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Goldscheider N, Klute M, Sturm S, Hötzl H (2000) The PI method – a GIS-based approach to mapping groundwater
vulnerability with special consideration of karst aquifers. Zeitschrift für angewandte Geologie, 46 (2000) 3: 157-166
The PI method – a GIS-based approach to mapping
groundwater vulnerability with special consideration of karst aquifers
NICO GOLDSCHEIDER, MARKUS KLUTE, SEBASTIAN STURM & HEINZ HÖTZL
vulnerability mapping, groundwater protection, karst aquifers, GIS
The PI method is a GIS-based approach to mapping the vulnerability of groundwater to contamination
with special consideration of karst aquifers. Vulnerability is classified on the basis of the product of
The P factor indicates the effectiveness of the protective cover as a function of the thickness and
hydraulic properties of all the strata between the ground surface and the groundwater table: the soil,
the subsoil, the non-karstic bedrock, and the unsaturated zone of the karstic bedrock. It is calculated
using a slightly modified version of a method proposed by Hölting et al. (1995).
The I factor (infiltration conditions) indicates the degree to which the protective cover is bypassed by
surface and near-surface flow, especially if it occurs within the catchment area of a sinking stream. It
takes into account the properties of the soil, land use and vegetation, the slope, and above all, the
locations of karst features that allow surface water to rapidly enter the groundwater, for example via
[Die PI-Methode – ein GIS-gestützter Ansatz zur Kartierung der Verschmutzungsempfindlichkeit (Vulnerabilität)
von Grundwasservorkommen mit spezieller Berücksichtung der Eigenschaften von Karstgebieten]
Die PI-Methode ist ein GIS-gestützter Ansatz zur Kartierung der Vulnerabilität (Verschmutzungsempfindlichkeit) von
Grundwasservorkommen, welcher auch die speziellen Eigenschaften von Karstgebieten berücksichtigt. Die Vulnerabilität
wird durch die Multipikation von zwei Faktoren abgeschätzt: Der P-Faktor beschreibt die Schutzwirkung der
Grundwasserüberdeckung (protective cover) in Abhängigkeit von der Mächtigkeit und den Durchlässigkeitseigenschaften
aller Schichten zwischen der Gelände- und der Grundwasseroberfläche, also dem Boden, den Lockergesteinsschichten, dem
nicht verkarsteten Festgestein und der ungesättigten Zone des Karstgrundwasserleiters; der P-Faktor wird nach einem
modifizierten Ansatz von Hölting et al. (1995) ermittelt.
Der I-Faktor (Infiltration conditions) beschreibt die teilweise oder vollständige Umgehung der Grundwasserüberdeckung
durch oberflächennahe Abflusskomponenten, insbesondere im Einzugsgebiet versinkender Oberflächengewässer. Er
berücksichtigt die Bodeneigenschaften, Vegetation und Landnutzung, die Hangneigung, sowie hydrologisch wirksame
Karstformen, die zu einer konzentrierten Infiltration führen können, also Schwinden, versinkende Oberflächengewässer und
Karst aquifers are among the most important sources of drinking water. A large part of the drinking
water supply in many European countries is abstracted from karst aquifers: 50 % in Austria and
Slovenia, 36 % in Croatia and 31 % in Belgium (COST 65, 1995). In Germany, karst water makes up
only 6.3 % of the total water supply. However, some karst aquifers are regionally very important for
the water supply, e.g., the limestones of the Upper Jurassic Malm in the largest German karst area, the
Swabian-Franconian Alb (VON HOYER & SÖFNER 1998).
However, karst aquifers are particularly vulnerable to contamination: Due to thin soils and surface
and near-surface concentration of flow in the epikarst zone and the catchments of sinking streams,
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contaminants can easily reach the groundwater, where they are transported rapidly in karstic conduits
over large distances without effective attenuation of contaminant concentration (HÖTZL 1996).
As karst areas are both vulnerable to contamination and important for drinking water supply, they
need special protection. However, protection zoning for karst is more complicated than for porous
aquifers: Karst catchment areas may cover several hundred km² and are characterized by high flow
velocities of frequently more than 100 m/h. Protection zones for porous aquifers are delineated in
Germany on the basis of the 50-day line of travel time – other countries use a 10-day line
(Switzerland), 60 (Austria) or 100 days (Ireland). If this were done for karst aquifers, the protection
zones would be enormous and lead to conflicts resulting from land-use restrictions.
As a consequence, it is essential to protect at least those areas within the catchment that are especially
vulnerable to contamination (SCHLOZ 1994). This leads to a concept of vulnerability mapping that is
not restricted to karst, but is the most relevant and most complicated when applied to karst areas. For
this reason, the COST Action 620 was set up by the Directorate General for Science, Research and
Development of the European Commission in order to propose an objective approach to "vulnerability
and risk mapping for the protection of carbonate (karst) aquifers". This paper is part of the German
contribution to this ongoing European research initiative.
