastal area A2(gray bars in Figure 5) emphasizes the importance of sourcelocation. Destouni et al. (27) showed that small near-coastalcatchment areas yield large pollutant and nutrient loads tothe sea due to their commonly large population pressure.The results in Figure 5 show that also the short advectivetravel times to the coast (section SI-B and Table SI-1 of theSupporting Information) contribute to large loading fromnear-coastal catchment areas. As expected in eq 2, the massdelivery fractions Rgw

SGD-i for sources in area A2 (gray bars inFigure 5) are larger than for any !gw-s scenario in the moreinland area A1 (black and slanted line bars in Figure 5),regardless of source pressure strength.

Figure 5 also compares results for Rgw and Rs from eqs 3and 4 (bars with slanted line pattern) with correspondingmass delivery fractions, Rgw

c ) exp[-#"gwc ] and Rs

c ) exp[-#"sc]

(bars with horizontal line pattern), based on single catch-ment-average travel time values "gw

c and "sc. This result

comparison shows the effect of neglecting the variability in

the whole spectrum of advective travel times from a diffusesource as is often done in nutrient transport modeling evenfor (sub)catchments that are much larger than the wholeForsmark catchment area. The neglect of the travel timevariability in the single-travel time expressions Rgw

c )exp[-#"gw

c ] and Rsc ) exp[-#"s

c] leads to systematic under-estimation of the total delivered mass fraction from thecatchment.

This underestimation bias occurs because the separateaveraging of " in the single-travel time expressions Rgw

c )exp[-#"gw

c ] and Rsc ) exp[-#"gw

c ] gives equal weight to all "realizations. In contrast, the averaging of the whole attenu-ation function, exp[-#"], in eqs 3 and 4 implies essentiallyzero weighting for all " values that yield a large enoughproduct #" for near-total mass attenuation to occur alongthe transport pathways to downstream waters. Neglect ofthe variability in the whole travel time spectrum (FiguresSI-1 and SI-2 of the Supporting Information) by use of aseparately averaged " in attenuation functions like Rgw

c )exp[-#"gw

c ] and Rsc ) exp[-#"s

c] will generally give greaterweight to the slow pathways, with resulting larger massattenuation and thus smaller mass delivery than entirefunction averaging like that in eqs 3 and 4. For analogousreasons, the underestimation bias will increase even moreif also the attenuation rates are variable, depending on theircross-correlation with advective travel time (29, 34, 51-53).

The biogeochemically more complex P transport examplepresented in the previous section showed an additionalunderestimation bias, resulting from model neglect of thedelayed load contributions from reversible mass transfer andreaction processes as well as from variable advection. Ingeneral, the nutrient and pollutant load implications of suchmodel neglects and assumptions, regarding either thephysical transport or the biogeochemical processes, mustbe consistently quantified. The model-independent quan-tification framework proposed in this study can be used forthis purpose in intermodel and intercatchment compar-isons.

FIGURE 5. Total solute mass delivery from the whole Forsmark catchment area to the coast. Results are shown for different sourcelocations and extents, attenuation rates (!gw ) !s ) !), groundwater flow ("gw-s) scenarios, and assumptions regarding thevariability of advective travel times. “Source over the entire catchment” denotes the delivery fraction estimates of eqs 3 and 4 foruniform source mass input at every pixel in the catchment area. For the same source input scenario, “Source over the entirecatchment, single (average) travel time approach” denotes the delivery fraction estimates rgw

c ) exp[-!#gwc ] and rs

c ) exp[-!#sc]

based on catchment-average travel times #gwc for the groundwater and #s

c for the stream network systems, respectively.

VOL. 44, NO. 6, 2010 / ENVIRONMENTAL SCIENCE & TECHNOLOGY 9 2053

AcknowledgmentsFinancial support for this work is provided by the SwedishResearch Council (VR), Swedish Geological Survey (SGU),and Swedish Nuclear Fuel and Waste Management Company(SKB).

Supporting Information AvailableAdvective travel time calculations for the Forsmark catchmentarea; spatial mapping and statistics of advective travel times,including Figures SI-1 (mean advective travel time from eachgrid cell to the coast), SI-2 (cumulative spatial distributionsof mean advective solute travel time to the coast), and SI-3(mass fraction delivered from each grid cell to the coast);and Table SI-1 (spatial mean and standard deviation (SD) ofadvective travel times). This material is available free of chargevia the Internet at http://pubs.acs.org.

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