Waterborne spreading of pollutants through hydrologicalcatchments: a general approach to its quantification
Klas Persson, Jerker Jarsjö and Georgia Destouni

Department of Physical Geography and Quaternary Geology, Stockholm University

Abstract
In order to protect water resources from contamination, it is necessary to assess the waterborne spreading of contaminants, both from all existing sources of pollution and from potential new sources (as a consequence of, for example, management changes and accidents
or incidents that lead to discharge of pollutants). In this paper we adopt an approach thathas previously been mostly used to quantify solute transport in soil and groundwater systems. Here, we develop the approach and apply it at the catchment scale for the estimationof waterborne contaminant spreading and the related risk for contamination of sensitive
water environments within and downstream from a catchment area.
The proposed approach consists of two calculation steps: (1) calculation and mapping oftravel times and travel time distributions for flowing water, and waterborne non-reactive
substances that directly follow the movement of the water, from identified or potential
sources of pollution to sensitive downstream waters, and (2) the previously estimatedtravel time distributions are used for calculation and mapping of the transport of specificreactive pollutants with the water, and of the related risks for contamination of sensitive
water environments.
In the two calculation steps, random variability of transport properties and processes
is represented statistically, while a scenario analysis is used to account for uncertainty
about present or future conditions that cannot be quantified in statistical terms (e.g. uncertainties related to the characterisation of the sources of pollution, the water flow, and thetransport of substances with the water). Through this approach one can relatively easily
assess how large the uncertainties are, and identify those intervals of transport conditions
and substance-specific mass attenuation properties for which the uncertainties are of greatpractical significance for water management in a catchment area, as well as the remaining
intervals for which they are not of such significance. In cases where the uncertainties arefound to be of minor importance from a management point of view, the scenario analysis
provides a relatively robust basis on which to make decisions concerning, for example, urban planning, emergency preparedness and the appropriate measures to reduce the spreading of contaminants. Also, by clearly identifying the cases for which the uncertainties areof great practical significance, one obtains a rational basis on which to assess the value offurther investigations in order to reduce the uncertainties.

1

Waterborne spreading of pollutants through hydrological catchments

Introduction
As a result of the recognition of the need for a holistic and integrated approach to water pollution problems (Wheater and Peach 2004, Jöborn et al. 2005,
Macleod et al. 2007), water quality management in
Sweden, the EU and other parts of the world is increasingly carried out at the scale of hydrologicalcatchments, for example in accordance with the EU
Water Framework Directive (European Commission 2000). As part of this ongoing development,
there is an emerging scientific effort attempting
to quantify catchment-scale pollutant transport bywater (e.g. Shepherd et al. 1999, de Wit 2001, Lindgren et al. 2004, Botter et al. 2006, Darracq et al.
2008, Bergknut et al. 2010, Destouni et al. 2010)
and the associated water pollution uncertainties
and risks (e.g. Foster and McDonald 2000, Verro etal. 2002, Wang and Yang 2008, Howden et al. 2011).
In order to protect the water resources withina catchment area from contamination, it is necessary to consider all of the sources of pollution that
may affect water quality in the area, such as atmospheric deposition, and runoff from agriculture, industry and waste deposits (Ritter et al. 2002). The
risk for future discharges of pollutants as a resultof accidents and management changes must also
be taken into account. After an industrial fire, forinstance, contaminated fire-fighting water can infiltrate the soil and pollute the groundwater. Alonga road that is trafficked by trucks carrying dangerous goods, an ill-timed nap at the wheel can lead toa tanker accident and the spillage of chemicals thatquickly infiltrate the normally permeable material
at the side of the road. From all existing and conceivable future sources of pollution in a catchment,
dissolved pollutants may be transported throughthe interconnected groundwater and surface water
systems threatening the quality of these water environments.
In this paper, we propose an approach to estimate
such waterborne spreading of pollutants throughcatchment areas. The purpose of the approach is toprovide a rational basis for overall water management and planning, for instance in the identification of high (and low) risk areas for various existingor future sources of pollution, and in the assessment of how different protection and remediation
measures can affect the contamination risks. In thepaper, we summarise and combine the results andmethods from a series of published studies (Jarsjö
et al., 2007, Persson and Destouni 2009, Darracq
et al. 2010a,b, Destouni et al. 2010, Persson et al.

22011) in order to provide a general description of
the approach and explore its applicability.

Problem description
Figure 1 illustrates a typical contamination situation, with a number of sources of pollution withina catchment area. From these sources, waterborne
pollutants can be transported through the interconnected groundwater and surface water systems tosensitive recipients downstream, such as drinking water supplies, lakes, streams and coastal areas. The risk for contamination of sensitive water
bodies is a combination of the environmental andhealth-related consequences of different levels ofpollution and the probability or possibility thatthese pollution levels will occur. An estimation of
the consequences of water pollution in a catchment
area can be used to decide upon the highest acceptable pollution levels, the exceedence of which implies intolerable environmental and health-relatedrisks. In this study we assume that the acceptable
limits for contamination have been pre-determined,
for instance on the basis of a toxicological assessment. Our focus is on the other, equally necessary
aspect of a comprehensive analysis of pollution
risk: the assessment of how likely it is that the predetermined limits will be exceeded.
Many environmental toxins are oil-based and,after a spill, they will infiltrate through the soil asa separate oil phase with limited horizontal spreading. Consequently, the oil phase itself is primarily alocal problem, while the pollutants that dissolve inthe soil water or the groundwater within the sourcezone can be transported by groundwater and surface water over large distances. The amount ofpollutants that are transferred to the water phasewithin a source zone can often be described as afunction of the solubility limit (Zhou et al. 2000),
independently of the total spilled mass or volume
in the oil phase.
The concentration and mass flow of pollutants
generally decrease as the transport distance fromthe source increases. This is a result of dilution
and natural attenuation processes such as biodegradation of organic substances, decay of radioactive substances, and retention processes (involving
temporary or permanent removal of the substancefrom the flowing water phase). Natural attenuation
processes operate on most substances including
metals and nutrients (Jardine 2008).
Field studies have shown that this process ofPersson et al.