Several methods have been suggested for vulnerability mapping. Some of them, like GOD (FOSTER
1987), DRASTIC (ALLER et al. 1987), and an approach proposed by the German State Geological
Surveys (the GLA method, HÖLTING et al. 1995), are applicable to all types of aquifers, but they do
not adequately take into account the special properties of karst aquifers. Methods like EPIK
(DOERFLIGER 1996, DOERFLIGER & ZWAHLEN 1998) and REKS (MALIK & SVASTA 1999) were
especially developed for karst and can only be applied there. VRBA & ZAPOROZEC (1994) give a
comprehensive overall survey of the concept of vulnerability mapping.
It is the authors’ opinion that a method for vulnerability mapping at the catchment scale should be
applicable for all types of aquifers as well as take into account the special features of karst. Therefore,
a new method was developed for all types of aquifers, but with special consideration of karst. It takes
into account the protective cover (P) – based on the GLA method (HÖLTING et al. 1995) – and the
infiltration conditions (I) and is, therefore, called the PI method.
This new method was first applied in the Engen karst area in the Swabian Alb in SW Germany. The
GLA method had already been applied at this test site: manually (DICKEL et al. 1993-1) and using a
GIS (DICKEL et al. 1993-2). On the basis of this study, STURM (1999) and KLUTE (2000) applied the
EPIK method and the PI method to the same area. In this paper, only the general concept of the PI
method is presented. The results of vulnerability mapping of the test site and a detailed comparison
and discussion of the three methods (PI, EPIK, GLA) will be published in Geologisches Jahrbuch in
The work was funded by the German Federal Institute for Geosciences and Natural Resources (BGR)
and carried out at the Department of Applied Geology of the University of Karlsruhe (AGK) in close
cooperation with BGR and the Geological Survey of Baden-Württemberg (LGRB).
2 Vulnerability and Groundwater Protection
2.1 The Concept of Groundwater Vulnerability, Definitions
Definitions for the following types of groundwater vulnerability have been proposed by COST Action
• Intrinsic vulnerability is the term used to define the vulnerability of groundwater to contaminants
generated by human activities. It takes into account the geological, hydrological and
hydrogeological characteristics of an area, but is independent of the nature of the contaminants.
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• Specific vulnerability is the term used to define the vulnerability of groundwater to a particular
contaminant or group of contaminants. It takes into account the properties of the contaminant(s)
and its (their) relationship(s) to the various aspects of the intrinsic vulnerability of the site.
This paper only deals with intrinsic groundwater vulnerability. Therefore, the term vulnerability is
always used in this sense.
As specific contaminants are not considered by intrinsic vulnerability, only those attributes that are
relevant for all types of contaminants are taken into account: Most important is travel time (also
referred to as residence time and transit time); in addition, proportion of released contaminant that can
reach the groundwater, and reduction of its concentration, e.g., by dilution, diffusion and dispersion,
are taken into consideration. Factors relevant only to specific contaminants – like pH or redox
potential – are not considered (DALY et al. 2000).
ANDERSEN & GOSK (1989) criticize defining intrinsic vulnerability on the basis of the travel time of a
general pollutant. They point out that it makes no difference whether a conservative pollutant reaches
the groundwater after 20 years or within one year. Consequently, they suggest that travel time should
be removed from the vulnerability concept and that vulnerability maps should be produced for
specified situations only.
This criticism has to be taken seriously. However, most natural processes that decrease contaminant
concentration are directly or indirectly related to travel time and most of the factors controlling transit
time are also relevant for reducing the concentration of specific contaminants, e.g., grain-size
distribution is relevant for travel time (intrinsic) and also for cation exchange capacity (specific).
Consequently, the concept of travel time is considered to be applicable for assessing groundwater
The COST 620 concept of groundwater vulnerability mapping uses a conventional source-pathway-
target model for environmental management. In this model, the source is the potential point of release
of a contaminant. COST 620 has proposed that the land surface be assumed as the source, i.e., hazards
resulting from fertilizing and the spreading of pesticides. The target is the water which has to be
protected. For drinking water resource protection the target is the groundwater in the aquifer, for
drinking water source protection it is the groundwater in the well or spring. The pathway includes
everything between the source and the target. For resource protection, the pathway only consists of
the mostly vertical passage within the protective cover, for source protection it also includes horizontal
flow in the aquifer.
2.2 Application of Vulnerability Maps
Before proposing a new method for vulnerability mapping, it is necessary to discuss the potential use
and application of such a map. Vulnerability maps (showing the sensitivity of an area to
contamination) are considered to be valuable tools for land-use planning at different scales (VRBA &
ZAPOROZEC 1994). In combination with hazard maps (showing the presence of a concrete possibility
of contamination) they can be used for risk mapping (showing the probability of the hazard actually
causing damage) and risk management. Above all, vulnerability maps can be used for resource and
source protection zoning on a catchment scale.
