Examination of structurally dynamic eutrophication model

Transcription

1 Ecological Modelling 173 (2004) Examination of structurally dynamic eutrophication model Jingjie Zhang, Sven Erik Jørgensen, Henrik Mahler a DFH, Institute A, Environmental Chemistry, University Park 2, DK 2100 Copenhagen 0, Denmark Received 19 March 2003; received in revised form 16 September 2003; accepted 16 September 2003 Abstract An ecological modelling software, named Pamolare, for planning and management of lakes and reservoirs was developed by Jørgensen et al., 2003 [PAMOLARE Training Package, Planning and Management of Lakes and Reservoirs: Models for Eutrophication Management, UNEP DTIE IETC and ILEC, 1091 Oroshimo-cho, Kusatsu, Shiga, , Japan, 2003]. The software has four eutrophication models including application of structurally dynamic models. We tested two models in the Pamolare program using data from Lake Glumsø, Denmark: one year for calibration, one year for validation and three years for a prognosis validation. Compared with observations, the simulations by the structurally dynamic approach yielded satisfactory results over all five years, whilst the two-layer model with trial and error approach in Pamolare did not give acceptable results. We also compared the results with that of two previously developed models, specifically designed for Lake Glumsø. We concluded that the structurally dynamic model from Pamolare in the Lake Glumsø case gave better results than the two-layer model included in Pamolare, and yielded equally good results as the two-eutrophication models specifically developed for Lake Glumsø. Furthermore, the model was far less time consuming to calibrate than the three other models, due to an automatic calibration procedure Elsevier B.V. All rights reserved. Keywords: Structurally dynamic model; Pamolare; Two-layer model; Calibration; Validation; Prognosis 1. Introduction The International Environmental Technology Center of UNEP (IETC-UNEP) and International Lake Environment Committee (ILEC) has recently developed a modeling software package named Pamolare (Planning and Management of Lakes and Reservoirs), offering four eutrophication models with different complexity levels: 1. The Vollenweider plot (one state variable, the phosphorus or nitrogen loading in g m 2 per year); 2. A model with four state variables; P and N in the water and in the sediments and several correlations to calculate other state variables; 3. A two-layer model with 21 state variables; and 4. A structurally dynamic model (SDM) developed from the two-layer model but applying the structurally dynamic approach (Jørgensen, 1999) for calibration, validation and prognosis simulations in addition to an automatic calibration for calibration of four other important physical chemical parameters, which are the settling velocity and the decomposed rate of the detritus, and the release rates of nitrogen and phosphorus in the sediments. Corresponding author. Tel.: ; fax: address: jz@dfh.dk (J. Zhang). SDM is a recent development in ecological modeling. The parameters are constantly varied to account for the adaptations and the shifts in the species /$ see front matter 2003 Elsevier B.V. All rights reserved. doi: /j.ecolmodel

2 314 J. Zhang et al. / Ecological Modelling 173 (2004) composition. The changes of the parameters are either based on expert knowledge under such and such conditions it is known that such and such species will be best fitted to the conditions or by an optimization of a so-called goal function that can describe the fitness to the changed conditions. Exergy has been the most applied goal function in the development of SDM (Jørgensen et al., 2002; Zhang et al., 2003a,b). Exergy expresses the distance from the thermodynamic equilibrium and can therefore be considered a measure of survival. The more biomass and information the system possesses, the bigger distance from thermodynamic equilibrium, and the more exergy and the better survival it has. Survival is biomass and information (including how to survive by suitable regulation mechanisms and feed backs) (Jørgensen, 1999). Exergy can be approximately calculated as β i C i (Jørgensen and Marques, 2001a; Xu et al., 2001), where β i is a weighting factor accounting for the information that the various species are carrying in their genes (β i, for example, is 1 for detritus and 0 for inorganic components at their highest oxidation states) and C i is the concentration of the various organism and component of the ecosystem. Exergy is thereby expressed in detritus exergy equivalents (Jørgensen, 1999). Fig. 1 shows how a SDM is developed with exergy as a goal function. At a certain frequency, a test is conducted to determine if a change in the selected biological parameters, would give the system a higher exergy. If it is the case, the parameters are changed accordingly. The allowed change of the parameters and the frequency of the change are determined by the possible rate of biological changes the biological dynamics. The structurally dynamic approach has been used by the calibration of biological parameters several times (Jørgensen et al., 2002; Zhang et al., 2003a) with some clear improvements of the modeling results. The SDM-approach uses the thermodynamic function exergy to express the survival as a goal function. The details about this approach can be found in Jørgensen et al. (2000, 2002), Jørgensen (1999, 2002) and Zhang et al. (2003a). For development of prognosis scenarios the SDM approach has been applied in 15 case studies, most of which, are referred to in Jørgensen et al. (2000, 2002). It would therefore be interesting to test the Pamolare SDM against a good database and compare the results with other models that have been applied on the same database to assess the differences in applicability and validate the results of the different modeling approaches. The Glumsø-data applied for development and testing of a eutrophication model in would be a candidate for such examinations. Lake Glumsø is situated about 70 km south of Copenhagen, Denmark. The main characteristics are shown in Table 1. The provided data set has the following advantages (Jørgensen et al., 1978; Jørgensen, 1976, 1986): 1. Use literature range for all sensitive parameters 2. Calibrate parameters of physical and chemical importance by trial and error Go back 3. Introduce size functions to phytoplankton and zooplankton parameters. 4. Find parameters giving max. exergy but with less than 45% deviation of model/observations 5. Use parameter combinations as calibration results if no difference between 2 and 4. Fig. 1. The procedure of development of SDM model with exergy as goal function.

