Ecological scenarios analyzed and evaluated by a shallow lake model

ARTICLE IN PRESS

Journal of Environmental Management 88 (2008) 120–135 www.elsevier.com/locate/jenvman

Ecological scenarios analyzed and evaluated by a shallow lake model Sascha Kardaetz,1, Torsten Strube, Rainer Bru¨ggemann, Gunnar Nu¨tzmann Leibniz-Institute of Freshwater Ecology and Inland Fisheries (IGB), Mu¨ggelseedamm 310, 12587 Berlin, Germany Received 13 July 2005; received in revised form 17 January 2007; accepted 29 January 2007 Available online 6 April 2007

Abstract We applied the complex ecosystem model EMMO, which was adopted to the shallow lake Mu¨ggelsee (Germany), in order to evaluate a large set of ecological scenarios. By means of EMMO, 33 scenarios and 17 indicators were defined to characterize their effects on the lake ecosystem. The indicators were based on model outputs of EMMO and can be separated into biological indicators, such as chlorophyll-a and cyanobacteria, and hydro-chemical indicators, such as phosphorus. The question to be solved was, what is the ranking of the scenarios based on their characterization by these 17 indicators? And how can we handle high quantities of complex data within evaluation procedures? The scenario evaluation was performed by partial order theory which, however, did not provide a clear result. By subsequently applying the hierarchical cluster analysis (complete linkage) it was possible to reduce the data matrix to indicator and scenario representatives. Even though this step implies losses of information, it simplifies the application of partial order theory and the post processing by METEOR. METEOR is derived from partial order theory and allows the stepwise aggregation of indicators, which subsequently leads to a distinct and clear decision. In the final evaluation result the best scenario was the one which defines a minimum nutrient input and no phosphorus release from the sediment while the worst scenario is characterized by a maximum nutrient input and extensive phosphorus release from the sediment. The reasonable and comprehensive results show that the combination of partial order, cluster analysis and METEOR can handle big amounts of data in a very clear and transparent way, and therefore is ideal in the context of complex ecosystem models, like that we applied. r 2007 Elsevier Ltd. All rights reserved. Keywords: Scenario building; Hasse diagram technique; Cluster analysis; Ecosystem model

1. Introduction In the near future we will be confronted with an extensive transition of the world’s environmental conditions. This transition is driven by global climate change. For the Elbe catchment area in the east of Germany temperatures are expected to increase around 1.4 K within the next 50 years and average precipitation will decline from around 600 mm/year to p400–450 mm/year (Jacob and Gerstengarbe, 2005). This change in temperature and precipitation will lead to major changes in the region’s water balance. Consequences such as declining runoff rates and a lowered groundwater level can already be noticed throughout the region. Corresponding author. Tel.: +41 44 261 87 39; fax: +41 44 242 07 11.

E-mail address: [email protected] (S. Kardaetz). Present address: Sascha Kardaetz, Langwiesstrasse 3, 8050 Zu¨rich, Switzerland. 1

0301-4797/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.jenvman.2007.01.037

The fluvial polymictic shallow lakes, common in the region Berlin–Brandenburg, are particularly sensitive towards changes of climatic or hydraulic conditions (Strube, 2005). Due to the small water depth of shallow lakes, no or only short stratification periods are characteristic. Higher temperatures at the lake bottom (compared to deep lakes), result in an increasing mineralization rate of the settled organic material, leading to a higher nutrient supply in shallow lakes (Scheffer, 1998). The influx of resuspended sediment phosphorus into the pelagic after short anoxic periods in summer, additionally stresses the nutrient budget of shallow lakes, and leads to a turbid state characterized by high algae biomasses usually dominated by cyanobacteria. Shallow lakes with a lower nutrient level often appear in a clear state dominated by submerged macrophytes. The switch between the two stable states, is described by Scheffer et al. (1993) as bi-stability. In order to predict the reactions of a shallow lake ecosystem to the changing climate conditions, the ecosystem

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model Ecological Mu¨ggelsee MOdel (EMMO) was built and described by Strube (2005). This model is, in contrast to other lake ecosystem models such as the algal dynamic model for West Lake, Hangzhou (Hongping and Jianyi, 2002) or PROTECH (Reynolds et al., 2001), very complex and focuses specifically on water–sediment interactions, nutrient–algae interaction and higher trophic levels (zooplankton, zoobenthos, fish). The lake ecosystem model EMMO allows the construction and calculation of ecological scenarios, and therefore it can be used as a lake management tool. By applying the model it is, for example, possible to quantify the consequences of different climatic- or economic developments on the water quality of a lake. It is crucial to evaluate and to compare the different options, in order to support decision-making processes. Since those evaluations often have to consider a wide range of different criteria, it is necessary to apply a multi-criteria decision method, such as PROMETHEE, AHP or Hasse diagram technique (Simon et al., 2004; Bru¨ggemann, 2002). The Hasse diagram technique, based on very simple elements of partial order theory, takes an environmental point of view. It avoids the inclusion of subjective preferences and can therefore be seen as a ‘‘data-driven method’’. The processing of large decision matrices especially by data driven multi-criteria decision methods often lead to a very high degree of complexity, confusion or information loss. These limitations restrict the use of strictly data driven multi-criteria methods within very complex decision situations. Thus the question arises: How can we deal with large quantity of data within data driven evaluation procedures? In the present paper, we introduce a new stepwise evaluation tool which can handle large quantity of data. We proceed as follows: Firstly a large set of different ecological scenarios is defined, secondly an extensive set of water quality indicators is calculated by EMMO, and thirdly a stepwise and structured evaluation procedure for data driven evaluations is introduced and applied. The core of the evaluation procedure is based on the Hasse diagram technique (HDT). Its extension is called METEOR, which provides a transparent and participatory decision support. The HDT is described below in Section 2.6, and details can be found in different studies (e.g. Bru¨ggemann and Steinberg, 2000; Bru¨ggemann et al., 2001; Hollert et al., 2002; Simon et al., 2004; Bru¨ggemann and Carlsen, 2006). 2. Material and methods