Figure 1: Hypothetical existing or possible future sources of pollution (black fields surrounded by redrings on the map) in a catchment area. The Forsmark coastal catchment area is used here as an example
to illustrate a typical contamination situation in which substances that are a threat to human health andto the environment are dispersed from various sources through the water systems of a catchment area
towards sensitive recipients, such as drinking water supplies, lakes and coastal zones.

attenuation can be estimated through the use of
constants that represent the speed of the process,similar to the decay constants derived for radioactive substances (Mulligan and Yong 2004). Unlike radioactive decay however, which is entirely
substance-specific, attenuation constants can vary
for different types of pollutants depending on thesite conditions. Nevertheless, substance-specificdifferences are often found to be dominant, making it of relevance to define characteristic attenuation constants for different substances or groups ofsubstances. One can, for instance, show that BTEX
compounds generally have significantly higher
degradation constants than chlorinated hydrocarbons (Suarez and Rifai 1999). As a result, BTEX
plumes seldom exceeds 500 meters, while chlorinated hydrocarbons can produce plumes that are sev-

eral kilometres long (Jarsjö et al. 2005).
In this research project we have performed example calculations of hydrological pollutant masstransport from every possible pollutant discharge
location within a catchment area to a downstream
recipient. For specific substances, or for groups ofsubstances with similar characteristics regarding
such features as the attenuation rate, we calculate
the mass delivery of pollutants from their sources
to downstream recipients. These mass delivery calculations are made on the basis of a substance-independent estimation of the flow paths and the travel
times of water from the pollutant input locations to
the recipients. In order to understand the relevanceof the example calculations, it is important to bearin mind that the amount of pollutants that dissolvein the soil water and groundwater within a given

3

Waterborne spreading of pollutants through hydrological catchments

source zone can be approximated for many common pollutants based on the substance-specificsolubility limits (as mentioned above). For thosepollutants one does not, therefore, require detailed
information about the actual amount of pollutants
discharged at the land surface.

Proposed approach to quantify pollutant spreading and the related riskof water pollution
The approach to quantify pollutant spreading andthe associated risk of water pollution that we propose consists of two steps:
1.

Step 1 consists of the calculation and mapping of travel times and travel time distributions for flowing water, and for nonreactive substances that directly follow the
movement of the water, from sources of pollution within a catchment area to recipientsof interest, such as sensitive groundwaterand surface water environments. Alreadyby way of this calculation of substance-independent water travel times, one is able toidentify the most critical pollutant input locations, from which the waterborne pollutant transport to a recipient occurs the mostquickly, leaving the least amount of time
available for pollution abatement measuresand for natural attenuation processes, suchas biological degradation, to occur along
the transport pathways to the recipient.

2.

Step 2 consists of the calculation and mapping of the transport of specific reactive
pollutant substances with the water and therelated risk for contamination. This is doneby coupling the substance-independent
water travel times and their distributions
that were calculated in Step 1 with suitable,
more or less complex process models that
describe degradation and other natural attenuation processes for different substances, or for groups of substances with similar
characteristics regarding these processes.

In the two calculation steps, measureable random parameter variability is represented statistically, while different scenarios are considered in orderto account explicitly for uncertainty about present

4

or future conditions that cannot be quantified instatistical terms.

Step 1: quantification of water travel times

Water travel times through a surface water
network depend on the flow velocities in watercourses and the residence times in lakes and wetlands. Groundwater travel times in different partsof a catchment are dependent on the local flow
velocities, which are in turn determined by thepermeability of soil or rock layers (the hydraulicconductivity), the groundwater surface gradient(the hydraulic gradient) and the pore volume thatthe water can flow through, as a percentage of thetotal soil or rock volume (the effective porosity).
The subsurface permeability, in particular, tends tovary greatly and irregularly in space, which meansthat the groundwater flow velocity also varies, both
between different flow paths as well as along thecourse of each flow path from source to recipient(see Figure 2).
Differences in transport distance to the recipient and variations in water flow velocity mean thatwater travel times to the recipient vary from different sources, as well as between different flow paths
from one and the same source. For this reason, onemust quantify the distribution of travel times instead of just one single travel time. The travel times
for water are by definition independent of the typeof pollutant that the water is transporting and represent a lower limit for the travel times for pollutantsdissolved in water, because waterborne substances
cannot be transported any quicker than the water itself, only slower. Consequently, a scenario analysisof possible water travel times for alternative representations of the water systems indicate the fastest
possible travel times for waterborne pollutants.
When we have estimated relevant distributionsof water travel times from a given source zone (orseveral source zones) to a recipient, we can thencalculate the waterborne transport of any pollutant substance by linking the estimated water travel
times to a model of relevant substance-specific attenuation and retardation processes (e.g. biodegradation and sorption to soil and sediment). This
travel time-based approach has previously mostly
been used to quantify the field-scale transport ofpollutants in subsurface systems. In this paper we
explore its usability for the assessment of the transport of pollutants in entire catchment areas, and we
also examine the uncertainties that are connectedwith the use of the approach on the catchment scale.
As an example case study area, we use thePersson et al.