3 J. Zhang et al. / Ecological Modelling 173 (2004) Table 1 Lake Glumsø characteristics Characteristics Range Annual average Drainage area (km 2 ) 10.9 Surface area (m 2 ) a Maximum depth (m) a 2.4 Average depth (m) a 1.8 Minimum transparency (cm) b 20 Retention time (months) a 5 6 Temperature ( C) b 4 25 Dissolved oxygen saturation (%) b Source: a Examination of a lake model (Jørgensen et al., 1978). b Management of a shallow lake (Jørgensen, 1986). - double determinations have consequently been used for all measurements, frequent measurements (three times a week) over a period of several weeks during algae spring blooms are available the data set is, in other words, of good quality; - the lake can be considered as a completely mixed tank due to its small size (see Table 1). The hydrodynamics are therefore simple; - significant changes have been recorded during a period of a few years (retention time is less than 6 months; see Table 1); - a prognosis validation is also possible. The objectives of this examination are: 1. Which advantages can the SDM-calibration procedure included in the Pamolare model number 4 (abbreviated SDM-p4) offer, compared with a normal calibration procedure? 2. How do the results from the SDM-p4 model on the Lake Glumsø case compare with the ones obtained by other models: - the previously applied Glumsø model (Jørgensen et al., 1978; Jørgensen, 1976, 1986), which has the advantage that it was developed for this particular case, but without the SDM approach (the model is abbreviated Glumsø-78); - the previously developed SDM approach model for Glumsø (Jørgensen et al., 2002) a model (abbreviated SDM-Glumsø) was developed for this particular case but with a simpler structure and less state variables than the Pamolare SDM and the earlier Glumsø-78 model; and - the two-layer Pamolare model without employing the SDM approach and automatic calibration (abbreviated 2L-p3). 3. In summary, the comparison of the results obtained by all the four models should be able to assess the advantages and disadvantages that result from the application of the SDM-approach for the calibration, the validation and the prognosis scenarios (comparison of SDM-p4 versus 2L-p3 and Glumsø-78, and SDM-Glumsø versus Glumsø-78); from the use of a specifically developed models versus a general model (comparison of Glumsø-78 and SDM-Glumsø versus SDM-p4 and 2L-p3); and from inclusion of more processes and state variables (Glumsø-78, SDM-p4 and 2L-p3 versus SDM- Glumsø). 2. Materials and methods 2.1. The applied models The details of the two Pamolare models are given below, while the details about other models including the validation results for Glumsø-78 can be found in Jørgensen et al. (1978) and for SDM-Glumsø in Jørgensen et al. (2002) The Glumsø-78 model and SDM-Glumsø model The most characteristic features of Glumsø-78 are: a two-step description of phytoplankton growth using intracellular concentrations of nutrients as state variables and allowing a variable P N ratio, a detailed sediment water nutrient exchange sub-model and a threshold limit for zooplankton. The model has 17 state variables, but 20 state variables when diatoms are included. If a thermocline (or halocline) is present the model has by other case studies been expanded with 13 more state variables. The conceptual diagram for the Glumsø-78 model is shown in Fig. 2. The SDM-Glumsø model also has a detailed sediment water exchange sub-model, but a fixed P N ratio for phytoplankton. The model has nine state variables. As opposed to Glumsø-78 it has only been applied in one case study, Lake Glumsø, whereas Glumsø-78 with modifications of the state variables

4 316 J. Zhang et al. / Ecological Modelling 173 (2004) N Z, NZ, PZ PF, NF Phy, NP, PP, CP ND, PD P P SED, N SED PB PI Fig. 2. The conceptual diagram of the Glumsø-78 model. and the equations has been applied to more than 23 case studies The two-layer Pamolare model (2L-p3) The two-layer model program was developed by IETC-UNEP and ILEC and Prof. H. Tsuno at Kyoto University. This model (2L-p3) applies a trial-and-error calibration. It divides the lake into two layers. For a shallow lake the 0.5 m water close to the sediment is considered the hypolimnion. The model has eight state variables in the epilimnion and eight state variables in the hypolimnion, including three state variables regarding the nutrients in the sediment (see the conceptual diagram in Fig. 3), plus dissolved oxygen in the epilimnion and hypolimnion. Phytoplankton is divided into three state variables: blue-green algae, diatoms and other phytoplankton classes. Totally, the model may have up to 21 state variables. The basic equations of this model are presented in Appendix A, Tables A.1 A.4. In this model, growth of three groups of phytoplankton (diatoms, blue-green algae and the other phytoplankton) is by photosynthesis which is governed by the uptake of inorganic nitrogen and phosphorus (paths 1 3), growth of and decays to detritus and inorganic compounds with oxygen consumption and mortality (paths 4 6). Zooplankton species, which are filter-feeders, grow via predation on phytoplankton (paths 7 9) and the process of mortality and decomposition to detritus and inorganic matter with oxygen consumption (path 10). A residual part of the phytoplankton in filter-feeding predation is directly transformed to detritus. Detritus settles in the sediment (sedimentation rate, v SD ) and decomposes to dissolved organics (path 11), which is then degraded to inorganic matter thus consuming oxygen (path 12). All of these paths occur in the upper layer of water column (epilimnion), and all paths, except for the growth of each group of phytoplankton because of the lack of light, also occur in the lower layer (hypolimnion). Release of inorganic nitrogen and phosphorus and dissolved organics (paths 13 15) from the sediments, and resuspension from the sediments (path 16), occur in the lower layer of water column. Exchange of the state variables between the upper and lower layers is expressed by dispersion, K D. The extent of exchange depends on the stratification, reflected in the value of K D. In the model, artificial circulation may also be incorporated by adding the circulation flow rate between the two layers. Release rates of inorganic nitrogen and phosphorus and dissolved organics (paths 13 15) can be determined by experiments or by a data-fitting method. These rates can be calculated by the material balance in the sediments. In this case, releasable sediment nitrogen (N sed ), releasable sediment phospho-