during 1980–1990, to 6.63 m3 s1 during 1991–2002 as a result of the flooding of the former coal mines in Lower Lusitia (Gru¨newald, 1997; Ko¨hler et al., 2005). The Mu¨ggelsee is mesotrophic–eutrophic (quality level II–III according to the water quality classification system of the Working Group of the Federal States on Water Issues (LAWA)) but had been highly eutrophic in the 1970s and 1980s (Ko¨rner, 2001). Although the nutrient load in the inflow decreased drastically during 1990s—the last decade—there is still a high phosphorus concentration in the lake. This is due to the high resuspension rates of phosphorus from the sediment during temporary anoxic periods (Behrendt et al., 1993). Table 1 shows the most important water quality parameters of the lake. More detailed limnological characteristics can be found in Driescher et al. (1993) and Ko¨hler et al. (2005). 2.2. Ecosystem model ‘‘EMMO’’ 2.2.1. General aspects In order to estimate the impacts of changing external conditions on the ecosystem of Lake Mu¨ggelsee, the ecosystem model EMMO was built and extensively documented (Strube, 2005; Schellenberger et al., 1983). Here we give a brief description to facilitate the understanding of the main topic of the present paper, namely, the building and evaluation of diverse scenarios. The EMMO model focuses on the essential processes of a shallow lake ecosystem and is divided into 14 main components: 9 components describing the state variables within the water body, and 5 components describing the state variables within the sediment (Fig. 1). The nutrient cycle in the pelagic is described by the following components: The phytoplankton (PHYT) which consists of 3 algae sub groups (diatoms, spring cyanobacteria, summer cyanobacteria), zooplankton (ZOOPL), herbivorous fish (FI), detritus (DET), bacteria (BAKT), dissolved inorganic phosphorus (P) and dissolved inorganic nitrogen (N). The state variables which refer to the sediment are: zoobenthos (ZOOB), sediment detritus (M), dissolved

Table 1 Principal water quality parameters of Lake Mu¨ggelsee in 1998 and 2002 (according to Ko¨hler et al., 2005) Parameter

Unit

2.1. Study site Lake Mu¨ggelsee is a shallow (mean depth 4.9 m) polymictic lake in the southeast of Berlin (Germany), with a surface area of 7.3 km2. It is flushed by the River Spree and has a catchment area of about 7000 km2. The water retention time of the lake is about 6–8 weeks. The mean discharge has declined by about 30% in the last two recent decades, from 10 m3 s1

121

TP SRP TN TIN Algae Secchi depth TP-retention Inflow

1

mg L mg L1 mg L1 mg L1 mm3 L1 M g Pm2 a1 m3 s1

Mean value (Vegetation period) 1988

2002

145 56 2530 1338 16.65 1.12 0.8 10

131 68 1217 561 5.8 1.92 0.1 6.63

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IO

N Nin, Pin DETin, PHYTin

PHYT

ZOOPL

P N, P DET, PHYT

BAKT DET

FI water sediment

burial

NS

ZOOB

UNS

M

PAS

PS

UM

UPAS

UPS

Fig. 1. Model structure of EMMO (Strube, 2005).

inorganic phosphorus in the interstitial water (PS), dissolved inorganic nitrogen in the interstitial water (NS) and phosphorus which is adsorbed by complexes such as iron hydroxide in the sediment (PAS) (Strube, 2005). The relationships between the different components are described by ordinary differential equations. The trophical matrix is static that is to say that the predator–prey relationships cannot be optimized by adaption. This kind of inflexible trophic system is criticized by Jørgensen (1996). The EMMO model was successfully calibrated and validated with time series of 1979–1981 and 1982–1985 (Strube, 2005). For the scenario simulations in the present paper, the model uses the time series of 1979–1981 (3 years). 2.2.2. Special aspects of EMMO in the context of scenario building In order to understand the building and evaluation of the later introduced group of circulation scenarios (see Section 2.3.3) it is crucial to know how EMMO realizes different mixing states and oxygen conditions at the sediment–water interface. Whether or not a lake shows a circulation of the entire water column depends on the value of the sigmoid stratification function ROX. The ROX function represents the redox state at the sediment–water interface, and is described by following equation: ROX ¼ 1 

1 1 þ b expðcDTðtÞÞ

DT is the temperature difference between the surface and the bottom of the lake. It can have values between 0.2 and 0.6 K. We fitted the parameters b and c, and found the values: b ¼ 100 000 and c ¼ 30. The ROX controls all oxygen depending processes in the sediment such as phosphorus release from the sediment

and denitrification. Depending on the temperature difference (DT(t)) between the surface and the bottom of the lake, ROX takes values between 0 and 1. As long as the temperature difference (DT(t)) is below 0.2 K, ROX is near to the value 1. By this a circulation is simulated, and a sufficient oxygen supply is provided. Hence processes triggered by low oxygen concentrations will not get affected. As soon as the temperature difference exceeds 0.6 K, ROX switches near to 0, simulates a stratification, and subsequent oxygen depletion. Thus an anaerobic state is simulated, causing for example higher phosphorus desorption rates and an intensified denitrification. It is important to know that when assuming ROX ¼ 0 (stratification), the concentration of dissolved phosphorus in the sediment increases since phosphorus desorption increases. However, the phosphorus transport from the sediment into the pelagic (where the phosphorus concentration becomes ecologically relevant) occurs only during the subsequent circulation period, i.e. when ROX is approximately 1. Hence a stratification period leads to intensified phosphorus release rates within the sediment, but a stratification period also acts as a sediment cover since nothing gets released into the pelagic. The relationships between DT, ROX and oxygen dependent processes in the EMMO model are shown in Fig. 2. Consequently, for the simulation of different mixing properties by EMMO we have to change DTp0.2 K in order to simulate circulation conditions, or DTX0.6 K in order to generate a stratification period. For the group of ice-scenarios (Section 2.3.3) it will be important to know how EMMO achieves an ice cover and which model parameters will be affected. In EMMO, the impact of ice or snow cover on productivity is provided by the sigmoid function SNOW (Strube, 2005). With respect to the presence or absence of an ice or snow cover, the SNOW-function switches between nearly 0 (ice/snow cover) and nearly 1 (no ice/snow cover). The SNOW

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calculates EMMO

Temp.difference between lake bottom and lake surface

Denitrification P − Adsorption P − Desorption Mineralisation

123

Time series of temperature difference

generates

Difference > 0.6K

Difference < 0.2K

ROX = 0

ROX = 1

PROCESSES Stratification

Circulation

Anaerobic

Aerobic

AFFECTED

Fig. 2. Relationship between temperature difference (DT), the sigmoid stratification function (ROX) and oxygen dependent processes in the EMMO model.

function influences the intensity of radiation, IM 1  expðEPSHÞ EPSH 1  expðEPSHÞ . þ SNOWbs IO EPSH