Vulnerability Map Source Protection Areas
Resource Protection Zones
target: uppermost groundwater
factors: subsoil conductivity
target: source, well
factors: travel time in aquifer
value and type
Land Surface Zoning
GROUNDWATER PROTECTION SCHEME
Source Protection Zones
Inner SI Outer SO
Extreme SI/E SO/E
High SI/H SO/H
Moderate SI/M SO/M
Low SI/L SO/L
Rk Lg Pu
Extreme Rk/E Lg/E Pu/E
High Rk/H Lg/H Pu/H
Moderate Rk/M Lg/M Pu/M
Low Rk/L Lg/L Pu/L
Fig. 1: The Irish groundwater protection scheme provides an excellent example of the application of
vulnerability maps: Resource protection zones are obtained by combining the information of the
vulnerability map with that of the aquifer map; source protection zones are obtained by combining the
vulnerability map with protection areas (after GSI 1999, modified).
In Ireland, the vulnerability map is not a stand-alone element, but an integrated component of a
comprehensive groundwater protection scheme (DALY & DREW 1998, GSI 1999). Therefore, the Irish
system will be discussed as an excellent example of the application of vulnerability maps for
protection zoning. The system consists of three main elements (Fig. 1):
1. The aquifer map, which shows the importance of the resource and its hydrogeological
characteristics (e.g., Rk: Regionally important karst aquifer; Lg: Locally important sand/gravel
aquifer; Pu: Poor aquifer, generally unproductive bedrock).
2. The vulnerability map is based mostly on the thickness and hydraulic conductivity of the subsoils.
It takes the vertical movement of water and contaminants in the subsoil (unsaturated or saturated).
An "extreme vulnerability" is assigned to karst features like dolines.
3. The source protection areas takes the horizontal movement in the saturated zone into consideration.
The Inner Source protection area (SI) is delineated according to the 100-day line of travel time in
the aquifer, the Outer Source protection area (SO) covers the entire catchment area.
Both source and resource protection zones can be obtained using the vulnerability map together with
one of the other two elements: For resource protection, the groundwater in the aquifer is the target.
Consequently, the resource protection zones are obtained by intersecting the aquifer map with the
vulnerability map. For source protection, the spring or well is the target. Therefore, the source
protection zones are obtained by a combination of the vulnerability map and the protection areas.
In Germany, groundwater is considered to be a valuable resource in every case. Consequently, any
activity endangering its quality is forbidden by law (WHG 1996). Special guidelines exist only for the
delineation of source protection zones for drinking water wells (DVGW 1995). The guidelines apply
to all types of aquifers, taking into account some special features of karst. The main criterion within
the German groundwater protection scheme is the travel time in the aquifer. The properties of the
protective cover are used as optional, additional criteria.
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The German term for vulnerability is not used in the DVGW guidelines. Consequently, a vulnerability
map is not part of the groundwater protection scheme of the guidelines. However, the general idea of
vulnerability is included, especially for the delineation of source protection zones in karst: According
to the guidelines, the 50-day line is often not applicable in karst areas, as the inner well protection
zone would cover the entire catchment area in many cases. For karst areas, the guidelines allow a
reduction in the size of well protection zone II but require protection of at least those areas that are
especially sensitive to contamination, such as dry valleys, dolines and swallow holes. It must be
emphasized that this means less protection than provided by a normal protection zone II (HÖTZL
1996). If the protective cover is sufficiently thick and has a low hydraulic conductivity, zone II may
be made smaller and zone III may be subdivided into zones III A and B.
The DVGW guidelines give suggestions about how to assess the effectiveness of the protective cover.
A more detailed method has been developed by the German State Geological Surveys (GLA) and the
Federal Institute of Geosciences and Natural Resources (BGR) and was published by HÖLTING et al.
in 1995. In the following sections, this method will be called the GLA method.
2.3 Assessing the Protective Cover According to the GLA method
The basic idea of the GLA method (Hölting et al. 1995) is that the effectiveness of all natural
processes in the protective cover (Grundwasserüberdeckung) for reducing contaminant concentration
is mainly dependent on the travel time. As a consequence, the protective function is dependent on the
main factors which control the travel time: the thickness of each stratum and the properties of the
material. The protective cover includes all strata between the ground surface and the groundwater
table: the soil, the subsoil, and the unsaturated bedrock.
The protective function of the soil is assessed according to its effective field capacity (eFC). The
subsoil, consisting of granular, nonlithified material, is the layer below the topsoil. Its protective
function is calculated according to its grain-size distribution, which is also related to its cation
exchange capacity (CEC). The protective function of the unsaturated part of the bedrock is calculated
taking into account the type of rock and structural features like fracturing and degree of karstification.