5 J. Zhang et al. / Ecological Modelling 173 (2004) Fig. 3. The conceptual diagram of the two-layer model.

6 318 J. Zhang et al. / Ecological Modelling 173 (2004) rus (P sed ), and releasable sediment organics (C sed ) are considered as state variables and increase and decrease by sedimentation of detritus, and the release processes from the sediments. The release rates of inorganic nutrients increase by an order of magnitude under anoxic conditions. Changes of dissolved oxygen concentrations occur by re-aeration at the water surface, primary production and consumption in the upper water column, and consumption by processes related to water sediment interface The SDM-Pamolare model (SDM-p4) This model deviates from the two-layer model, 2L-p3, by the following features: 1. Phytoplankton covers all classes of phytoplankton, blue-green algae are found by the equations presented in Appendix A, Table A.5, because the structurally dynamic approach accounts for adaptations and shifts in species composition. 2. The sizes of phytoplankton and zooplankton are varied and determined by optimization of the exergy level in the model. Exergy is found as phytoplankton biomass zooplankton biomass 35+detritus biomass (see the equation in Jørgensen et al., 2000 and Jørgensen, 2002). The exergy optimization takes place with a selected frequency from 5 to 30 days, and the possible change of the sizes within a range between 0.02 and 0.25 in log scale ( m 3 ) can also be selected. A graph showing the change in size as function of time produced by the software is shown in Fig The sizes of phytoplankton and zooplankton determine the parameters associated with these two state variables. The equations can be found in Appendix A, Table A As the zooplankton mortality by the formulation K dz = LVZ only covers the non-predation mortality, an extra parameter covering the predation mortality is introduced. 5. A carrying capacity of zooplankton is introduced as a parameter. It was previously found necessary to introduce this parameter in the Glumsø-78 model (Jørgensen and Bendoriccho, 2001b). 6. Four parameters can be calibrated automatically: sedimentation rate of detritus, decomposition rate of detritus, sediment release rates of phosphorus and nitrogen. The criteria are the minimizing sum square of the standard deviations for all of the state variables, based on the differences between observed and simulated values, giving a weighting factor of 10 to phytoplankton, of 3 to zooplankton, of 2 to the two nutrients (nitrogen and phosphorus) and of 1 to the remaining state variables. It is possible to select the state variables that should be included in the calculations, as some state variables in some lake studies may not be measured or may be measured with at a frequency or ac- Fig. 4. The size change of phytoplankton and zooplankton over 1 year simulation in the validation.

7 J. Zhang et al. / Ecological Modelling 173 (2004) Table 2 Characteristic features of the four models Model No. of state variables SDM General/ specific No. of layers Glumsø No Specific 1 ( 2) SDM-Glumsø 9 Yes (Specific) 1 2L-p3 21 No General 2 SDM-p4 19 Yes General 2 curacy that are deemed insufficient for modeling purposes. For the strategy of the calibration procedure, it is recommended first to test a relatively wide range of these four parameters and afterwards use the automatic calibration to fine tune the calibration. A comparison of the characteristic features of all the four models is shown in Table 2. Table 3 illus- trates the different state variables applied for the four models The simulations All the four models were calibrated using one year s observed data set commencing 15 October Another year s records between 1 April 1973 and 31 March 1974 were employed for the validation of the two Pamolare models (2L-3p and SDM-p4). The prognoses resulted in a three years period between 1 April 1981 and 1 April 1984, when the wastewater was discharged into the down-stream of the lake, starting 1 April The phosphorus loading was thereby correspondingly reduced 88%. In order to be fully synchronous with the calibration, the simulation for the prognoses was conducted for the period between 15 October 1980 and 14 October Table 3 The applied state variables in the Glumsø-78, SDM-Glumsø, 2L-p3 and SDM-p4 and models State variables Glumsø-78 SDM-Glumsø 2L-p3 a SDM-p4 a E H S E H S Dissolved nitrogen X X X X X X Soluble reactive phosphorus X X X X X X Total phytoplankton X X X X Diatom X X Blue-green algae X X X X Other phytoplankton X X Nitrogen in phytoplankton X Phosphorus in phytoplankton X Zooplankton X X X X X X Nitrogen in zooplankton X Phosphorus in zooplankton X Nitrogen in fish X Phorsphorus in fish X Detritus X X X X X Nitrogen in detritus X Phosphorus in detritus X Dissolved organics X X X X Dissolved oxygen X X X X Nitrogen in sediment X Phosphorus in sediment X Releasable sediment nitrogen X X X Releasable sediment phosphorus X X X X Releasable sediment dissolved organics X X Nitrogen in pore water X Phosphorus in pore water X X Biologically released P from sediment X a The two models cover state variables in epilimnion (E), hypolimnion (H) and sediments (S).

8 320 J. Zhang et al. / Ecological Modelling 173 (2004) Phytoplankton (mg Chl. a/l) Obs. SDM 2L-P Time (days) Fig. 5. The comparison of simulated results obtained by calibrations of SDM-p4 and 2L-p3 models in Pamolare with observed results of phytoplankton. 3. Results 3.1. The results obtained by the two Pamolare models The results obtained by Glumsø-78 and SDM- Glumsø have previously been published. The details are given in Jørgensen et al. (1978) and Jørgensen (1986, 2002). The results will be summarized in tables, where all the four models are compared in the next section. Fig. 5 shows the phytoplankton results obtained by the two Pamolare models (2L-p3 and SDM-p4) after applying exergy optimization calibration for the SDM-p4 model and using a trial and error calibration for the 2L-p3 model. The calibration is, however, much more cumbersome with the two-layer model than with the SDM, because the exergy optimization procedure and the automatic calibration allow a relatively rapid determination of 10 important parameters. The results of the nutrients calibration as function Dissolved N (mg N/l) Obs. SDM 2L-P Time (days) Fig. 6. The comparison of simulated results obtained by calibrations of SDM-p4 and 2L-p3 models in Pamolare with observed results of dissolved nitrogen.