IM ¼ ð1  SNOWÞbIO

IO is the radiation, b the reduction coefficient of the radiation without ice cover, bs the reduction coefficient of the radiation with ice cover, EPS the vertical optical density, and H the depth of the lake. Algae productivity in particular, depends strongly on the IM-function. In order to change the duration of ice cover on the lake it is necessary to manipulate the SNOW-function. In Section 2.3.4 we introduce sediment cover scenarios which totally prevent phosphorus resuspension. In order to achieve the sediment cover scenarios in EMMO, it is crucial to know how EMMO mathematically describes phosphorus release from the sediment into the pelagic: Two quantities of EMMO are suitable for controlling resuspension, namely ROX, and the parameter which describes the exchanging rate at the sediment–water interface: zgel. By manipulating ROX not only will resuspension be affected, but also sediment-specific processes such as desorption of phosphorus or denitrification. The parameter zgel is part of the equation which describes the resuspension of phosphorus into the pelagic (ZP). The quantity ZP is described by the following equation: ZP ¼ MAXðzgel ðPS  PÞROX; 0Þ. The quantity zgel is the exchanging rate at the sediment–water interface, PS is the dissolved inorganic phosphorus in the sediment water, P is the dissolved inorganic phosphorus in the pelagic, and ROX the sigmoid stratification function. By setting zgel ¼ 0, the resuspension of phosphorus can be permanently prevented without other processes being affected.

2.3. Scenarios 2.3.1. Overview A total of 33 scenarios were developed which deal with different climate, economic and manmade impacts on the lake ecosystem. The scenarios are not meant to be realistic but ‘conceptually meaningful’, meaning that the scenarios shall stimulate specific model compartments, and show no redundancies among each other. Furthermore, the scenarios are rather extreme and diverse, since we want to force EMMO to show a strong reaction to an input signal and to facilitate an analysis of the evaluation results. All 33 scenarios can be thought of as resulting from the combination of 3 basic groups of scenario’s basic groups depending, on the kind of impact: 1. 3 different nutrient loadings of the inflow, 2. 10 different climatic conditions (different mixing- and ice conditions), 3. 2 different artificial manipulation actions. Each one of the 33 scenarios is composed of one element taken from the nutrient loading, one from climatic effects, and one from manipulation actions (see Table 1A in Appendix A). Each scenario receives a numerical designation, and an acronym (Table 1A in Appendix A). The reference scenario 1Ia (acronym ‘‘P1’’) was constructed by a combination of following scenario elements: unchanged nutrient loading (variable ‘‘1’’), unchanged climatic conditions (variable ‘‘I’’), and no manipulation action (variable ‘‘a’’).2 Scenario P1 represents the conditions found from 1979 to 1981. The other scenarios (D1, Dsw1, y) are analogously constructed. Scenario 2Ib (D2) for example is 2 The different scenario elements will be extensively described in Sections 2.3.2, 2.3.3 and 2.3.4.

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a combination of the nutrient loading 2, the unchanged climatic condition I, and the manipulation action b which defines that a manipulation had been done. The exact meaning of the single scenario elements will be explained in the following subsections. 2.3.2. Nutrient scenarios Nutrient load changes can be a consequence of land use variations, anthropogenic activities, and climate changes. With regard to the latter while it is expected that the frequency of rainfall will decrease (and consequently nutrient outwash will decline) it is also expected that extreme short time events such as flooding will occur more often (nutrient outwash will increase within a rather short time period) (Jacob and Gerstengarbe, 2005). The nutrient scenarios (P1, P2 and P3) simulate 3 different nutrient concentrations (phosphorus and nitrogen) in the inflow. Scenario P1 is the reference scenario with, compared to the initial conditions found in 1979–1981, unmodified nutrient conditions, P2 is a scenario where a 10 times higher nutrient concentration than in P1 is assumed, while in scenario P3 a 10 times lower nutrient concentration than in P1 is assumed. P3 approximately matches the present situation (2005). The nutrient scenarios give information about EMMO’s ability to process extremely different nutrient loads in the inflow.

Table 2 Description of the 6 circulation scenarios Climate scenario

Acronym Properties and description

II

Dsw

III

Ds

IV V VI

S Z Szs

VII

Szf

Circulation in spring and fall; stratification in summer and winter (dimictic) Circulation in winter, spring and fall; stratification in summer (summer dimictic) Total stratification (3 years ¼ monomictic) Total circulation (3 years ¼ monomictic) 1.5 years of stratification followed by 1.5 years of circulation (change in summer of the second year) 2.2 years of stratification followed by 0.8 years of circulation (change in spring of the third year)

Table 3 Description of the 3 ice scenarios Climate scenario

Acronym Properties/description

VIII

Ep

IX

Em

X

En

According to P1 the ice cover length was extended by 3 weeks According to P1 the ice cover length was shortened by 3 weeks No ice cover at all throughout the 3 years of simulation

2.3.3. Climatic scenarios The climatic scenarios can be divided into two scenario groups where climate changes are causing: 1. different types of water body circulation (circulation scenario group) and 2. differences in the ice duration (ice scenario group). Changes in the circulation properties of the water column are mainly influenced by climate changes. For Lake Mu¨ggelsee, it is expected that there is going to be a shift towards more frequent and long lasting stratification (Strube, 2005). Since stratification intensifies the phosphorus desorption, this shift can have major consequences for the water quality. By creating different circulation scenarios in EMMO, we want to identify the consequences of different circulation properties on the lake ecosystem. An achievement of circulation scenarios in EMMO means that we have to replace the natural circulation properties generated by the model, by a time series as assumed in the scenarios. In particular, the differences between water temperature at the surface and at the bottom of the lake (DT(t)) have to be modified, as this temperature difference determines, via the ROX-function, whether the water column in the lake will circulate or is stratified (see Section 2.2.2). The 6 different circulation scenarios are shown in Table 2. Climate scenario I is not listed since it just represents that compared to 1979–1981 unmodified state.

Differences in the duration of the ice cover have a major impact on the productivity of algae and higher trophic levels (Adrian et al., 1999; Blenckner et al., 2002). Shorter ice cover periods result in more favorable temperature conditions and a better light climate within the lake. Correspondingly, the productivity in all trophic levels is expected to be intensified (Adrian et al., 1999). The 3 ice scenarios are achieved by a change of the input time series (Table 3). In particular, we want to identify the impact of different ice durations on the primary production, and how the model transfers the signal to the different trophic levels. In order to achieve the scenarios, the input time rows had been manipulated (see Section 2.2.2).

2.3.4. Manipulation scenarios The sediment of Lake Mu¨ggelsee is a significant phosphorus reservoir (Kleeberg and Kozerski, 1997), with an estimation of about 10 000 t phosphorus in the entire sediment (Kozerski, 2004, personal communication). Since 1988, almost 30 t of the sediment phosphorus had been resuspended into the water column, causing high productivity in the pelagic (Kleeberg and Kozerski, 1997). This phosphorus load still stresses the nutrient budget of Lake Mu¨ggelsee, even though nutrition loads in the inflow decreased constantly since 1990 (Ko¨hler et al., 2005).