The total protective function of the cover is obtained as follows: The value for the protective function
of each stratum is multiplied by the thickness of that stratum. The resulting values are added and
multiplied by a factor reflecting the amount of recharge. An additional protective function term is
included for artesian conditions and for a perched aquifer above the aquifer in question. The final
value is called "Protective function, total score", PTS (in German: SG). It can be any positive value
and the range of possible values is subdivided into five classes: very high, high, medium, low and
very low. P
TS ≤ 500 (e.g., for 20 m of sand) indicates a very low degree of natural protection;
PTS > 4000 (e.g., for 8 m of clay) indicates a very high degree of protection.
The GLA method assumes that infiltration occurs diffusely and that all the infiltrating water slowly
percolates vertically through the unsaturated zone towards the groundwater table. In non-karstic areas
with permeable soils and gentle topography, this assumption is often fulfilled and the GLA method
leads to good results. But especially in karst areas and in mountainous landscapes, concentration of
flow occurs frequently at or near the surface or in the epikarst zone. This flow can bypass the
protective cover partially or completely. In this case, the GLA method is not applicable. This is the
starting point for the PI method, which takes into account concentration of flow via the I factor (Fig.
3 General Concept of the PI Method
The PI Method is a combined GIS-based approach to mapping groundwater vulnerability for all types
of aquifers but with special consideration of karst. It is based on a source-pathway-target model: The
ground surface is assumed to be the potential source of contamination, the groundwater table in the
uppermost aquifer is the target. Thus, the pathway includes everything between the ground surface
and the groundwater table. The PI vulnerability map can be used for resource protection. In
combination with travel time in the aquifer it can also be used for source protection (Fig. 1).
The acronym PI stands for the two factors protective cover (P factor) and the infiltration conditions (I
factor) (Fig. 2). The P factor describes the effectiveness of the protective cover resulting mainly from
the thickness and hydraulic conductivity of all the strata between the ground surface and the
groundwater table – the soil, the subsoil, the non-karstic bedrock and the unsaturated zone of the
karstic bedrock. The P factor is calculated according to a modified version of the GLA method
(HÖLTING et al. 1995) and divided into five classes: P = 1 indicates an extremely low degree of
protection, P = 5 indicates a very effective protective cover. The spatial distribution of the P factor is
shown on the P map.
I = 1 I = 00 < I < 1
diffuse infiltration and vertical percolation
Fig. 2: Illustration of the PI method: The P factor takes into account the effectiveness of the protective cover
as a function of the thickness and permeability of all the strata between the ground surface and
groundwater table. The protective cover consists of up to four layers: 1. topsoil, 2. subsoil, 3. non-
karstic bedrock, 4. unsaturated karstic bedrock. The I factor expresses the degree to which the
protective cover is bypassed by surface and near-surface flow, especially within the catchment of a
The I factor indicates the degree to which the protective cover is bypassed as a result of surface and
near-surface concentration of flow. The I factor is 1 if the infiltration occurs diffusely without
significant concentration of flow, e.g., on a flat, highly permeable surface. In contrast, the protective
cover is completely bypassed by a swallow hole, through which surface water may pass directly into
the karst aquifer. In such a case, the I factor is 0. The catchment of a sinking stream is assigned a
value between 0 and 1, depending on the degree to which the protective cover is bypassed. The I map
shows the spatial distribution of the I factor.
The final protection factor π is the product of P and I. It is subdivided into five classes. A protective
factor of π ≤ 1 indicates a very low degree of protection and extreme vulnerability to contamination;
π = 5 indicates a high degree of protection and very low vulnerability. The spatial distribution of the π
factor is shown on the vulnerability map; small I and P maps are also printed as insets on this map so
that it can be distinguished whether the vulnerability of a particular area is due to a thin protective
cover or to surface and near-surface concentration of flow (Fig. 3).
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the protective cover
of the uppermost groundwater
to be presented together
on the final map
Fig. 3: Flow chart for the PI method: The vulnerability map is obtained using the P map together with the I
map. The P map shows the effectiveness of the protective cover as a function of the thickness and
permeability of all the strata above the groundwater table. The I map shows the degree to which the
protective cover is bypassed. It is obtained by intersecting the map showing the catchment areas of
sinking streams with the I' map, which shows the distribution of surface and near-surface flow.
4 Protective Cover (P)
The P factor indicates the effectiveness of the protective cover and is calculated using a slightly
modified version of the GLA method (HÖLTING et al. 1995). The calculation and assessment scheme
is shown in Fig. 4. Please note: All the original letter symbols of the GLA method have been changed
for the English translation.