9 J. Zhang et al. / Ecological Modelling 173 (2004) Dissolved P (mg P/l) Obs. SDM 2L-P Time (days) Fig. 7. The comparison of simulated results obtained by calibrations of SDM-p4 and 2L-p3 models in Pamolare with observed results of dissolved reactive phosphorus. of time for the two models are presented in Figs. 6 and 7. Figs show the comparisons of the validated results from SDM-p4 and 2L-p3 with the observations for phytoplankton and nutrients (N and P), respectively. Compared with the results in the calibration, SDM-p4 gained a better performance in the validation in simulating the seasonal dynamics of the nutrients, especially the soluble reactive phosphorus. The validated result for phytoplankton also produced an acceptable result with smaller than 50% S.D. (see Table 5). Figs. 11 and 12 show the results of the prognoses for phytoplankton from the SDM-p4 and the 2L-p3 models, respectively. The predicted 3-year transparency by the SDM-p4 model is presented in Fig. 13. The results demonstrate that though there were differences in the calibration and validation results between the two models, there were little differences between the models in the prognoses in the first year. But the big differences were found in the second year, especially in the third year the 2L-p3 predicted no significant change compared with the previous years results. Compared with the two-layer model, it is obvious that Phytoplankton (mg Chl. a/l) Obs. SDM 2L-P Time (days) Fig. 8. The comparison of simulated results obtained by validations of SDM-p4 and 2L-p3 models in Pamolare with observed results of phytoplankton.

10 322 J. Zhang et al. / Ecological Modelling 173 (2004) Dissolved N (mg N/l) Obs. SDM 2L-P Time (days) Fig. 9. The comparison of simulated results obtained by validations of SDM-p4 and 2L-p3 models in Pamolare with observed results of dissolved nitrogen. the validation and prognosis validation using SDM-p4 also gave better results. It can be seen that for transparency, the SDM-p4 model made good predictions, too. Over all the 3-year simulation, the prognosis validation yielded a very good result for phytoplankton in the first spring, but it under-estimated the biomass of phytoplankton in the second and third spring. However, the SDM-p4 gave a right description of the trend of the phytoplankton change over 3-year prediction Comparison of the calibration, the validation and the prognosis validation results of the four models Tables 4 and 5 respectively give the standard deviation resulting from the calibrations of the four models and the validation of the 2L-p3 model and the SDM-p4 model. The standard deviation was calculated as the average values of the annual phytoplankton values of (the observed phytoplankton concentration the simulated phytoplankton concentration) 100/the 2.5 Dissolved P (mg P/l) Obs. SDM 2L-P Time (days) Fig. 10. The comparison of simulated results obtained by validations of SDM-p4 and 2L-p3 models in Pamolare with observed results of dissolved reactive phosphorus.

11 J. Zhang et al. / Ecological Modelling 173 (2004) Fig. 11. The prognosis result from 15 October 1980 to 14 October 1984 for phytoplankton obtained by SDM-p4 in Pamolare. Fig. 12. The prognosis result from 15 October 1980 to 14 October 1984 for phytoplankton (represented as diatom) obtained by 2L-p3 in Pamolare. Fig. 13. The prognosis result from 15 October 1980 to 14 October 1984 for transparency obtained by SDM-p4 in Pamolare.

12 324 J. Zhang et al. / Ecological Modelling 173 (2004) Table 4 Comparison of standard deviations and correlation coefficients from the calibrated results among the four models Species Model S.D. (%) Correlation coefficients Phytoplankton Glumsø SDM-Glumsø L-p SDM-p Dissolved nitrogen Glumsø SDM-Glumsø 2L-p3 >100 Negative SDM-p Soluble reactive Glumsø phosphorus SDM-Glumsø 2L-p SDM-p average observed concentration. The calculated correlation coefficients for a plot observed versus simulated phytoplankton in the calibration and validation years are also presented in these tables. Phytoplankton is the most important state variable for a eutrophication model and it is therefore naturally to focus on the discrepancy between observed and simulated phytoplankton in the validation. The calibrated results using the four models can be found in Table 6, where it compares the obtained Table 5 Comparison of standard deviations and correlation coefficients from the calibrated results between SDM-p4 and 2L-p3 models Species Model S.D. (%) Correlation coefficient Phytoplankton 2L-p SDM-p Dissolved nitrogen 2L-p3 >100 Negative SDM-p Soluble reactive 2L-p3 93 Negative phosphorus SDM-p values of phytoplankton, nitrogen and phosphorus in the period between 15 October 1974 and 14 October The results of the prognosis validation in the period for the four models are summarized in Tables 7 and Discussion 4.1. Comparison of the results obtained by the calibration of the four models The acceptable standard deviations and high correlation coefficients demonstrate that the calibrated Table 6 Important calibration results Species Methods Results Spring Summer Autumn Max. value Date Phytoplankton (mg/l) Observations 42 Early May 60 Middle July 47 Early September Glumsø Early May 70 Late July 36 Early September SDM-Glumsø 32 Early May 37 Middle July 35 Early September 2L-p3 53 Early May 59 Middle June 26 Late August SDM-p4 52 Middle April 60 Middle July 49 Early September Soluble nitrogen (mg N/l) Observations 7.0 Early February 2.5 Middle August Glumsø Early March 4.0 Early September SDM-Glumsø 8.1 Middle February 4.7 Early October 2L-p3 8.4 Late February 9.0 Middle October SDM-p4 7.0 Early February 0.47 Early October Soluble reactive phosphorus (mg P/l) Max. value Date Max. value Observations 1.3 Middle March 2.0 Early August 2.0 Late August Glumsø Middle March 0.8 Early August 1.5 Middle October SDM-Glumsø 2.6 Middle March 1.5 Middle October 2L-p3 1.8 Early February 1.7 Middle October SDM-p4 1.5 Early February 0.1 Middle October Date