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With respect to the high resuspension rates of Lake Mu¨ggelsee, the manipulation scenarios simulate a sediment cover which totally prevents resuspension of phosphorus from the sediment. By creating a sediment cover, we want to demonstrate which ecological consequences can be expected if resuspension of sediment phosphorus can be totally prevented. In order to simulate a sediment cover, we can manipulate the sigmoid stratification function ROX as well as the parameter zgel (exchanging rate at the sediment–water interface) (see Section 2.2.2). Since it is important that the system’s reaction can be clearly traced back to a specific chosen scenario, a manipulation of ROX should be avoided. Therefore it was decided to set zgel ¼ 0 in order to achieve the sediment cover in the manipulation scenarios, these manipulation scenarios received the acronym ‘D’. All climatic and manipulation scenarios were combined with the 3 nutrient loads defined in the nutrient scenarios. Therefore, the scenario acronyms can be understood as a combination of circulation, manipulation and nutrient load properties. 2.4. Indicators 2.4.1. General aspects 2.4.1.1. Selection criteria. In order to choose the needed indicators for the evaluation of the scenarios, 3 aspects had to be considered: 1. Selection of the lake parameters which were qualified to show, with respect to a certain water quality goal, effects of different scenarios on the water quality. 2. Scaling of the parameters. 3. A proper statistical processing of the parameter depending on the time series. The selection of the indicators was based on the demands of the new water framework directive of the EU (WFD) (Water Frame Directive, 2000). This directive requires indicators which represent hydro-chemical, biological and hydromorphological elements. Since EMMO cannot generate hydromorphological elements, only hydro-chemical and biological outputs were considered as potential indicators. 2.4.1.2. Time periods. In order to avoid model dependencies on initial values, we took the simulation results of the 3rd simulation year (1981). Furthermore, we selected the vegetation period (March–September) within the 3rd year as the specific time frame, since relevant water-ecological effects do not occur during the winter season. The vegetation period was further divided into 2 seasons: spring (March–June) and summer (June– September).

125

2.4.2. Hydro-chemical indicators As hydro-chemical indicators we selected the following:





The total amount of dissolved phosphorus in the pelagic (P) was calculated for the total vegetation period (vp), for spring (sp) and also for summer (su). Due to the fact that for most of the year phosphorus is the vital limiting factor for the productivity of a limnic ecosystem, this parameter is qualified to indicate the degree of eutrophication. The danger of phosphorus release from the sediment into the pelagic was temporally differentiated, and represented by the following parameters pertaining to summer (su): 1. short term: resuspension (ZP), 2. medium term: desorption (DES), 3. long term: accumulated phosphorus in the sediment (PAS).

2.4.3. Biological indicators As biological indicators we selected the following:













The chlorophyll-a (CHLA) concentration was calculated for the vegetation period (vp), since chlorophyll-a is an important parameter for the indication of the lake’s trophical state. The amount of summer cyanobacteria (BCS) was calculated for the vegetation (vp) and summer periods (su). Since some cyanobacteria species produce cyanotoxins and persistent aggregates (e.g. Aphanizomenon flosaquae), the concentration of BCS is a very important factor for a lake ecosystem. Furthermore, cyanobacteria have special importance for public health (Gilroy et al., 2000). For a detailed simulation of possible ecological consequences see Bru¨ggemann et al. (2003). Secchi depth (SD) was calculated for the spring period (sp). In this present study, secchi depth was related to the probability of a recolonization of Lake Mu¨ggelsee by submerged macrophytes and a possible switchback to the clear state. The zooplankton concentration (ZOOP) was calculated for the summer period (su). Zooplankton is the trophical link between algae and fish. Since zooplankton deplete algae, high zooplankton concentrations indicate good water quality. The zoobenthos concentration (ZOOB) was calculated for the vegetation period (vp). The modeling of the zoobenthos in EMMO is based on the single species Chironomus plumosus, which is adapted to anaerobic conditions. Therefore high values of ZOOB indicates a worsening of the water quality. The biomass of herbivorous fish (FI) was calculated for the vegetation period (vp). Herbivorous fish deplete zooplankton by grazing, and favor in this respect high algae concentrations. Therefore, high amounts of herbivorous fish indicate a potential worsening of the water quality.

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2.4.4. Indicators as a basis for decision making Scaling routine: We clarify that we speak of ‘parameters’ as an outcome of the simulation model EMMO. By scaling the parameters and giving them an orientation according to a ‘good’/‘bad’—scale, we obtain ‘indicators’. Most of the parameters were scaled by using the minimum principle: ‘‘the less the better’’ (White et al., 1995). By not paying any attention to limit values (maximum permission errors) lower values always get a better evaluation than higher values. The parameter zooplankton is an exception and does not follow the minimum principle but the maximum principle. Since high zooplankton concentrations indicate a positive impact on the lake ecosystem we determine: ‘‘the more the better’’. The scaling of most parameters do not follow specific limit values, however for the parameters phosphorus, chlorophyll-a, short term phosphorus resuspension and secchi depth, it was useful to determine upper and lower limits in order to facilitate the subsequent statistical processing. For the parameters phosphorus and chlorophyll-a target values according to Behrendt and Opitz (1996) were applied. The target values refer to the goal of reaching the mesotrophic state within the next 20 years. Consequently the upper limit for phosphorus is 30 mg/m3 and for chlorophyll-a 27 mg/m3. For the parameter short term phosphorus resuspension (ZP), it was defined that no release shall be tolerated (limit value ¼ 0 mg/m3). For secchi depth the lower limit was defined by 1.94 m. This depth guarantees that 33% of the bottom of the lake receives light during spring time: this area is approximately that which was covered by submerged macrophytes before the lake switched into a turbid state in the beginning of the 1970s (Ko¨rner, 2001). For the parameter short term phosphorus resuspension (ZP), it was defined that no release shall be tolerated (limit value ¼ 0 mg/m3). 2.4.5. Statistical processing All parameters with an upper or lower limit were statistically processed by the use of exceeding probability (to exceed a certain limit (ep)), and extent of exceeding (ee). These statistical measures were applied with respect to the tolerance of the lake ecosystem towards these parameters. To calculate the exceeding probability, all days in which the limit was exceeded were counted, and related to the number of days within the base period P¼

D N

P is the exceeding probability, D the number of days in which the limit was exceeded, and N the number of days within the base period. The extent of the exceeding is going to be calculated by the mean value of the transgression intensities 1 XD H¼ x i¼1 i D