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Topsoil - T Recharge - R
Subsoil - S
Lithology - L Fracturing - F
PT SM BMRA
TS i i j j
=+ ⋅+ ⋅
Bedrock - B
Thickness of each
stratum in [m] - M Artesian pressure A
Type of subsoil (grain size distribution) S Type of subsoil (grain size distribution) S
clay 500 very clayey sand, clayey sand, 140
loamy clay, slightly silty clay 400 loamy silty sand
slightly sandy clay 350 sandy silt, very loamy sand 120
silty clay, clayey silty loam 320 loamy sand, very silty sand 90
clayey loam 300 slightly clayey sand, silty sand, 75
very silty clay, sandy clay 270 sandy clayey gravel
very loamy silt 250 slightly loamy sand, sandy silty gravel 60
slightly clayey loam, clayey silty loam 240 slightly silty sand, slightly silty sand with gravel 50
very clayey silt, silty loam 220 sand 25
very sandy clay, sandy silty loam, 200 sand with gravel, sandy gravel 10
slightly sandy loam, loamy silt, clayey silt gravel, gravel with breccia 5
sandy loam, slightly loamy silt 180 non-lithified volcanic material (pyroklastica) 200
slightly clayey silt, sandy loamy silt, silt, 160 peat 400
very sandy loam sapropel 300
Lithology L Fracturing F
claystone, slate, 20 non-jointed 25.0
marl, siltstone slightly jointed 4.0
sandstone, quarzite, 15 moderately jointed, slightly karstified 1.0
volcanic rock or karst features completely sealed
plutonite, metamorphite moderately karstic or karst 0.5
porous sandstone, 10 features mostly sealed
porous volcanic rock (e.g. tuff) strongly fractured or strongly 0.3
conglomerate, breccia, 5 karstified and not sealed
limestone, dolomitic rock, Epikarst strongly developed, not sealed 0.0
gypsum rock not known 1.0
score PTS effectiveness P-factor example
of protective cover
0-10 very low 10-2 m gravel
>10-100 low 21-10 m sand with gravel
>100-1000 medium 32-20 m slightly silty sand
>1000-10000 high 42-20 m clay
>10000 very high 5> 20 m clay
eFC [mm] up to 1 m depth T
> 250 750
> 200-250 500
> 140-200 250
> 90-140 125
> 50-90 50
Fig. 4: Determination of the P factor (tables and formula modified after Hölting et al. 1995). The protective
function of the topsoil is assessed on the basis of the effective field capacity eFC down to a depth of
1 m and assigned a T score. An S score is assigned for the subsoil on the basis of the grain-size
distribution. The R score is assigned on the basis of the amount of recharge, i.e., the difference
between precipitation P and the potential evapotranspiration ETp.
The score B for the bedrock is obtained by multiplying the factor L (for the lithology) and the factor F
(for the degree of fracturing and karstification). The F factor was modified in order to describe the
development of the epikarst and its influence on groundwater vulnerability.
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The epikarst, or subcutaneous zone, is defined as the uppermost zone of outcropping karstified rocks,
in which permeability due to fissuring and diffuse karstification is substantially higher and more
uniformly distributed than in the rock below (KLIMCHOUK 1997). Its thickness often ranges between a
few meters and several tens of meters. The possible functions of epikarst are storage and
concentration of flow (FORD & WILLIAMS 1989). If the epikarst is developed in a way that leads to
extreme concentration of flow, e.g., a bare karrenfield connected with hidden, karstic shafts (Fig. 5),
the structural factor is assigned a value of zero, expressing that the protective cover of the unsaturated
zone below this epikarst is completely bypassed.
moderately jointed, slightly karstified
no significant flow concentration
F = 1.0
epikarst strongly developed
extreme flow concentration
F = 0.0
Fig. 5: Concentration of flow in highly developed epikarst leads to a bypassing of the protective cover of the
unsaturated zone; this is taken into account by assigning a score of zero to the factor F (F for fracturing)
(modified after Drew et al. 1999).
Surface karst features are only one expression of epikarst, but most of it cannot be seen at the surface.
The epikarst zone can be highly developed without any visible karst features. As a consequence, it is
assumed that epikarst is present (even if it is not visible everywhere) if we find conditions that are
favourable for epikarst development, such as pure limestone with widely spaced fractures or
geomorphological indicators of extensive development of epikarst, such as dolines and karrenfields
(DREW et al. 1999).
It is the personal opinion of the authors that it is misleading to assign a low vulnerability to an area
where there is an aquifer above the aquifer under consideration in a multiaquifer system – in this case,
the uppermost aquifer needs protection. Therefore, the PI method always takes the groundwater table
in the uppermost aquifer as the target. As a consequence, a higher aquifer is not considered to be
protection for the underlying aquifer, in contrast to the GLA method. Consideration of artesian
pressure in the aquifer by an additional score of A = 1500 points was not modified.
The scores for the subsoil and the bedrock are multiplied by the respective thickness in m (factor M).