13 J. Zhang et al. / Ecological Modelling 173 (2004) Table 7 The results of 3 year prognosis validation after the treatment of wastewater Species Methods Results First spring Second spring Third spring Max. value Date Phytoplankton (mg/l) Observations 55 Middle April 50 Early May 38 Late March Glumsø Early May 38 Early May 30 Early May SDM-Glumsø 42 Middle April 36 Early April 28 Early April 2L-p3 61 Early June 56 Middle May 55 Middle May SDM-p4 51 Middle April 24 Early February 18 Early February Min. transparency (cm) Observations 20 Middle April 25 Early May 50 Late March Glumsø Early May 30 Early May 45 Early May SDM-p4 20 Middle April 34 Early February 41 Early February Max. value Date Max. value Date results of the phytoplankton are satisfactory for all the models, except for the two-layer Pamolare model, where it was difficult to simulate the phytoplankton concentration as function of time very well within the time framework, which has been devoted to the trial and error calibration. It was also very time consuming to formulate, calibrate and validate the Glumsø-78 model. We might therefore not exclude that the two-layer model may be able to yield better results, if more time was devoted to the calibration. This does, however, not change the facts that the two-layer model, due to the high number of parameters, is very difficult and time consuming to calibrate. The two SDM approaches of SDM-p4 and SDM-Glumsø both gave a slightly better calibration of phytoplankton, although the calibration results for the soluble reactive phosphorus concentration and other state variables such as zooplankton were not better for these two models than for the Glumsø-78 model. This may probably be due to the high weighting factor (10) given to phytoplankton in the calibration, while other state variables had weighting factors less than 3. Therefore, it is clear that the SDM-calibration procedure (applied in both SDM-Glumsø and SDM-p4 models) offers better and faster calibration than the two other approaches, because the results reflect seasonal dynamic changes in the ecosystem. This can be found in Fig. 14, where the two SDM model gave phytoplankton higher growth rates in the summer and lower ones in the winter, as it should also be expected from an ecological view-point: higher specific surface in the summer when there is more competition Table 8 Comparison of the four tested models Criteria Items Glumsø-78 SDM-Glumsø 2L-p3 SDM-p4 Calibration Time consuming Long Medium Long Short Phytoplankton Very good Good Good Very good Date of max. phytoplankton Good Very good Acceptable Good Nutrient N Good Good Acceptable Good Nutrient P Good Very Good Good (Acceptable) Validation Phytoplankton Good a Acceptable Good Nutrient N Good a Not acceptable Good Nutrient P Good a Not acceptable Good Prognosis Phytoplankton Very good Very good Very good Good Date of max. phytoplankton Good Very good Not good Good Min. transparency Very good Very good a Another year applied for the validation than in this study.

14 326 J. Zhang et al. / Ecological Modelling 173 (2004) Range of the measured rates The average measured rate Glumsø-78 6 Max. Growth rate of Phy (1/d) SDM -P4 SDM -Glumsø 1 2L-P Time (days) Fig. 14. The maximum growth rates of phytoplankton obtained by the four models over 1 year simulation in the calibration. for the nutrients (Peters, 1983). It was determined in the Lake Glumsø case (Jørgensen 76 and Jørgensen et al., 1978) that the measured maximum growth rate was 4.1 ± 1.8 per day (see Fig. 14). It is noticeable that the changes of the growth rates for the two SDM models are in the range of the measured growth rate (the change of the rate for SDM-Glumsø is almost covered), whereas the calibrated growth rates for the Glumsø-78 model is 4.1 and for two-layer model is in discordance with the measured value Comparison of the results obtained by the validations and prognoses of the four models Compared with the observed results, the prognoses were satisfactory for all the three applied models, whereas the two-layer model yielded an acceptable result but with the maximum growth of phytoplankton appearing too late. It was most probably due to the unsatisfactory calibration. The two structurally dynamic models generally gave for the prognosis validation a better accordance for the date of the phytoplankton peak and the minimum transparency, which was in accordance with the idea behind the introduction of the structurally dynamic modeling approach to account for a shift in species composition, included the seasonal adaptation and structural change of species in the ecosystem (Zhang et al., 2003a), but it cannot be excluded that these results were at least partly due to the application of a weighting factor of 10 for phytoplankton in the automatic calibration procedure for SDM-p4. The SDM-p4 model was tested with an acceptable result. The over-all results were, however, not better than the previously developed Glumsø-78 model, which was specifically developed for the Glumsø conditions. In some respects the SDM-p4 model performed better: the validation of the phytoplankton and the prognosis validation of the dates at which the various peaks of the state variables occur (in the first and the third years); in some other respects the Glumsø-78 model gave better results: the validation of the nutrients observations and the size of the peaks at the prognosis validation. The Glumsø-78 model is tailored to Lake Glumsø while SDM-p4 is a general model, and the same accuracy should normally not be expected for the validation and prognosis validation. SDM-Glumsø has only been tested on the Lake Glumsø data but in principle it was not developed particularly for Glumsø, but rather for testing an alternative calibration method by the application of the structurally dynamic approach. Glumsø-78 was developed through