H is the extent of the exceeding, D the number of days on which the limit was exceeded, and xi the height of the single exceeding event. For the parameter secchi depth, only the exceeding probability was applied because it does not matter to which extent the limit was exceeded. Any limit violation would negate an achievement of the goal. In order to facilitate a quick overview and comparison between the different scenarios, the mean value (mv) was used for three parameters: dissolved phosphorus in spring, zooplankton and fish. Except for dissolved phosphorus in spring the lake ecosystem has a high tolerance towards these parameters. Hence it is acceptable to apply the mean value, even though extreme values will be hidden. The statistic measure of median (md) was used whenever the skewness parameter (x) was too high (xo0.5; x40.5), and consequently the mean value could not be applied. The median value was applied for the parameters phosphorus in summer, desorption, sediment phosphorus and concentration of the zoobenthos. The parameter cyanobacteria in summer was statistically processed by calculating the standard deviation (dev). This statistical measure was chosen in order to embrace the high sensibility of the lake ecosystem towards this parameter. The parameter summer cyanobacteria in the vegetation period was statistically processed by the calculation of the percentage (per) of summer cyanobacteria compared to spring cyanobacteria and diatoms. In total 16 water quality indicators were developed, the acronyms for those follow the systematic shown in Fig. 3. 2.4.6. Indicator ‘relevance’ In addition to the 16 biological and hydro-chemical water quality indicators described in Sections 2.4.2 and 2.4.3, the indicator ‘relevance’ was established. This special indicator does not follow the development scheme of the other indicators since it is not related to biological or physical–chemical parameters. The indicator ‘relevance’ is subjectively motivated, and reflects the importance of a scenario as perceived by the first author. The decision whether a scenario is important or not, is based mainly on its expected impact on the ecosystem, and the components which are affected in the model. In order to identify the relevance of a scenario, a simple scale was built: 1 ¼ scenario of major relevance, 2 ¼ intermediate relevance and 3 ¼ minor relevance. Each scenario was classified by this scale. 2.5. Cluster analysis 2.5.1. Overview With cluster analysis, a set of objects can be classified and reduced to a limited set of groups (clusters). The classification of objects into clusters is based on the similarity of their properties (Bru¨ggemann and DrescherKaden, 2003). Cluster analysis in connection with HDT was described by Hollert et al. (2002), Pudenz et al. (2000)

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water quality parameter

statistical measure

indicator

exceed. prob. (ep)

Pvpep

extent of exceed. (ee)

Pvpee

summer (su)

median (md)

Psumd

spring (sp)

mean value (mv)

Pspmv

summer (su)

exceed. prob. (ep)

ZPsuep

extent of exceed. (ee)

ZPsuee

time range

vegetation period (vp) phosphorus (P)

phosphorus release (ZP)

127

desorption (DES)

summer (su)

median (md)

DESsumd

sediment phosphorus (PAS)

summer (su)

median (md)

PASsumd

chlorophyll a (CHLA)

vegetation period (vp)

exceed. prob. (ep)

CHLAvpep

extend of exceed. (ee)

CHLAvpee

vegetation period (vp)

percentage (per)

BCSvpper

summer (su)

deviation (dev)

BCSsudev

Secchi deapth (SD)

spring (sp)

exceed. prob. (ep)

SDspep

zooplankton (ZOOP)

summer (su)

mean value (mv)

ZOOPsumv

zoobenthic (ZOOB)

vegetation period (vp)

median (md)

ZOOBvpmd

fish (FI)

vegetation period (vp)

mean value (mv)

FIvpmv

cyanobacteria (BCS)

Fig. 3. Schematic illustration of the development of water quality indicators.

and Bru¨ggemann (2002). Cluster analysis in the present study is applied in order to:

 

simplify the complex data matrix by reducing scenarios (objects) and indicators (attributes) to the cluster representatives, and consider only numerically relevant differences within the evaluation process.

In the present study, we apply a complete linkage procedure (hierarchical clustering ) for the reduction of scenarios and indicators. The complete linkage procedure aggregates two clusters when the distance between the most diverse objects within the clusters is small enough. Hence only similar objects are going to be aggregated into the same cluster. In order to provide that just similar objects aggregate in a cluster, we define a certain similarity level at which the clustering process stops. The results of the cluster

analysis can be visualized by dendrograms (e.g. Fig. 5). The clustering procedure was supported by the statistic program SPSSs. 2.5.2. Clustering of scenarios The scenarios, which are described in Section 2.3 in detail, were clustered on the basis of the squared Euclidean distance. In order to consider the different value scales, data had to be transformed. By using the SPSSs ztransformation, the values were downscaled to a range between +3 and 3. The resulting clusters of similar scenarios were labeled by A0 , B0 , C0 and so on. 2.5.3. Clustering of indicators The water quality indicators, which are discussed in Section 2.4, were clustered on the basis of the correlation matrix. Therefore no data transformation had to be done. The indicator clusters are called A, B, C and so on.

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2.6. Hasse diagram technique (HDT) The Hasse diagram technique (HDT) is a simple multicriteria decision support tool, based on partial order theory (Bru¨ggemann et al., 1999, 2001; Sørensen et al., 2003). In order to evaluate scenarios which are characterized by a set of different indicators, the evaluation by the HDT is done with respect to all indicator values simultaneously, based on a simple pcomparison (Bru¨ggemann and Steinberg, 2000). This proceeds as follows: a certain scenario (x) will be ranked higher compared to another scenario (y) only if all indicators of x have lower values (provided that low values receive a better evaluation than higher ones) than the indicator values of the scenario y (‘‘generality principle’’). In the case that all scenarios are evaluated better in one indicator and worse in at least one other indicator compared to the other scenarios, it cannot be given a mutual order relative to each other, they are said to be incomparable. Often a subset of indicators can be identified which causes the incomparabilities among objects. These indicators are called antagonistic (Simon et al., 2004). The result of all pcomparisons is visualized by a so-called Hasse diagram (HD) (Simon, 2003). An example data matrix and the associated HD for 3 scenarios and 2 indicators, is shown in Fig. 4. The scenario S1 has got a worse evaluation (higher values), compared to the scenarios S2 and S3 in all indicators, and therefore receives the highest position within the HD. Connecting lines visualize a linear order between scenarios (chain). In contrast to scenario S1, scenario S2 receives in the indicator I1 a better evaluation and in the indicator I2 a worse evaluation than scenario S3. In order to illustrate that the scenarios S2 and S3 are incomparable, they stand side by side (antichain) (Simon, 2003) (Fig. 4). The HDT is a so-called data driven evaluation method, which neither allows the compensation of indicator values, nor the aggregation of different indicators. Thus, the HDT is a highly objective and transparent decision support tool which facilitates intensive data analysis. By uncovering the incomparabilities due to a certain subset of indicators, it is possible to identify potential conflicts, that is to say for example between different protection aims. The Hasse diagram technique (HDT) was carried out by using the software WHASSE, which can be obtained for non-commercial use from the corresponding author (R.B.)