Thin, low-permeability strata can be bypassed if they are not laterally extensive, but occur in form of
lenses. As a consequence, the lateral continuity of each layer should be taken into account in order to
avoid overestimation of the protective function (DALY et al. 2000). The score for the total
effectiveness of the protective cover PTS is calculated according to the formula in Fig. 4, which is
similar to the one used in the GLA method (HÖLTING et al. 1995).
The range of possible scores for the total protective function PTS is subdivided into five classes, which
are the final P factors in the PI method. Each class covers a score range of one magnitude. The
classes are much wider than those in the original GLA method, allowing a better description of the
high natural variation of protective cover: PTS ≤ 10 (e.g., < 2 m of gravel) is considered to provide a
very low degree of protection and to be extremely vulnerable (P = 1), while a very high degree of
natural protection and a very low vulnerability (P = 5) is assigned to PTS > 10,000 (e.g., > 20 m of
clay). The spatial distribution of the P factor is shown on a P map. For flat areas with a high
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– 10 –
infiltration capacity, the P factor is multiplied by an I factor of 1. Consequently, the final vulnerability
map will be identical to the P map for this area.
A P factor of 5 is assigned to areas outside the considered aquifer from which recharge enters the
aquifer by surface and lateral near-surface flow; these areas can be subdivided and classified according
to different I values (see next chapter).
5 Infiltration Conditions (I)
5.1 General Concept
The ground cover can protect the groundwater only if the precipitation infiltrates directly into the
ground without significant concentration of flow. The disappearance of an intermittent or perennial
surface stream into a swallow hole is common in karst areas. In this case, the protective cover is
completely bypassed at the swallow hole and bypassed in part by the surface runoff in the catchment
area of the sinking stream.
Therefore, the I factor was introduced. It expresses the degree to which the protective cover is
bypassed as a result of surface and near-surface concentration of flow, especially within the catchment
area of a sinking stream. If the infiltration occurs directly on a flat surface without significant
concentration of flow, the I factor is 1, indicating that the protective cover is not bypassed and is
100 % effective. On the other hand, the protective cover is completely bypassed by a swallow hole
through which surface water directly enters the karst aquifer. In such a case, the I factor is 0. The
catchment area of a sinking stream is assigned a value between 0 and 1 according to the extent of
surface and near-surface flow.
It has to be emphasized that the I factor is not precisely defined in terms of hydrology. It is a
semiquantitative tool to express the vulnerability of groundwater resulting from bypassing of the
protective cover by surface and lateral near-surface flow. The I factor is used for further GIS
operations to generate the vulnerability map.
5.2 Hydrological Basis
The vulnerability of an area to groundwater contamination is dependent on the pathway of a possible
contaminant from the ground surface to the groundwater table. As contaminants are usually
transported in water, it is necessary to describe the possible flow paths of the water. We can
distinguish between three relevant processes: infiltration with subsequent percolation, surface flow,
and subsurface flow. Which of these processes predominates depends on both the properties of the
site and the characteristics of the rainfall event, as well as the previous precipitation history and the
degree of saturation of the soil.
Diffuse infiltration of rain water from the surface into the soil and the subsequent downward
percolation through the soil is the dominant hydrological process if the rainfall intensity is less than
the capacity of the soil to absorb the water and if the hydraulic conductivity of the total soil profile is
high enough to allow downward movement of the water. Gentle slopes, dense vegetation – especially
forest cover – and coarse-textured soils with thick organic horizons and stable peds favour infiltration
(DYCK & PESCHKE 1995).
Surface flow occurs when not all of the rain water is able to penetrate the soil surface. We can
distinguish two main types:
Hortonian runoff occurs when the intensity of a rainfall event exceeds the infiltration capacity of the
topsoil and the surplus rain water flows away on the surface. The necessary condition for Hortonian
runoff is that the intensity of the rain is significantly higher than the hydraulic conductivity of the
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topsoil. The amount (depth) of surplus water which is sufficient to produce surface runoff is
dependent on the slope of ground surface (PESCHKE et al. 1999).
Saturated overland flow occurs when a rainfall event is sufficiently long and intense to saturate the soil
and exhaust its throughflow capacity or if the soil was saturated due to previous precipitation and the
additional precipitation cannot infiltrate but flows away on the surface. This process is favoured when
lower permeability layers are present below thin, relatively highly permeable topsoil. The necessary
condition for this type of flow is that the total amount of precipitation is more than the effective
porosity; similar to Hortonian runoff, the amount of surplus water that is sufficiently high to produce
surface runoff depends on the ground surface gradient (PESCHKE et al. 1999).