15 J. Zhang et al. / Ecological Modelling 173 (2004) testing a number of expressions for the key processes, and some of the sub-models were developed on basis of in situ or laboratory measurements made on basis of Glumsø-conditions. It could therefore be expected (as a hypothesis), that Glumsø-78 would yield a better validation and prognosis validation than SDM-p4 that has been developed for a general use. For SDM-Glumsø it has previously been concluded that the structurally dynamic approach offers a better calibration and validation for phytoplankton (Jørgensen et al., 2002), but it can not be concluded that it is the case for SDM-p4, although it is possible to conclude that the results of the validation and the prognosis validation of phytoplankton were satisfactory for both structurally dynamic models Comparison of models with the inclusion of more processes and state variables (Glumsø-78, SDM-p4 and 2L-p3) with a simple structural model (SDM-Glumsø) The results of the SDM-p4 model are as good as that of the earlier SDM-Glumsø model. Provided that a good database is available, it might be expected that a more complex model may yield a better result. In a comparison of the two models, we found: 1. The calibrated phytoplankton in Table 4 shows that SDM-Glumsø is slightly better than SDM-p4. 2. The time of appearing peaks is equally good for the two models, but the sizes of the peaks are clearly better for SDM-p4 than for SDM-Glumsø (see Table 6). 3. The prognosis validation is better for SDM-p4 in the first year, but better for SDM-Glumsø in the second and third year. This better performance is clearly demonstrated in the Glumsø-78 model, where it has more state variables than the SDM-Glumsø model. However, the SDM-Glumsø clearly gave a better performance than the 2L-3p model. 5. Conclusions The two Pamolare models (SDM-p4 and 2L-p3) have been tested against a high quality database from the Lake Glumsø. It was found that: 1. The calibration with the SDM models is considerably less time consuming than the usually applied calibration. 2. The two SDM models yielded a calibration, a validation and a prognosis validation approximate to the same quality as the Glumsø-78 model. It indicates that the general Pamolare SDM model (SDM-p4) is with other words as effective as the Glumsø-78 model, a specially developed model for Lake Glumsø. 3. The Pamolare 2L-3p model did not yield as good results as the three other models probably owing to the difficulty to calibrate the model and to the lack of structurally dynamic approach. 4. The result from the SDM-Glumsø model with nine state variables reflects that the more processes may not necessarily be needed, provided that the most important processes and state variables are already included in the model. For all the four models it should not be expected that they could give very accurate values when applied for a prognosis, but that they only can give relatively acceptable values for scenarios testing different environmental strategies. This is what eutropication models can offer today not exact prognoses but relatively acceptable results. The structurally dynamic approach has demonstrated the advantages over other methods. It may be possible with the results presented here to conclude, that the SDM-p4 model a general model may be applied equally successfully in other case studies. However, in order to have a more accurate result it is suggested to develop a specific SDM model. Acknowledgements We thank Mr. Vicente Santiago-Fandino for kindly providing the Pamolare program for this study. The authors are grateful to Dr. Gideon Gal and the two anonymous referees for their critical reading of this manuscript and giving constructive and valuable comments and suggestions that have improved the clarity of the paper.

16 328 J. Zhang et al. / Ecological Modelling 173 (2004) Appendix A See Tables A.1 A.5. Table A.1 Rate equation of each process Process Equation 1. Growth of diatom (mg Chl.a/(l day)) R 1 = µ M1 f T1 f I1 f N1 M1 2. Growth of blue-green algae R 2 = µ M2 f T2 f I2 f N2 M2 (mg Chl.a/(l day)) 3. Growth of other phytoplankton (mg Chl.a/(l day)) R 3 = µ M3 f T3 f I3 f N3 M3 (T 20) DO 4. Death of diatom (mg Chl.a/(l day)) R 4 = k dm1 θ M1 K DO + DO M1 5. Death of blue-green algae (mg Chl.a/(l day)) 6. Death of other phytoplankton (mg Chl.a/(l day)) 7. Grazing of diatom by zooplankton (mg Chl.a/(l day)) 8. Grazing of blue-green algae by zooplankton (mg Chl.a/(l day)) 9. Grazing of other phytoplankton by zooplankton (mg Chl.a/(l day)) R 5 = k dm2 θ (T 20) DO M2 K DO + DO M2 (T 20) DO R 6 = k dm3 θ M3 K DO + DO M3 T K mz R 7 = F max Z 20 K mz + (M1 + M2 + M3) M1Z T K mz R 8 = F max Z 20 K mz + (M1 + M2 + M3) M2Z T K mz R 9 = F max Z 20 K mz + (M1 + M2 + M3) M3Z (T 20) DO 10. Death of zooplankton (mg DW/(l day)) R 10 = k dz θ Z K DO + DO Z 11. Decomposition of detritus (mg DW/(l day)) 12. Decomposition of dissolved organics (mg COD/(l day)) 13. Release of nitrogen from sediment (mg N/(l day)) 14. Release of phosphorus from sediment (mg P/(l day)) 15. Release of dissolved organics from sediment (mg COD/(l day)) 16. Release of detritus from sediment (mg DW/(l day)) (T 20) R 11 = k dd θ D D (T 20) DO R 12 = k dc θ C K DO + DO C A Model (a) R 13a = k sran 1000V L A Model (a) R 14a = k srap 1000V L A Model (a) R 15a = k srac 1000V L A R 16 = k srd 1000V L A(DO sat DO) 17. Re-aeration (mg O 2 /(l day)) R 17 = k L V L 18. Oxygen consumption by sediment R 18 = k DO θ (T 20) A DO 1000V (mg O 2 /(l day)) L Model (b) R 13b = k srn N sed H sed H Model (b) R 14b = k srp P sed H sed H Model (b) R 15b = k src C sed H sed H

