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A Structurally Dynamic Approach to Ecological and Environmental Models

Jingjie Zhang

Structurally dynamic approach to ecological and environmental models is a recent development. The parameters in the models are constantly varied to account for the adaptations and the shifts in the species composition. The changes of the parameters are either based on expert knowledge or by optimization of a so-called goal function that can describe the fitness to the changed conditions. This new approach overcomes the weaknesses that follow by traditionally used models: 1). The fixed and rigid parameter sets are used in these models, although we know that the properties of the species and the compositions of the species change according to the prevailing condition of the ecosystem; and 2). Calibration is often difficult, because we have to deal with a number of parameters simultaneously and test them within a wide range of possible values. The structurally dynamic models (SDMs) attempt to solve these problems by introduction of a goal function. Although good theoretical bases for application of a serial of goal functions have been developed, only few case studies have shown that this approach may be applicable. Further examinations are therefore needed.

One of the main objectives of this thesis is to develop and test a new modelling method using the thermodynamic function exergy and size-related functions for two state variables, namely phytoplankton and zooplankton in eutrophication models. It is assumed that an ecosystem develops towards the highest possible exergy under prevailing conditions, which is used in calibration of several of the most crucial biological parameters. Furthermore, the thesis gives an overview of the application of the SDM-approach, examines the application of this approach both in calibration, validation and prognosis validation in three cases, and attempts to explain the observed results of bio-manipulation by new case studies: submerged plants / phytoplankton for competition of nutrients and application of silver carp.

For Lake Mogan, located nearby Ankara, Turkey, a structurally dynamic model based on phosphorus nutrient limitation has been developed for examination of this new calibration method. This eutrophication model, which includes dense submerged vegetation, was calibrated using a standard procedure described by Jørgensen and Benoricchio (2001a). Furthermore, exergy was applied as a goal function to consider the dynamic adaptation and the seasonality of plankton species (presented by size shifts). This study is the second example of application exergy as a goal function in the calibration phase. The model was also validated using data from another year. The results yielded a validation similar to or better than that obtained by several lake models (Jørgensen, 1997a, 1998 and 2001b). The model gives a good performance in describing the competition between phytoplankton and submerged plants. This model was furthermore used to set up a prognosis for the response of the lake to the increased phosphorus input (Zhang et al., 2003b). It was found that a shift to a turbid water state takes place at phosphorus concentration between 0.16-0.25 mg TP l-1 resulting in a significant decrease in the submerged plants. Above the threshold P level, the submerged plants abruptly disappeared, while phytoplankton became dominant. The model simulated the recovery of the lake through reducing the phosphorus concentration in the inflow to the original level. Submerged plants redeveloped at a lower phosphorus concentration (about 0.1 mg TP l-1). However, the recovery took very long time because the lake had a high resilience probably due to the accumulation of phosphorus in the sediment. The shifts between the clearwater and turbid water states followed a hysteresis for the structurally dynamic model based on the maximum exergy storage hypothesis (Jørgensen & Mejer, 1979). The results presented are furthermore completely in accordance with how shallow lakes respond to the changing phosphorus levels with a hysteresis in the range 0.10-0.25 mg TP L-1 (Scheffer, 1997; Scheffer et al., 2001). Therefore, the model result may be considered a support for the maximum exergy storage hypothesis.

An ecological modelling software, named PAMOLARE, for planning and management of lakes and reservoirs, developed by Jørgensen et al. (2003), was applied on the study of Lake Glumsø, a small shallow Danish lake, situated about 70 km south of Copenhagen, Denmark. The software has four eutrophication models including application of a structurally dynamic model. Two of the models in the PAMOLARE program were tested against the data from Lake Glumsø: one year for calibration, one year for validation and three years for a prognosis validation (Zhang et al, 2003 c). Compared with observations, the simulations with the structurally dynamic approach yielded satisfactory results over all 5 years, whilst the two-layer model with a trial and error calibration approach did not give acceptable results. The results were also compared with those of two previously developed models, specifically designed for Lake Glumsø. It was concluded that the structurally dynamic model from PAMOLARE in the Lake Glumsø case gave better results than the 2-layer model included in PAMOLARE, and yielded equally good results as the two other eutrophication models specifically developed for Lake Glumsø. Furthermore, the model was far less time consuming to calibrate than the three other models, due to the SDM approach.

Lake Tai, a large shallow Chinese lake with a surface area more than 2000 km2, was used for the third case study in the thesis to examine the SDM application in combination with a 3D-model developed by Weiping Hu (Hu et al., 2004). A structurally dynamic model using nutrients (N and P) and silver carp (Hypophthalmichthys molitrix) as forcing functions found by the use of a 3D-model and covering phytoplankton and zooplankton as state variables, was developed (Zhang et al., 2004). The model was calibrated and validated with different data sets from different stations. Both the calibration and validation produced reasonable results. The model was also applied to explain the use of bio-manipulation by silver carp to restore the lake ecosystem. It was found that the model yielded the same results as other researchers obtained: silver carp with a middle range of biomass can reduce eutrophication, but a higher concentration of the big-head fish in the lake could result in a turbid water state.

The application of structurally dynamic models has been shown by all the SDM-case studies to be of importance for the prognosis made by the model. The prognoses are, however, also made on basis of our best knowledge about the future loading of nutrients. The success of the structurally dynamic approach is therefore also dependent on our tools to calculate or estimate the future loading of nutrients. The modelling literature contains several loading models; but they are all difficult to apply and do not consider all the nutrient sources. Many models focus for instance entirely on the non-point agricultural pollution and do not consider the point sources and the nutrient concentrations in the rainwater. The Pamolare software contains, however, also a loading model, that has been tested and validated on the Lake Glumsø case study (Zhang and Jørgensen, 2003d), where the loading is known reasonable well. The result of the test was that the loading model yielded a good estimation of the loading. It may therefore be recommended to apply it in combination with SDMs to set up prognoses for various environmental strategies.

In a summary, through the three successful case studies- a small shallow lake (Lake Glumsø), a middle-size shallow lake (Lake Mogan) and a large shallow lake (Lake Tai), it was demonstrated that the SDM methodology may be applied beneficently on different lake ecosystems (Jørgensen et al., 2002; Zhang et al., 2003 a, b, c) both for the calibration, validation and prognosis validation. The frequently applied eco-technology, bio-manipulation, is also well explained by SDM approach: 1). For the application of a higher ratio of carnivorous / planktivorous fish (Jørgensen and Bernardi, 1997); 2). For the application of herbivorous fish (Zhang et al., 2004); and 3) For the application of submerged plants (Zhang et al., 2003b).


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