Figure 2: (a) In an assumed ideal case with homogeneous subsurface conditions, the solute transport
velocity in soil water and groundwater is the same along the course of all possible flow paths from a sourcezone to a downstream recipient, which means that dissolved pollutants that are discharged at the sametime and at the same distance from the recipient will reach the recipient simultaneously. (b) In reality, thesubsurface conditions are heterogeneous and the solute transport velocity can vary greatly, even oversmall distances, both between different flow paths as well as along the course of each flow path. Consequently, the solute travel times for dissolved pollutants to the recipient will be different along different flow
paths from the same source zone.

Forsmark coastal catchment area in northern Uppland, Sweden. For this 30 km2 catchment detailed
geographical and hydrological data are available(Johansson et al. 2005). Despite the abundance ofsuch data, there are, however, several possible alternative model representations of the groundwatertransport. Later on in this paper, we will show how
uncertainties about groundwater transport can affect the assessment of travel time distributions andthe transport of pollutants. We will also show how
key uncertainties can be addressed using scenario
analysis.
Figure 3 illustrates calculated travel times ingroundwater from every 10•10 meter model pixelin the Forsmark catchment area to the nearest inland or coastal surface water. Results are shown foran example transport scenario that represents relatively shallow transport near to the groundwater
surface. The average value of the subsurface permeability is assumed to vary within the catchment
area in accordance with the available geographicalsoil data and information about the permeability ofdifferent types of soil.
Maps representing water travel times to thenearest surface water, or to some other sensitive
water body, can be used directly to guide environmental planning and management. The travel timemaps indicate those parts of a catchment area inwhich discharge of pollutants entails the greatest
risk for contamination. These are the areas with theshortest travel time to the recipient (shown in red
on Figure 3), since a short travel time means that agreater fraction of the total amount of discharged
pollutants will reach the recipient without undergoing degradation or other attenuation processes.

For the areas with the longest travel times to the recipient, there is much time available for natural attenuation and a discharge of pollutants is therefore
less likely to result in serious contamination of therecipient. These last-named areas may then be themost suitable for the allocation of human activities
that can be expected to cause continuous, or sudden
accidental, release of pollutants into natural waters.

Figure 3: The map shows estimated water travel
times from different locations (model pixels) in the
Forsmark catchment area to the closest surface
water recipient (lake, stream, wetland or coastal
water).

5

Waterborne spreading of pollutants through hydrological catchments

Step 2: quantification of the spreading of specific pollutants based on the estimated water
travel times

In Step 2 of the approach, the previously estimated substance-independent water travel times
and their distributions are linked with more or lesscomplex models that describe attenuation and retardation processes that also affect the spreadingof pollutants. In this section, we show example results for different attenuation scenarios in order todemonstrate how the spreading of pollutants can be
estimated for different substances and with accountfor uncertainty about the natural attenuation of agiven substance.
One possible measure of contaminant spreadingis the mass delivery from a pollutant source zone toa downstream recipient. By calculating that pollutant mass delivery from different sources in a catchment area, we can assess the contamination burdenthat each pollutant sources place, or will place, on
the recipient. In such a way, we are able to identify
the pollutant sources that pose the greatest risks forthe environment and for people’s health.
For the Forsmark example area, we have quantified the spreading of pollutants for different attenuation cases. Each attenuation case is characterisedby the product of a typical first-order attenuation
rate for a specific substance, or group of substances,and the substance-independent catchment-averagegroundwater travel time to the nearest surface water. Table 1 illustrates examples of different organic
pollutants, metals and nutrients that, on the basis of
their reported attenuation rates derived from field
experiments and model studies, and the average estimated groundwater travel time of 1.5 years in the
Forsmark catchment area, can be characterised as
belonging to different attenuation cases. Reported
attenuation rates for many substances vary overgreat intervals. This is because natural attenuation is affected by the site-specific environmental
conditions (e.g. geochemistry, water flow and microbial activity), and because the process speeds
cannot be estimated in the field without considerable uncertainty (Bekins et al. 1998, Suarez and
Rifai 1999, Washington and Cameron 2001, Mulligan and Yong 2004). In order to reduce the rangeof possible attenuation rates, one could perform amore careful evaluation of the available information in relation to the specific case in question. If
the the degree of uncertainty is still unacceptably
high, it may be necessary to carry out more studiesof the actual field conditions that prevail in the area.
Figure 4 shows maps of the pollutant mass de-6