17 J. Zhang et al. / Ecological Modelling 173 (2004) Table A.2 Rate equation of each process Effect of water temperature: f Tk (k = 1, 2, 3) ( ) f Tk = (T T optm k ) 2 ToptM k Effect of solar radiation: f Ik (k = 1, 2, 3) ( ) f Ik = e [ { exp I } ( exp( εh) exp I )] εh I optmk I optmk Effect of nutrients: f Nk (k = 1, 2, 3) ( ) f Nk = N P K nmk + N K pmk + P Re-aeration rate constant (m/day) K L = max(0.04, W 0.317W W 2 ) Saturated dissolved oxygen (mg O 2 /l) DO sat = T Table A.3 Materials balance equations Upper layer dc ju = Q UC jin Q Uout C ju δ h Q UL C ju + (1 δ h )Q LU C jl dt V U dd U dt = Q UD IN Q Uout D U δ h Q UL D U + (1 δ h )Q LU D L V U j = N,P,M1,M2,M3,Z,C,DO,C i = concentrations of j D: concentrations of detritus F i : rate of change of j U: upper layer, L: lower layer Lower layer dc jl = Q LC jin Q Lout C jl + δ h Q UL C ju (1 δ h )Q LU C jl dt V U dd L dt = Q LD IN Q Lout D L + δ h Q UL D U (1 δ h )Q LU D L V U j = N,P,M1,M2,M3,Z,C,DO,C i : concentrations of j D = concentrations of detritus F i : rate of change of j U: upper layer, L: lower layer Sediment part dc js dt = F js + v sdd L γ Dj f sed j H sed j = N sed,p sed,c sed, C i : concentrations of j F i : rate of change of j U: upper layer, L: lower layer δ h = 1: when the thermocline goes up δ h = 0: when the thermocline goes down + F ju K da (C ju C jl ) C ju dh U HV U H U dt + F ju v sdd U H U K da (D U D L ) D U dh U HV U H U dt + F jl + K da (C ju C jl ) C jl dh L HV U H L dt + F jl + v sdd U H L v sdd L H L + K da (D U D L ) D L dh L HV U H L dt In the upper layer, the material balance equation for each state variable consists of input (inflow rate and concentration) from the watershed, output (flow out) from the layer, the rate of change F i and the exchange rate between the upper and lower layer. For detritus, the sedimentation rate is also incorporated.

18 330 J. Zhang et al. / Ecological Modelling 173 (2004) Table A.4 Material balance equations variable depth in calculation Table A.5 The equations of parameters of phytoplankton and zooplankton associated with the their sizes Max. growth rate of phytoplankton: µ m = LVP Max. growth rate of zooplankton: µ mz = LVZ Michaelis Menten s half saturation constant for grazing by zooplankton: K mz = LVZ Michaelis Menten s half saturation constant for nitrogen uptake by phytoplankton: K nm = LVP Michaelis Menten s half saturation constant for phosphorus uptake by phytoplankton: K pm = LVP Mortality rate of phytoplankton: K dm = LVP Mortality rate of zooplankton: K dz = LVZ Ratio of blue-green algae: ((5 (concentration of N/concentration of P))/5) 2 0; if concentration of N>(5 concentration of P) Appendix B. Notation State valuables N (mg N/l) P (mg P/l) Phy (mg Chl.a/l) M1 (mg Chl.a/l) M2 (mg Chl.a/l) M3 (mg Chl.a/l) NP (%) PP (%) CP (mg C/l) Z (mg DW/l) NZ (%) PZ (%) D (mg DW/l) ND (mg/l) PD (mg/l) NF (%) PF (%) C (mg COD/l) DO (mg O 2 /l) N sed (mg N/l-sed) P sed (mg P/l-sed) PI (mg P/l) PB (mg P/l) C sed (mg C/l-sed) C j (mg/l) Dissolved nitrogen Soluble reactive phosphorus Total phytoplankton Diatom Blue-green algae Other phytoplankton Nitrogen in phytoplankton Phosphorus in phytoplankton Carbon in phytoplankton Zooplankton Nitrogen in zooplankton Phosphorus in zooplankton Detritus Nitrogen in detritus Phosphorus in detritus Nitrogen in fish Phosphorus in fish Dissolved organics Dissolved oxygen Releasable sediment nitrogen Releasable sediment phosphorus Phorsphorus in the pore water Biologically released phosphorus in the sediment Releasable sediment dissolved organics Concentrations of j Lake conditions (morphology and mixing condition) V (m 3 ) Volume of each part H (m) Water depth of each part A (m 2 ) Surface area of each part H (m) Water depth between each part H sed (m) Sediment depth Q c (m 3 /(d unit)) Circulation flow K d (m 2 /d) Mixing rate