Subsurface flow occurs when the hydraulic conductivity of the topsoil is high enough for the
infiltration of rain water while lower permeability layers in or below the soil do not allow the further
downward percolation to continue. In this case, the layers above the low permeability zone become
temporarily saturated, allowing movement parallel to the slope. The velocity of the subsurface flow is
strongly dependent on the slope gradient, the hydraulic conductivity of the topsoil, and on preferential
flow paths. We can distinguish between two relevant types:
Subsurface storm water flow in diffuse pathways is a fast flow process, which occurs in very highly
permeable soils. The flow velocity depends on the hydraulic conductivity and the slope gradient
Subsurface storm water flow in preferential pathways is another fast flow process. Soil pipes,
desiccation fissures, worm holes and mouse holes are usually dry but become filled with water during
intensive rain events, enabling very fast flow (LEHNHARDT 1984).
5.3 The I Factor
The I factor expresses the degree to which the protective cover is bypassed by surface and lateral near-
surface flow. The spatial distribution of the I factor is shown on the I map. Such flow is considered to
be especially dangerous within the catchment area of a sinking stream because contaminants can
directly enter the karst groundwater. Therefore, the I factor (the I map) is obtained using the following
two components (Figs. 3 & 7):
• The I' factor expresses the estimated direct infiltration relative to surface and lateral near-surface
flow. The controlling factors are soil properties, slope and vegetation. The spatial distribution of
the I' factor is shown on the I' map.
• The ‘surface catchment map’ shows the surface catchment areas of sinking streams disappearing
into a swallow hole and buffer zones of 10 m and 100 m on both sides of the sinking streams.
The amount of surface and near-surface flow is dependent on rainfall intensity and site properties.
Characteristics of single events, like precipitation rate, cannot be included in the concept of
vulnerability – otherwise we would have to draw a different vulnerability map for each rain event.
Therefore, the proportion of surface and near-surface flow is estimated only on the basis of the site
properties and assuming average storm rainfall, which might occur several times per year.
On the basis of the hydrological concepts described in the previous section, KLUTE (2000) worked out
a system to deduce the dominant flow process from the hydraulic conductivity and depth of lower
permeability layers within or below the soil). The critical values for hydraulic conductivity and
thickness were calculated using data and theoretical approaches from the hydrological literature,
mainly from ZUIDEMA (1985), DYCK & PESCHKE (1995) and PESCHKE et al. (1999) (Fig. 6):
• Infiltration is the dominant process when the hydraulic conductivity of the topsoil is greater than
10-5 m/s and the thickness is more than 100 cm.
• Fast subsurface storm-water flow is the dominant process when the thickness is between 30 and
100 cm and the conductivity is greater than 10-5 m/s; if it exceeds 10-4 m/s, very fast subsurface
flow of more than 50 m/d is to be expected. Macropores favour subsurface storm-water flow.
• Saturated overland flow is the dominant process if we find low permeable layers at depths of less
than 30 cm and if the conductivity of the topsoil is greater than 10-5 m/s.
• Hortonian flow occurs rarely (rainfall intensity of 30 mm/h on steep slopes and 50 mm/h on gentle
slopes) if the conductivity of the topsoil is between 10-5 and 10-6 m/s.
• Hortonian flow occurs frequently (rainfall intensity of 3 mm/h on steep slopes and 30 mm/h on
gentle slopes) if the conductivity of the topsoil is less than 10-5 m/s.
depth to low permeable layer [cm]
hydraulic conductivity [m/s]
Hortonian surface flow rarely
(only during storm rainfall)
Hortonian surface flow frequently
(also during low intensity precipitation)
< 30 cm 30-100 cm > 100 cm
Fig. 6: The predominant flow processes as a function of saturated hydraulic conductivity and to low
permeability layers within or below the soil (modified after KLUTE 2000; based on data from PESCHKE
et al. 1999 and ZUIDEMA 1985).
This system makes it possible to delineate areas with different flow processes predominate (KLUTE
2000). The proportion of each of these flow processes depends on the factors vegetation (land use)
and slope of the ground surface. In general, forest cover favours infiltration, whereas agricultural
areas are more likely to produce surface runoff. The flow velocity of subsurface flow can be estimated
using the Darcy equation (except for preferential flow) and is directly proportional to the slope
gradient. Hortonian runoff and saturated flow can occur even on very gentle slopes if the precipitation
exceeds infiltration or if the topsoil is saturated, but steep slopes favour surface flow and increase its
We have developed a system based on the dominant flow process – derived from the hydraulic
conductivity and thickness of the soil – and the factors vegetation and slope to assess the proportion of
surface and near-surface flow (Fig. 7). The slope was done using the divisions of the German soil
mapping guidelines (AG-Boden 1996).