livery from different possible input locations within
the Forsmark catchment area to the nearest surface
water. The results shown in Figure 4 are calculatedon the basis of the estimated travel time distribution that is shown in Figure 3. The spreading ofpollutants is indicated by the varying coloured
fields on the map, which represent different massdelivery to the surface water recipient. The massdelivery is expressed as the percentage of the total
pollutant mass input that is transported from the
input location to the recipient without being subject
to degradation or some other natural attenuation
process along the way. In the case of a pollution
accident in the red-coloured zone, for instance, themajor part of a pollutant mass input to groundwater
will reach the nearest surface water if no preventative measures are taken.
For substances that, in light of the prevailingfield conditions, are characterised by the attenuation case referred to as “slow attenuation” (forwhich the characteristic product of the attenuation
rate and the average value for travel time is 0.1 orless), almost the entire area is red-coloured – meaning that the greater part of a mass input of such substances to groundwater reaches the nearest surface
water without time for any significant attenuation to
occur along the transport pathways. For substancescharacterised by the attenuation case “very fast attenuation” (for which the characteristic attenuation
product is 1000 or greater), the attenuation occurs
so quickly that less than 1% of a pollutant mass input to groundwater would reach the surface water
recipient, almost independently of input location.
The uncertainty about the pollutant input, thenatural attenuation and the variation in the travel
times from different input locations may or may
not be of practical significance, depending upon
what information about the spreading of contaminants that water management decisions require. For
decisions about appropriate measures to limit contaminant spreading, for instance, it may not be necessary to calculate precisely the mass delivery to arecipient from different parts of a catchment area.
For such decisions, the main issue is often if thepollutant loads to the recipient will exceed given
water quality standards (the water quality standards can, for instance, be expressed in terms of thehighest acceptable concentration, mass flow or total pollutant load to the recipient and should reflect
the level of pollution that implies the maximum acceptable risk to people and the environment). For
example, if pollutants are discharged somewherein the Forsmark example area and these pollutants
can be characterised by the “quite slow” or “slow”

Persson et al.

Table 1: Examples of pollutants that can be characterised as belonging to various attenuation cases, given
their reported first-order attenuation rates. The attenuation product shown in the table is the product of
the substance-specific attenuation rate and the substance-independent catchment-average groundwater
travel time to the nearest surface water (in this case 1.5 years for the Forsmark catchment area).

Attenuation Value of thecaseattenuation
product for theForsmark
catchment area
Slow
0.1 or lessattenuation

Quite slow
attenuation

1

Quite fastattenuation

10

Fast
attenuation

100

Very fastattenuation

1000 or greater

Examples of pollutants, with references made to studies
where attenuation rates corresponding to the given
attenuation case have been reported based on field data
Polychlorinated biphenyls (PCBs)(1), benzene(anaer; 2,3,4,5),ethylbenzene(anaer; 2,3,5), toluene(anaer; 2,3,6), m,p,o-xylene(anaer;
2,3), vinyl chloride(anaer; 2,3), trichloroethene(anaer; 2,3),
naphthalene (anaer; 2,6), acenaphthylene(anaer;6), zinc(7,8),
phosphorus(9)Benzene(2,3,4,6,10), ethylbenzene(2,3,5,10), toluene(2,3,6,10,11), oxylene(2,3,10), m,p-xylene(2,5,101), vinyl chloride(2,6),
trichloroethene(2,6,10), naphthalene(2,6,10),
acenaphthylene(6,11), fluoranthene(10), cadmium(7), copper(7),zinc(7,8), phosphorus(9,12), nitrogen(12)Benzene(aer; 3,5,10), toluene(2,3,10,11), ethylbenzene(2,3,11),m,p,o-xylene(2,3,5,6,10,11), vinyl chloride(2,3),
trichloroethene(2,3,10), naphthalene(2,11), acenaphthylene(11),acenaphthene(11), anthracene(11), fluoranthene(6,11)
Benzene(aer; 3,11), toluene(aer; 3,10,11), ethylbenzene(aer; 3),trichloroethene(aer; 3,10), vinyl chloride(aer; 3)
Benzene (aer; 3), toluene(aer; 3,10), ethylbenzene(aer; 3)(1)

Sinkkonen and Paasivirta (2000), (2)Aronson and Howard (1997), (3)Suarez and Rifai (1999),
Mulligan and Yong (2004), (5)Essaid et al. (2003), 6)Rogers et al. (2002), (7)Baresel et al. (2006),(8)
Baresel and Destouni (2007), (9) Destouni et al. (2010), (10)Aronson et al. (1999), 11) Bayer-Raich etal. (2006) (12)Darracq et al. (2008); (aer)Mainly relevant for aerobic conditions, (anaer)Mainly relevant for
anaerobic conditions.
(4)

attenuation cases, then Figure 4 would indicate thatthe risk to the surface water recipient is generally
unacceptable if the pollutant mass input to groundwater is more than 10 times the highest acceptableload to the recipient (in that case the maximum acceptable load to the recipient is exceeded for pollutant input in the red- and pink-coloured areas in
Figure 4b). By contrast, if the discharged pollutants
can be characterised by the “fast” or “very fast”
attenuation cases and the pollutant mass input isdetermined to be less than 100 times greater thanthe maximum acceptable load, then Figure 4 would
indicate acceptable pollution risk for the recipientfrom most potential pollutant input locations in thecatchment area (green areas in Figure 4d).
Figure 5 shows the estimated average mass delivery to surface water resulting from a dischargeof pollutants somewhere (or everywhere) over theland surface area in the Forsmark catchment. The
black columns in the figure show the mass delivery

results for the travel time distribution illustrated in
Figure 3; in this transport scenario, the travel times
to the recipient from different locations in the areavary depending on both transport distance and flow
velocity. The green columns show corresponding
mass delivery results if we choose to neglect thefact that the travel time is different from different
locations, and simply quantify the transport of pollutants for one single, average travel time to the recipient from the entire upstream area (1.5 years inthis case). We can see from the figure that for thelast-named case of neglected travel time variability
in the catchment, the estimated mass delivery to
the surface water recipient is zero for those attenuation cases characterised by “quite fast” to “fastattenuation” (for which the characteristic productof attenuation rate and catchment-average travel
time is 10 or greater). If we, by contrast, accountfor travel time variability in our calculations, thena significant amount of pollutants is estimated to7