(Bru¨ggemann and Halfon, 1995). In the present paper we show a combination of HDT, cluster analysis and dimension reduction by a stepwise aggregation method (METEOR, see Section 2.7).

2.7. METEOR The decision support system METEOR described by Simon et al. (2005) and Pudenz and Bru¨ggemann (2001) can be carried out by the software WHASSE. METEOR is an extension of the HDT and should be applied at the end of the evaluation process in order to maximize data analysis. METEOR has two goals: 1. To eliminate, step by step, the incomparabilities in the HD, and thus lead the evaluation process towards a distinct decision. 2. To allow participation within the evaluation process (Pudenz and Bru¨ggemann, 2001). METEOR enables a stepwise aggregation of indicators until a unique best or worst solution can be identified. This procedure requires a preliminary step to standardize all indicator values (z-transformation, see Section 2.5.2). The aggregation process includes a weighting procedure of any subsets of indicators which confirm the subjective preferences. In the aggregation process, details of characteristics are lost, since a weighted sum of indicators bears less information than the indicators alone. However at the same time more comparabilities, and hence a simplification of the decision problem, will be obtained (Simon et al., 2005). Criteria for given weights were the ecological sensitivity of an indicator and its position within the trophical matrix (subordination of biological indicators). Furthermore, the weighting process takes into regard that prediction uncertainties increase with the trophic level: the prediction of phosphorus concentrations (abiotic) for example is more precise than for algae biomasses (biotic) (Leibundgut and Hildebrand, 1999). Due to the better quality of abiotic indicator values compared to the biotic ones, the abiotic indicators will receive a higher weight.

3. Results bad

Scenarios Indicators

S1

I1

I2

2

3

S2

1

2

S3

2

1

S1

S2

S3 good

antagonistic indicators Fig. 4. Hasse diagram of the data matrix for the example explained in the text (Simon, 2003).

3.1. Evaluation of the scenarios by Hasse diagram technique The direct evaluation of the 33 scenarios by the HDT led to no clear result. A distinct decision is not possible since each scenario has advantages and disadvantages on this very detailed level of description. In order to find a clear decision, in a first step we simplify the very complex decision matrix by the application of the cluster analysis.

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similarity level

A

Pvpep CHLAvpee Pvpee ZOOBvpmd Pspmv PASsumd DESsumd CHLAvpep SDspep FIvpmv

B

BCSsudev

C

PSumd ZPsuee

D

ZPsuep

E

RELEVANCE

F

BCSvpper ZOOPsumv

0

5 6

10

15

20

129

25

Fig. 5. Dendrogram of the indicator clusters.

3.2. Application of the cluster analysis Since detailed cluster analysis is not the focus of the present paper, we arbitrarily selected a similarity level for both indicator and scenario clustering at moderate levels namely 6 in the case of the indicators and 4 in the case of the scenarios. This way 6 indicator clusters (Fig. 5) and 8 scenario clusters (Fig. 6) were identified. Since indicator cluster A is very extensive, we additionally divided it and made two clusters out of it. Thus, we finally received 7 indicator clusters. By the analysis of the scenario clusters (Fig. 6), certain regularities are noticeable.3 The nutrient load in the inflow is the most important attribute for the classification of the scenarios in different clusters: all scenarios of any one cluster (A0 , B0 , C0 , y) have the same nutrient load in the inflow (either normal (1), maximum (2) or lowest nutrient load in the inflow (3)). Hence any cluster can be characterized by its nutrient load. Scenarios which are characterized by same nutrient load but a different cluster location get separated by the attribute ‘phosphorus resuspension from the sediment’. This is the second most important attribute for a separation of scenarios in different clusters. For example, all scenarios in the cluster A0 do not allow phosphorus release from the sediment (ZP ¼ 0 during indicator time

3

For the goals of the present paper a discussion the indicator clusters is not necessary.

range). In contrast, all scenarios in the cluster B0 do allow phosphorus release from the sediment. Exclusively for scenarios with maximum nutrient loads in the inflow, it is essential to know how phosphorus release is prevented (ROX or zgel), and if circulation starts after a stratification period of 2.2 years. Scenarios which prevent phosphorus release by setting ROX ¼ 0 are getting classified in cluster G0 , while scenarios which prevent phosphorus release by setting zgel ¼ 0 are getting classified in cluster H0 . The scenario which is characterized by a very long stratification period (2.2 years) followed by a circulation for the rest of the simulation time range, is classified in cluster F0 . The scenario properties appear to have a crucial impact on the indicator values. The regularity of scenario allocation in different clusters can be illustrated by a lexicographical order (Table 4). The lexicographical order implies a very strict order of criteria importance (nutrient load most important, phosphorus release second important, y), which is avoided by other decision aids. In this paper we will demonstrate this by the use of METEOR in Section 3.6. Since the evaluation of the scenarios by METEOR follows the same criteria as shown in Table 4, we expect that the ranking of scenarios follows this scheme. 3.3. Selection of scenario and indicator representatives After classification of the scenarios and indicators, we choose one representative from each indicator and scenario cluster, whereby we reduce the decision matrix from 33

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130

similarity level

A’

4 5

0

10

15

20

25

Ds1 Dsw1 D1 S1

B’

P1 Em1 Z1 Ep1 Szs1 En1 Szf1

C’

Ds3 Dsw3 D3 S3

D’

P3 Em3 Z3 Szf3 Szs3 En3 Ep3

E’

Em2 En2 Szs2 Z2 Ep2 P2

F’

Szf2

G’

S2 Ds2 Dsw2

H’

D2 Fig. 6. Dendrogram of the scenario clusters.