– 12 –
Settlements: I' = 0.8
1st Step: Determination of the soil properties
2nd Step: Determination of the I'-factor
3d Step: Determination of the I-factor
Depth to low permeable layer
< 30 cm 30-100 cm > 100 cm
Saturated > 10-4 Type D Type C Type A
hydraulic 10-5-10-4 Type B
conductivity 10-6-10-5 Type E
[m/s] < 10-6 Type F
Soil properties Slope
< 3.5 % 3.5 - 27 % > 27 %
Type A 1.0 1.0 1.0
Type B 1.0 0.8 0.6
Type C 1.0 0.6 0.4
Type D 0.8 0.6 0.4
Type E 1.0 0.6 0.4
Type F 0.8 0.4 0.2
Soil properties Slope
< 3.5 % 3.5 - 27 % > 27 %
Type A 1.0 1.0 0.8
Type B 1.0 0.6 0.4
Type C 1.0 0.4 0.2
Type D 0.6 0.4 0.2
Type E 0.8 0.4 0.2
Type F 0.6 0.2 0.0
Surface Catchment Map I'-factor
0.0 0.2 0.4 0.6 0.8 1.0
swallow hole, sinking stream, 10 m buffer 0.0 0.0 0.0 0.0 0.0 0.0
100 m buffer 0.0 0.2 0.4 0.6 0.8 1.0
catchment of sinking stream 0.2 0.4 0.6 0.8 1.0 1.0
rest of the area 0.4 0.6 0.8 1.0 1.0 1.0
Fig. 7: Determination of the I factor: The value of the I' factor is assigned on the basis of the saturated
hydraulic conductivity K and depth to low permeability strata within or below the soil, slope, and
vegetation. An I' value of 0.8 is assigned to built-up areas. The final I factor/map is obtained using the
I' factors together with the surface catchment map.
This I' factor reflects only the extent of surface or subsurface flow. For vulnerability mapping in karst
areas, it is indispensable to distinguish whether this flow occurs inside or outside the catchment area of
a sinking stream as well as to take into account the distance of the evaluated site to the stream.
Therefore, the final I map is obtained by intersection of the I' map with a map showing the catchment
areas of sinking streams. Four zones are delineated on this surface catchment map in order of
• the swallow hole, the sinking stream and a 10 m buffer zone on both sides of the stream;
• a 100 m buffer zone on both sides of the stream;
• the rest of the surface catchment area of the sinking stream;
• the areas outside the catchment areas of sinking streams.
The I' map and the map of the surface catchment area are used as illustrated in Fig. 7. The final I map
shows the degree to which the protective cover is bypassed by surface and near-surface flow. It takes
into account the intensity of surface and near-surface flow as a function of soil, vegetation and slope
and of the position of a given area inside or outside the catchment area of a sinking stream.
– 13 –
6 Construction of the Vulnerability Map
The vulnerability map shows the intrinsic vulnerability and the natural protection of the uppermost
aquifer. The map shows the spatial distribution of the protection factor π, which is obtained by
multiplying the P and I factors:
π = P · I
The π factor ranges between 0.0 and 5.0, with high values representing a high degree of natural
protection and low vulnerability. Small maps of the protective cover and the infiltration conditions are
also printed as insets on the vulnerability map so that it can be determined whether the vulnerability of
a particular area is due to a thin protective cover or to surface and near-surface concentration of flow.
The areas on each of the three maps are assigned to one of five classes, symbolized by five colours:
from red for high risk to blue for low risk. Consequently, one legend can be used for all three maps
Table 1: Legend for the vulnerability map, the P map and the I map
Vulnerability Map P-map I-map
Vulnerability of uppermost Aquifer Effectiveness of Protective Cover Degree of Bypassing
verbal description π-factor verbal description P-factor verbal description I-factor
red extreme 0-1 very low 1 very high 0-0.2
orange high >1-2 low 2 high 0.4
yellow moderate >2-3 moderate 3 moderate 0.6
green low >3-4 high 4 low 0.8
blue very low >4-5 very high 5 very low 1.0
As the information on the vulnerability map is always for the uppermost aquifer, aquifers above the
main aquifer under consideration are indicated graphically by a thick line.
Dolines that are too small to be classified using the P and I factors are given special treatment: An
extreme vulnerability is assigned to dry dolines that contain no infilled sediments and a high
vulnerability is assigned to partially filled dolines; dolines with perennial or intermittent sinking
streams and their catchments can be classified using the I factor (chapter 5). In any case, the existence
of dolines serves as an indicator for extensively developed epikarst and for a low degree of protection
provided by the unsaturated karstic bedrock (chapter 4). They should be shown on the vulnerability
map with the customary symbols.
We want to thank Dr. M. v. Hoyer and Dr. B. Söfner (BGR Hannover) for the constructive
cooperation during the whole project. We also thank Dr. W. Weinzierl (LGRB Freiburg) for
reviewing the paper and for many interesting discussions. Many thanks to G. Sokol, Dipl.-Geogr.
(LGRB Freiburg), for his help. Many thanks also to Dr. D. Drew (Trinity College, Dublin) for many
valuable suggestions and remarks. Many thanks to all our colleagues in the COST Action 620 for
many interesting discussions and for the good cooperation.
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