Waterborne spreading of pollutants through hydrological catchments

Figure 4: Maps of the Forsmark catchment area that show the amount of pollutants (given as percentage
of pollutant mass input) that reaches the nearest surface water recipient (lake, stream, wetland or coastal
water) from different pollutant input locations. The calculations are based on the water travel time distribution that is illustrated in Figure 3.

reach the recipient for the same attenuation cases(specifically from those areas that have much shorter travel times than the average travel time of 1.5
years). When calculating the spreading of pollution
from a larger area to a downstream recipient it is,therefore, important to include the entire distribution of transport times in the calculations. If weonly use the average travel time for the entire area
in our calculations, we may systematically under-

8

estimate the total mass delivery to the recipient.
We have also explored the applicability of theapproach for different catchment areas, by way of adirect comparison between the results for the Forsmark catchment area and the equivalent results for
the Norrström catchment. Norrström is much larger
than Forsmark (22 000 compared to 30 km 2), andthe approaches used to calculate water travel times
through these two catchments must, of necessity,

Persson et al.

Figure 5: The percentage of total pollutant mass input that reaches the surface water network of the Forsmark catchment area after a discharge of pollutants over the entire area upstream from surface waters.
The columns show the results for two different assumptions regarding how the travel times in the area varyaround the average travel time value for the entire area of 1.5 years: (1) the travel time is the same for theentire area and equates to the average value for the area of 1.5 years (represented by the green columns);(2) the travel times from different locations in the area vary as previously illustrated in Figure 3 (represented
by the black columns).

differentiate themselves from each other, due tothe differences in the available data resolution andthe thereby possible model resolution. The data andmodel resolution was 1 km for Norrström and 10 m
for Forsmark.
For the two catchments we quantified pollutant
spreading through the interconnected groundwaterand surface water systems all the way out to theBaltic Sea coast. Figure 6 shows estimated pollutant mass delivery to the Baltic Sea from different
potential discharge locations in the catchments.
The results for equivalent attenuation cases (inother words, the results corresponding to the same
product of characteristic attenuation rate and catchment-average travel time of water) are similar forboth of the catchment areas, despite the differencein size, and despite that water travel times were
quantified in different ways.
For both areas, the pollutant input location affects the mass delivery to the Baltic Sea primarily
for substances that are characterised by the attenuation cases in between the “very fast attenuation”
and “slow attenuation” cases. For substances characterised by the attenuation case “slow attenuation”(for which the characteristic attenuation product is
0.1 or less), both of the areas will be more or lesstotally red-coloured – meaning that the greater partof a dissolved pollution mass reaches the recipient
without having time to be attenuated. For substanc-es characterised by the attenuation case “very fastattenuation” (for which the characteristic attenuation product is 1000 or greater), the attenuation
occurs so quickly that less than 1% of a pollutant
mass input reaches the Baltic Sea coast, unless thepollutants are released directly into those parts ofthe surface water network that are very close to thesea. In the case of Norrström, the parts of the surface water network for which this is of relevanceare those that are closest to the outlet to the Baltic
Sea in the south-east corner of the catchment. In thecase of Forsmark, where the flow paths through thesurface water systems are generally much shorter
than in Norrström, it is of relevance for a considerably larger part of the surface water network in thecatchment.
The results for these catchment areas demonstrate that the proposed approach to estimate pollutant spreading in catchments is applicable forboth large and small areas, despite significant differences in the availability of data for quantification of water travel times. The similarities in the results for the two catchments indicate a high degreeof generality of the results for our main example
area, Forsmark.

9

Waterborne spreading of pollutants through hydrological catchments

Figure 6: Maps of the Norrström (a, c and e) and Forsmark (b, d and f) catchment areas that show theestimated amount of pollutants (given as percentage of mass input) transported from different input
locations, through the interconnected groundwater and surface water systems, to the Baltic Sea coast
downstream from the catchment areas.

10Persson et al.

Examples of scenario analysis for risk
assessments
Example 1: Assessment of pollution risk incatchments considering different scenarios ofsubsurface heterogeneity

In the previous section, we went through thefundamental steps of the proposed approach. Now,
we shall demonstrate its applicability for the assessment of pollution uncertainty and risk withina catchment area.
Through the calculation and mapping of substance-independent water travel times and theirdistributions, as performed in Step 1 of the approach, potential hotspot areas for pollution discharge are identified: areas from which discharged
pollutants can quickly be transported to environmentally sensitive water bodies downstream, withlittle time available for degradation and other attenuation processes to occur. The estimation of travel
times is, however, uncertain, since the availabilityof reliable data is always limited. We must then relyon different simplified assumptions about, for instance, the variability of subsurface characteristics
and the relation between topography and groundwater surface gradient. In order to take these calculation uncertainties into account in the proposed
approach, alternative travel time distributions arecalculated for different scenarios that cover a rangeof possible transport conditions. In this way, one
can relatively easily assess how large the uncertainties are and identify those contamination situations
for which the uncertainties have great, or small, effect on estimated contaminant loads and the related
risk for contamination.