Table 4 Lexicographical order of the scenario clusters Cluster Scenario attribute responsible for the cluster allocation

F0 E0 G0 H0 B0 A0 D0 C0

1. Nutrition load in the inflow

2. Depression of phosphorus release from the sediment?

3. How is the resuspension of phosphorus depressed?

High

Yes

ROX

Normal

Low

X X X X

No

zgel

X X X X X X

X

X X X

X X

Yes

No

X X

X

4. Circulation starts after 2.2 years of stratification?

X X X

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(scenarios) 17 (indicators) down to 8 (scenarios) 7 (indicators). Thus, a significant simplification of the decision matrix was achieved. The scenario representative of each scenario cluster was selected as that scenario with an indicator value that fitted best with the mean indicator values of all scenarios within one cluster. The indicator representatives were arbitrarily chosen out of each indicator cluster. For a detailed discussion see Section 3.4 and Kardaetz (2004). 3.4. Analysis of the scenario and indicator representativeHD The HD of scenario and indicator representatives (see Section 3.3) still did not provide a clear decision, as no comparability relation could be found. However, the reduced decision matrix allowed a much easier identification of antagonistic indicators (see Section 2.6). Antagonistic indicators are zooplankton and phosphorus and chlorophyll-a. The reasons for the antagonism are (i) the different scaling routine of the zooplankton indicator compared to all other indicators(‘the more the better’, see Section 2.4.4), and (ii) the functional dependence of zooplankton on phosphorus and chlorophyll-a. Since herbivorous zooplankton feed mainly on algae, it is clear that high algae/nutrient concentrations result in increasing zooplankton biomasses. This relationship means that a positive evaluation in the zooplankton indicator (high concentrations), will always imply a negative evaluation in the chlorophyll-a and phosphorus indicators (high concentration). This phenomenon makes use of the zooplankton indicator within the evaluation very problematic. The uncovering of such obvious conflicts4 confirms the analytical advantage of the HDT compared to other decision aids, such as PROMETHEE. The indicator summer cyanobacteria (BCSsudv, see Fig. 3) is another antagonistic indicator which always lead to opposed evaluations with the indicators phosphorus and chlorophyll-a. This is not a matter of orientation or functional dependence, but a competitive advantage of summer cyanobacteria during times with a lowered nutrient supply (for Lake Mu¨ggelsee this phenomenon was observed and described by Ko¨hler et al., 2005). The competitive advantage is a result of the N-fixing ability of some cyanobacteria species (e.g. Aphanizomenon flosaquae). Low nutrient concentrations in the inflow and the lake lead to simulated high cyanobacteria concentrations. 3.5. Visualization of information losses (‘zoom’) Since clusters are not really homogenous, it is inevitable that a loss of information occurs when working with scenario and indicator representatives, since the decision matrix is simplified. However, by generating HDs of 4 Obvious from an ecological modelling point of view, but hidden from the decision making point of view.

Fig. 7. ‘‘Zoom’’ into the indicator cluster A by the generation of a clusterspecific HD.

indicators taken from a single cluster (‘‘zoom’’) the information loss can be visualized. The notion ‘‘zoom’’ points out that the analytical view is focused on the single cluster. The ‘‘zoom’’ into the clusters by HDT can be considered as a method for visualizing the degree of individuality of scenarios/indicators in the clusters and for the quality of the selected cluster-representatives. The ‘‘zoom’’-HD for the cluster A is shown in Fig. 7. All 33 scenarios are spread over just 5 levels, which are primarily separated by the different nutrient loads in the inflow. The great number of incomparabilities (426) shows that many conflicts (oppositional indicator characteristics, that is to say conflicts between different protection goals) remain unsolved and are not taken into consideration by the selection of only one indicator representative. 3.6. Final evaluation by METEOR All analytical steps described above are important in order to identify conflicts (conflicts between different protection goals, such as water quality and biodiversity) within the decision matrix, but they do not lead to a clear decision. In order to facilitate the decision making, METEOR was applied for the scenario and indicator representatives. A total of 6 aggregations were needed to receive a clear result, that is to say a total order. The indicators zooplankton and chlorophyll-a were aggregated first, as they showed the highest degree of negative correlation (r ¼ 0.921). Since chlorophyll-a is one of the most important parameters for determining the trophic state of a lake, and the zooplankton indicator is characterized by a problematic orientation (see Section 3.4), chlorophyll-a weighed much higher (0.9) than zooplankton (0.1). The HD of the first aggregation by METEOR is shown in Fig.

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Ds2

D2

Em2

Szf2 D1

Z1 Dsw3

Em3

Fig. 8. Hasse diagram of the representatives after the 1st aggregation by METEOR.

Em2

Ds2

D2

Z1

Dsw3

Szf2

D1

Em3

Fig. 9. Hasse diagram of the representatives after the 4th aggregation by METEOR.

8. A total of 6 comparabilities and the two best scenarios Dsw3 (stratification summer/winter, circulation spring/ autumn, lowest nutrient load in the inflow, prevention of phosphorus release from the sediment during summer) and Em3 (a reduced ice cover by 3 weeks, lowest nutrient load in the inflow, no prevention of phosphorus release from the sediment during summer) are now identifiable. In order to demonstrate METEOR’s functioning of a stepwise reduction of incomparabilities, we demonstrate the result of the 4th aggregation (Fig. 9). After aggregation of 4 indicators out of a total of 7, it can clearly be recognized that the HD evolves towards a total order, as it must be from theoretical considerations (Simon et al., 2005). A total of 21 comparabilities and 14 incomparabilities can be found. The scenario representatives are spread over 4 levels (out of 8 possible) and are mainly separated by the nutrient load in the inflow (1, 2 or 3), Scenarios with the lowest nutrient input (Dsw3, Em3) receive the best evaluation. The scenario representative Em2 is the worst scenario.5 After the 6th aggregation the final result is:

5

All single aggregation steps can be looked up in Kardaetz (2004).

Dsw3 (Ds3, D3, S3) 46 Em3 (P3, En3, Ep3, Szs3, Szf3, Z3)4D1 (S1, Dsw1, Ds1)4Z1 (P1, Em1, Ep1, Szs1, En1, Szf1)4D24Ds2 (Dsw2, S2)4Em2 (En2, Szs2, Z2, Ep2, P2)4Szf2. By analyzing the final evaluation result, it becomes obvious that the scenarios are strictly ranked by the nutrient load in the inflow. Scenarios with the highest nutrient load in the inflow (2) get a worse ranking then scenarios with the normal (1) and lowest (3) nutrient load in the inflow. The worst scenario is Szf2, characterized by a phosphorus accumulation in the sediment water for 2.2 years (stratification) and a sudden release of the accumulated phosphorus into the pelagic in spring of the 3rd year. This scenario characteristic has a substantial influence on the water quality indicators. The ranking of the next worse scenarios with maximal nutrient load in the inflow shows the importance of the phosphorus release properties in the scenarios. Scenario Em2, where phosphorus release from the sediment is not prevented, receives a worse evaluation than do scenarios Ds2 and D2 which prevent phosphorus release from the sediment either by setting ROX approximately 0 (Ds2) or zgel ¼ 0 (D2). The reason for the better ranking of D2 compared to Ds2 is primarily based on the way phosphorus release from the sediment is prevented: By setting ROX near 0, the indicators PASsumd and DESsumd receive higher values (bad evaluation) than compared with a manipulation by zgel, where these indicators stay unaffected (see Section 2.2.2). The ranking of scenarios with unchanged and minimum nutrient loads is depending by the nutrient load in the inflow and the possibility of phosphorus release. The way how phosphorus release is prevented (ROX or zgel) and the circulation timing is irrelevant for the explanation of the ranking of scenarios with unchanged and minimum nutrient loads. The reason for this difference is that low nutrient loads in the inflow affect the ecosystem indicators less than high nutrient loads. Scenario Dsw3 as the best scenario confirms the explanation scheme. The different periods of ice cover are not relevant for the ranking of the scenarios. In summary the ranking of the scenarios depend on: 1. the nutrient load in the inflow and 2. whether phosphorus release from the sediment is prevented or not. For scenarios with maximum nutrient load in the inflow, the ranking of the scenarios further depends on: 3. how phosphorus release from the sediment (zgel or ROX) is prevented and 4. the timing of the start of the circulation.