In order to exemplify this scenario analysis
approach, we consider four different scenarios ofsubsurface heterogeneity (spatial variations in subsurface characteristics) in the Forsmark example
area. The scenarios are explained in Table 2 andillustrated in Figure 7. In scenarios 1–3, the average value of the subsurface permeability (hydraulicconductivity) is assumed to be the same over theentire area (representing transport in a particularly
permeable layer at the interface between the soil
and the underlying bedrock). In scenario 1, we assume that there are no local variations in permeability. In scenarios 2 and 3, we account for the
existence of random local variations in permeability assuming two different extreme cases of subsurface structure: layered subsurface profile (scenario 2) and mixed subsurface profile (scenario 3).
For a contrasting comparison with these first three
scenarios, all of which assume a uniform averagesubsurface permeability in the area, we also havescenario 4, which was the scenario considered forthe calculation of the travel times shown in Figure
3. In scenario 4, which represents transport in thesoil above the interface between the soil and the
bedrock, the average value of the subsurface permeability varies throughout the catchment area, butthere are no random variations around these local
average values.
The maps in Figure 8 show the travel times ingroundwater from every 10•10 meter model pixelin the Forsmark area to the nearest surface water.
The catchment-average travel time is the same (1.5
years) in all of the scenarios, once the travel times
in scenario 4 have been normalised for the sakeof comparison (it is these normalised travel times

Figure 7: Schematic illustration of solute transport velocities along transport pathways in the four different scenarios of subsurface heterogeneity (see Table 2 for additional descriptions of these scenarios).
Different arrow colours represent different transport velocities. Scenarios 1–3 represent transport at therelatively homogeneous and permeable interface between soil and bedrock, while scenario 4 represents
transport in the soil above this border zone.

11

Waterborne spreading of pollutants through hydrological catchments

Table 2: Description of the four considered scenarios of subsurface heterogeneity.

Scenario 1
Scenario 2

Scenario 3

Scenario 4

The subsurface permeability (the hydraulic conductivity) is assumed to be constantover the entire area, in order to represent transport in the relatively homogeneousborder zone between soil and bedrock.
The subsurface permeability is assumed to vary randomly, with the same averagevalue and variance (coefficient of variation 130%) in the entire area. The subsurface
profile is assumed to be layered in order that the permeability only varies between
different flow paths, but not along each flow path throughout the area.
The subsurface permeability is assumed to vary randomly, with the same averagevalue and variance (coefficient of variation 130%) in the entire area. The subsurface
profile is assumed to be mixed in order that the permeability varies both along andamong different flow paths.
The average value of the subsurface permeability is assumed to vary within the area,in accordance with the soil data and available information about the geographicaldistribution of different types of soil in the area. Consequently, the permeability istreated as locally known and constant; in other words, we assume in this scenario thatno local fluctuations occur around the local average value for permeability.

that are also shown in Figure 3). In scenarios 2 and3, local variations in the subsurface permeability
imply that the travel time varies between different
flow paths from each model pixel to the surface water recipient. For both of these scenarios (2 and 3)
the maps show the 10th percentile of the travel time
distribution for each model pixel (i.e., the travel
time that is exceeded along 10 % of the transport
pathways from that model pixel), instead of the average travel time, which is the same as in scenario 1.
Figure 8 shows that different model representations of variations in subsurface permeability inan area can lead to large differences in calculated
groundwater travel times to a recipient. For a robust
analysis of the risk for contamination in a catchment area, it is therefore necessary to account for
uncertainty about how the subsurface permeability varies between, and along, different flow paths
throughout the area.
Figures 9 and 10 illustrate how the different
assumptions about subsurface heterogeneity thatare represented by scenarios 1–4 affect the massdelivery to surface water from all potential input
locations within the Forsmark catchment area. For
substances characterised by the attenuation case“slow attenuation” (for which the characteristic attenuation product is 0.1 or less – Figure 9a), the greater part of a pollutant mass that has dissolved ingroundwater somewhere within the area is estimated to reach the surface water recipient, regardlessof which scenario is applied concerning subsurface
heterogeneity. Consequently, substances that arecharacterised by this attenuation case under theprevailing field conditions must be prioritised interms of quick and comprehensive measures aimed
at reducing the level of contamination, regardlessof where in the area the source of the contamina-

12

tion is situated, or where it could conceivably besituated in the future. For substances characterisedby the attenuation case “very fast attenuation” (forwhich the characteristic attenuation product is 1000
or greater – Figure 9b), a relatively small amount of
the pollutant mass reaches the recipient from mostpotential pollutant input locations in the catchment
for all four of the subsurface heterogeneity scenarios. For substances characterised by the uncertainty-sensitive attenuation cases that exist between
these two extreme cases (in other words, attenuation cases for which the characteristic attenuation
product is greater than 0.1 but less than 1000 – Figure 10), the results for the four different scenarios
vary considerably. If the estimated mass delivery to
the surface water recipient from upstream sources
exceeds given water quality standards in some possible scenarios but not in others, one must either
decide to perform more investigations in order toreduce the uncertainties involved, or else assess therisks for contamination in a conservative fashionand plan for the worst of all possible scenarios.
Which of these alternatives is most appropriate
should reasonably be decided based upon analysesof the costs involved with performing additional
uncertainty-reducing investigations, in comparison
to the additional cost of measures taken as a resultof conservatively assuming the worst possible scenario. Such cost-effectiveness analyses of effective
environmental measures in situations of uncertainty have been described in various scientific studies(Gren et al 2000, 2002, Andersson and Destouni
2001, Baresel et al. 2006, Destouni et al. 2006, Baresel and Destouni 2007).

Persson et al.

Figure 8: The maps show the water travel times from different locations (model pixels) in the Forsmark
catchment area to the nearest surface water recipient (lake, stream, wetland or coastal water), for the four
considered scenarios concerning subsurface heterogeneity that are described in Table 2 and illustrated
in Figure 7. In scenarios 2 and 3, in which allowance is made for local variations in the subsurface permeability, the travel time from each model pixel to the recipient varies between different flow paths. For bothof these scenarios, the maps show the travel time that is undercut along 90 % of the flow paths from eachmodel pixel to the recipient, instead of the average travel time, which is the same as in scenario 1.

Figure 9: Maps of the Forsmark catchment area showing that uncertainties about subsurface heterogeneity and variations in water travel times can be of little practical significance in certain attenuation cases,
when it comes to estimating if the discharge of pollutants in an area has little or great consequence to theenvironment. In the case of “slow attenuation”, more than 50% of the pollutant mass input to groundwaterreaches the surface water recipient for almost all possible input locations, regardless of which of the four
scenarios concerning subsurface heterogeneity (Table 2, Figure 7) we apply. In the case of “very fast attenuation”, less than 1% of the pollutant mass input to groundwater reaches the surface water recipient
for almost all possible input locations, once again regardless of which of the four scenarios concerning
subsurface heterogeneity (Table 2, Figure 7) we apply.

13

Waterborne spreading of pollutants through hydrological catchments

Figure 10: Maps of the Forsmark catchment area that show, for the attenuation case “quite fast attenuation” (for which the characteristic attenuation product is 10), and for each of the four considered scenarios
concerning subsurface heterogeneity, what percentage of the total mass of discharged waterborne pollutants that will reach the nearest surface water recipient after discharge at different locations (model pixels)
in the area.

Example 2: Risk assessment based on exceedence probability estimates

Because the conditions for contaminant spreading in nature are not constant in time and space, local pollutant mass flows and concentrations generally vary, depending upon which transport pathway
the pollutants follow. In all of the scenarios 1–4
that have been described above (Table 2, Figure 7),
there is variability in the travel time along different transport pathways to the considered recipient.
Along slow or long flow paths, the transported substances may have time to be completely attenuatedbefore they reach the recipient, while substancesthat are transported along the fastest and shortest
flow paths have almost no time to be attenuatedat all. As a result, there can be a relatively large
probability that given water quality standards for asensitive recipient will be exceeded at some pointin space or time, even if the average pollutant concentration in the water that reaches the recipient isless than the pre-determined acceptable value. In
14water quality management one should therefore not
only establish relevant water quality standards ofmaximum allowable pollution levels, but also decide what is the acceptable probability of exceeding
those standards.
The probability that given water quality standards will be exceeded at a recipient location downstream from a source zone is dependent upon theamount of pollutants that have leaked out from thesource zone, and upon the processes that control
the spreading of pollutants from the source zone
to the recipient. Figure 11 shows how both of thesefactors affect the probability of exceeding a pre-determined acceptable pollutant concentration limit
at varying distances downstream from a source
zone, the distances being expressed as the numberof source zone lengths along the main flow direction (see Figure 1). As in the previous sections, we
calculate the contaminant spreading for different
attenuation cases that are expressed in terms of acharacteristic attenuation product, which is here

Persson et al.

Figure 11: The black curves surrounded by grey zones illustrate the probability that the pollutant concentration at different distances downstream from a short-term pollutant discharge exceeds a pre-determined
concentration limit. Results are shown for leakage of polluted water from the source zone with a pollutant
concentration that is: 100 times the limit (black curves), 10 times the limit (the bottom boundary of the greyzone) and 1000 times the limit (the top boundary of the grey zone). The assumption of a layered subsurface
profile means that the transport velocity only varies between different flow paths and not along each flow
path from the source zone; while the assumption of a mixed subsurface profile means that the transport
velocity varies both along the flow paths as well as between them.

15

Waterborne spreading of pollutants through hydrological catchments

between the assumed constant first-order attenuation rate and the average water travel time along asection of a flow path that is equivalent to the sourcezone length in the main flow direction. Figure 11
shows the results for the two very different cases ofsubsurface heterogeneity that were described in theprevious section: mixed subsurface profile, which
entails relatively small variations in travel timealong different flow paths from source to recipient;and layered subsurface profile, which entails large
variations in travel times along different flow paths.
The dotted line at probability level 1% in the graphs
is an example of a possible maximum acceptable
likelihood that local concentrations of pollutants
exceed the pre-determined acceptable limit.
The results in Figure 11 indicate that uncertainty about the prevailing subsurface heterogeneity (mixed or layered subsurface profile) andthe relevant attenuation case (fast or slow attenuation in relation to the average travel time) often
have a greater impact on the probability that given water quality standards will be exceeded thanhas uncertainty about the actual concentration of
the substance that has leaked out from the sourcezone. The conditions for the spreading of pollutants downstream from the source zone is then morecrucial information than is the input concentration
at the source, for water managers to make rational
decisions on the measures required to undercut thehighest acceptable probability of exceeding given
water standards (1% probability in our illustrative
example). In the attenuation case “fast attenuation”(for which the characteristic attenuation product is
1 or greater), for instance, the probability that the
pre-determined maximum concentration will be
exceeded decreases very rapidly as the distancefrom the source zone increases, even in cases
where the levels of concentrations discharged fromthe source zone are up to 1000 times greater thanthe pre-determined acceptable limit, and regardlessof whether the subsurface profile is mixed or layered. Hence, for substances that are characterisedby this attenuation case, the pollution risk, and as aconsequence the need for protection or remediation
measures, can generally be judged to be low, despite considerable uncertainty about the concentration of pollutants leaking out from the source zone.
For substances that undergo slower attenuation, theconcentration at the source is more likely to beimportant for whether or not the probability of exceeding given water quality standards is acceptably
low; but that source concentration effect then largely depends upon the prevailing subsurface heterogeneity, so it is still the conditions for the spreading

16of pollutants downstream from the source zone thatare of primary importance for assessing the risk forunacceptable contamination of sensitive water environments, and for deciding upon the appropriate
measures to reduce those risks.