6

‘4’ means ‘better than’.

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4. Discussion Our comprehensible evaluation results show that the combined approach of HDT, cluster analysis and METEOR can successfully handle large data sets. Additionally we confirmed that the prediction quality of the EMMO model is suitable. Thus, we not only developed an evaluation procedure, but also a method to verify complex ecosystem models by scenarios. By using the cluster analysis at the beginning of the evaluation, the data matrix is simplified. Thus cluster analysis saves both effort and time. By using METEOR, it is possible to get a comprehensible ranking of the scenarios. In the present study, one might expect that cluster analysis is able to substitute for METEOR as the decision making tool. However since cluster analysis does not directly allow a comparison of scenarios characterized by several indicators, it is not feasible to declare METEOR redundant. It would be unrealistic to reduce the evaluation process to cluster analysis only. The cluster analysis can simplify the decision finding by METEOR, but cannot substitute for it. The zoom by the HDT is a useful tool to visualize the heterogeneity of a cluster and for identifying conflicts which will be not taken into consideration by selecting just one representative. In this note ‘‘zooming’’ enables a quality proof of the chosen cluster representatives. Thus by identifying too many conflicts and differences between the cluster elements one should consider repeating the cluster analysis and chose a lower similarity level. As a criterion for the decision whether a cluster is too heterogeneous or not, the number of incomparabilities can be used. This however requires a discussion about a limit value which determines—on the basis of comprehensible criteria—at which number of incomparabilities a cluster, can be called ‘‘too heterogeneous’’. The combined application of HDT and METEOR for the handling of complex decision problems was already documented by Simon et al. (2005) and Voigt and Bru¨ggemann (2005). This combined approach integrates the advantage of real decision support (identifying one best solution), with participation and transparency (Simon et al., 2005). However, often the number of indicators and objects is very large whereby the clarity and traceability of the evaluation is suffering. Therefore the evaluation procedure described in the present paper extends the common approach, by newly using the cluster analysis and the ‘‘zoom’’ into the clusters. Thus it is possible to handle a large set of objects and attributes while retaining clarity. It is evident that the presented stepwise evaluation method is very complex and time-consuming. Even though the evaluation procedure considers objectivity, data analysis, participation and a distinct result (clear decision) at the same time, whether it is also an attractive tool for decision makers in real conflict situations is question-

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able. Therefore the presented stepwise evaluation procedure needs some simplification and test runs with realistic scenarios. In order to simplify the procedure, it is eligible if this new evaluation procedure could be done by the help of computer software, which however is still not available. Nevertheless there are other methodical approaches which could be an alternative to the combination of cluster analysis and METEOR. Mucha (2002) linked cluster analysis with reordering techniques in order to handle complex data matrices. The Formal Concept Analysis (FCA) focuses on identifying conceptual structures between data sets. It was successfully applied in several studies as a method for dimension reduction and reordering of data (Ganter and Wille, 1996; Kerber, 2005). By classifying and systematically ordering data the Facet Theory (FT) can be seen as a tool for handling complex data as well (Borg and Shye, 1995). The Principle Component Analysis (PCA) (see, e.g. Legendre and Legendre, 1998) is just structuring the data. However it can only be seen as a preprocessing step, as it does not take into regard the ‘‘good–bad’’ orientation of the data. We did not follow those approaches but present a promising new one for the handling of very complex data within evaluation procedures. So far only ecological scenarios have been evaluated. However we propose that the procedure is also able to handle complex economic and social decision problems, or a combination of all. Thus the presented stepwise evaluation procedure can be extended to other relevant areas of decision making and it would be possible not only to evaluate complex decision situations (scenarios, chemicals, policies, etc.) from a sustainable point of view, but also to make this decision support tool more attractive for decision makers.

5. Conclusion The reasonable and comprehensive results show that the combination of HDT, cluster analysis and a step-wise iterative procedure to include subjective preferences can successfully handle large data sets.

Acknowledgments We thank for fruitful discussions Sabine Hilt, Rita Adrian, Jan Ko¨hler and Horst Behrendt, and especially Sarah Poynton for reviewing the paper and correcting the English.

Appendix A The systematics of development for the 33 scenarios is given in Table 1A.

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Table 1A Systematics of development for the 33 scenarios Scenario Acronym Different kinds of impact

1Ia 1Ib 1Iia 1IIIa 1Iva 1Va 1Via 1VIIa 1IIXa 1Ixa 1Xa 2Ia 2Ib 2IIa 2IIIa 2IVa 2Va 2VIa 2VIIa 2IIXa 2IXa 2Xa 3Ia 3Ib 3Iia 3IIIa 3IVa 3Va 3VIa 3VIIa 3IIXa 3IXa 3Xa

P1 D1 Dsw1 Ds1 S1 Z1 Szs1 Szf1 Ep1 Em1 En1 P2 D2 Dsw2 Ds2 S2 Z2 Szs2 Szf2 Ep2 Em2 En2 P3 D3 Dsw3 Ds3 S3 Z3 Szs3 Szf3 Ep3 Em3 En3

Nutrient loadings of inflow

Different climate effects on the lake (changing mixing- and ice duration properties)

Artificial manipulation made?

1

I

a (no)

2

3

X X X X X X X X X X X

II

III

IV

V

VI

VII

IIX

IX

X

X X

X X X X X X X X X X X

X X X X X X X X X X X

X X

X X X X X X X X X X X

X X X X X X X X X X X X X X X X X X X X

b (yes)

X X

X X X X X X X X X X X

X X X X X X X X X

X X X X X X X X X

Each scenario is composed of one element from nutrient loading, one from climate effects, and one from manipulation actions. Detailed explanations will be given in Section 2.3.

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