The applicability of the approach forgroundwater risk assessment
The focus of this paper has been on the quantification of contaminant spreading through groundwater and surface water systems and the associatedwater pollution risks. The two-step scenario analysis approach that we have proposed for this quantification can, however, also be applied to the quantification of vertical pollutant spreading from thesoil surface down to the groundwater level, and therelated risk for contamination of the groundwater
directly at the source zone. As for pollutant transport in groundwater and surface water, one cancalculate substance-independent water travel times
for this vertical transport component (Destouni andCvetkovic 1991, Destouni and Graham 1995), andthen subsequently the vertical transport of waterborne substances down to the groundwater, basedon those estimated travel times (Destouni 1992,
1993, Eriksson and Destouni 1997, Graham et al.
1998, Foussereau et al. 2000, 2001). From estimatesof pollutant transport for alternative possible pollutant input and transport scenarios, one can assess
the risk for contamination of the groundwater at
the source zone, and the need to instigate protection or remediation measures in order to ensure thatthe likelihood or possibility to exceed given water
quality standards is acceptably small.
All such calculations for various substances in
the chemical phase and water phase become functions of the prevailing moisture level, which is anindependent parameter that can be estimated relatively easily and quickly in the field, for instancein the case of a situation arising from an accident
involving contaminants.

Conclusions and recommendations
In this study we have developed an approach forcalculation and mapping of the spreading of pollutants and the associated risk for contamination inhydrological catchment areas. By summarising andcombining the results from earlier studies, we havePersson et al.

illustrated the different steps of the approach andexemplified its applicability.
The approach consists of two calculation steps:(1) calculation and mapping of travel times andtravel time distributions for flowing water, and waterborne non-reactive substances that directly follow the movement of the water, from various sources of pollution to sensitive groundwater and surface
water environments within and downstream froma catchment area, and (2) the calculation and mapping of the waterborne transport of specific reactive pollutants, and of the related risks for contamination of sensitive water bodies.
In the two calculation steps, random variability
in key processes is represented statistically, while a
scenario analysis is used to account for uncertainty
about present or future conditions that cannot be
quantified in statistical terms (e.g. about pollutant
input and transport). In this way, one can relatively
easily assess how large the uncertainties are andidentify those intervals of transport conditions andmagnitude of pollutant input for which the uncertainties are of great practical significance as well as
the other, often wider intervals within which they
are not of significance. In cases where the uncertainties are found to be of minor importance from amanagement point of view, one obtains, despite theexistence of uncertainties, a relatively robust foundation on which to base decisions concerning water
management and emergency preparedness. Even
regarding those cases for which the uncertainties
are of greater significance, the scenario analysis approach still provides a rational basis for making decisions. The alternatives are then either to perform
more investigations in order to reduce the uncertainties, or to manage the uncertain conditions on
a conservative basis and consider the scenario thatentails the greatest risk for contamination.
A central point of the proposed two-step approach is that one is able, already after performing
the calculations and mapping of water travel times
in Step 1, to use these results in order to identify
hotspot areas for water contamination in a catchment, that is, those parts of the catchment fromwhich discharged pollutants can most quickly betransported by the water to sensitive recipients.
The travel times for water represent a conservative assessment of the equivalent travel times forreactive, waterborne pollutant substances, since nosuch substances can be transported more quickly
than the actual water that bears them, only more
slowly due to reaction processes that cause retardation along the transport pathways.
Another central point of the two-step calculation

approach is that the substance-independent water
travel times estimated in Step 1 are also relatively
easy to use in order to calculate the waterborne
transport of reactive substances, or groups of substances with similar reaction characteristics, in
Step 2 of the approach. Based on the calculationand mapping of the pollutant spreading in a catchment area for alternative possible scenarios, one
can then also relatively easily assess the related riskthat given water quality criteria for pollution may
or may not be exceeded within a catchment area orin its recipient.
Our calculation examples for the Forsmark andNorrström catchment areas were based solely on
the type of data that can realistically be expected to
be available for a catchment area, either locally oroverall. These examples showed that the approach
is well-suited to use in water resource management
and planning. Potential areas of use include theidentification of high-risk areas in relation to thedischarge of certain pollutants, the delineation ofwater protection areas and the choice of appropriate measures required in order to prevent or limit
water pollution. Finally, it is our recommendationthat an assessment of the water pollution risks incatchment areas should always be based upon the
explicit calculation and mapping of water travel
times and their distributions.

Acknowledgements

This work was funded by the Swedish Civil Contingencies Agency (MSB) and the Swedish Nuclear
Fuel and Waste Management Company (SKB). We
also acknowledge the members of the MSB project’s reference group for rewarding discussions in
the course of the project.

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