19 J. Zhang et al. / Ecological Modelling 173 (2004) Appendix B (Continued ) Values of constants and coefficients Containing ratio γ M1P (mg P/mg Chl.a) P: Chl.a, diatom γ M2P (mg P/mg Chl.a) P: Chl.a, blue-green algae γ M3P (mg P/mg Chl.a) P: Chl.a, other phytoplankton γ ZP (mg P/mg DW) P: dry weigh, zooplankton γ CP (mg P/mg COD) P: COD, dissolved organics γ DP (mg P/mg DW) P: dry weigh, sediment γ M1N (mg N/mg Chl.a) N: Chl.a, diatom γ M2N (mg N/mg Chl.a) N: Chl.a, blue-green algae γ M3N (mg N/mg Chl.a) N: Chl.a, other phytoplankton γ ZN (mg N/mg DW) N: dry weight, zooplankton γ CN (mg N/mg COD) N: COD, dissolved organics γ DN (mg N/mg DW) N: dry weigh, sediment γ DC (mg COD/mg DW) COD: dry weigh, sediment Conversion coefficient γ M1DO (mg O 2 /mg Chl.a) γ M2DO (mg O 2 /mg Chl.a) γ M3DO (mg O 2 /mg Chl.a) γ CDO (mg O 2 /mg COD) γ M1Z (mg DW/mg Chl.a) γ M2Z (mg DW/mg Chl.a) γ M3Z (mg DW/mg Chl.a) γ ZDO (mg O 2 /mg DW) γ M1D (mg DW/mg Chl.a) γ M2D (mg DW/mg Chl.a) γ M3D (mg DW/mg Chl.a) DO: diatom DO: blue-green algae DO: other phytoplankton DO: dissolved organics Zooplankton: diatom Zooplankton: blue-green algae Zooplankton: other phytoplankton DO: zooplankton Detritus: diatom Detritus: blue-green algae Detritus: other phytoplankton Appendix B (Continued ) Yield coefficient Y M1D ( ) Y M2D ( ) Y M3D ( ) Y ZD ( ) Y M1Z ( ) Y M2Z ( ) Y M3Z ( ) Respiration of diatom Respiration of blue-green algae Respiration of other phytoplankton Respiration of zooplankton Prediction of diatom Prediction of blue-green algae Prediction of other phytoplankton Extinction of sunlight α (1/m) (m 3 /g Chl.a) Extinction coefficient, algal ɛ 0 (1/m) Extinction coefficient, water Diatom I optm1 MJ/(m 2 d)) Optimum solar radiation Z optm1 ( C) Optimum temperature µ M1 (1/d) Maximum growth rate K pm1 (mg P/l) Half saturation constant, P K nm1 (mg N/l) Half saturation constant, N k dm1 (1/d) Mortality rate θ M1 ( ) Temperature constant Blue-green algae I optm2 (MJ/(m 2 d)) Optimum solar radiation Z optm2 ( C) Optimum temperature µ M2 (1/d) Maximum growth rate K pm2 (mg P/l) Half saturation constant, P K nm2 (mg N/l) Half saturation constant, N k dm2 (1/d) Mortality rate θ M2 ( ) Temperature constant Other phytoplankton I optm3 (MJ/(m 2 d)) Optimum solar radiation Z optm3 ( C) Optimum temperature µ M3 (1/d) Maximum growth rate K pm3 (mg P/l) Half saturation constant, P

20 332 J. Zhang et al. / Ecological Modelling 173 (2004) Appendix B (Continued ) K nm3 (mg N/l) k dm3 (1/d) θ M3 ( ) Zooplankton F mz (l/(d mg DW)) F mz (mg Chl.a/l) k dz (1/d) θ Z ( ) Detritus v sd (m/d) k dd (1/d) θ D ( ) Dissolved organic k dc (1/d) θ C ( ) Floatation of sediment k srd (mg DW/(m 2 d)) Half saturation constant, N Mortality rate Temperature constant Maximum growth rate Half saturation constant Mortality rate Temperature constant Sedimentation velocity Decomposition rate Temperature constant, decomposition Decomposition rate Temperature constant, decomposition Release rate Oxygen consumption rate by sediment k DO (mg O 2 /(m 2 d)) Oxygen consumption constant K DO (mg O 2 /l) Half saturation constant, DO θ DO ( ) Temperature constant, decomposition Release rate from sediment (a) k srap (mg P/(m 2 d)) Release rate, phosphorus k sran (mg N/(m 2 d)) Release rate, nitrogen k srac (mg COD(m 2 d)) Release rate, dissolved organics Release rate from sediment (b) f sedp ( ) Fraction ration, phosphorus k srp (1/d) Release rate, phosphorus f sedn ( ) Fraction ration, nitrogen k srn (1/d) Release rate, nitrogen f sedc ( ) Fraction ration, dissolved organics Appendix B (Continued ) k src (1/d) Weather condition T ( C) I (MJ/(m 2 d)) W (m/s) Q (m 3 /d) Q out (m 3 /d) Q UL (m 3 /d) Q LU (m 3 /d) δ h ( ) Rate equations R 1 (mg Chl.a/(l day)) R 2 (mg Chl.a/(l day)) R 3 (mg Chl.a/(l day)) R 4 (mg Chl.a/(l day)) R 5 (mg Chl.a/(l day)) R 6 (mg Chl.a/(l day)) R 7 (mg Chl.a/(l day)) R 8 (mg Chl.a/(l day)) R 9 (mg Chl.a/(l day)) R 10 (mg DW/(l day)) R 11 (mg DW/(l day)) R 12 (mg COD/(l day)) Release rate, dissolved organics Selection of release rate from sediment 1: Method (a), 2: Method (b) Water temperature Intensity of sunlight Wind speed Inflow rate of each part Outflow rate of each part Flow rate from upper layer to lower layer Flow rate from lower layer to upper layer 1: When the thermocline goes up, 0: when the thermocline goes down Growth of diatom Growth of blue-green algae Growth of other phytoplankton Death of diatom Death of blue-green algae Death of other phytoplankton Prediction of diatom by zooplankton Prediction of blue-green algae by zooplankton Prediction of other phytoplankton by zooplankton Death of zooplankton Decomposition of detritus Decomposition of dissolved organics

21 J. Zhang et al. / Ecological Modelling 173 (2004) Appendix B (Continued ) R 13 (mg N/(l day)) R 14 (mg P/(l day)) R 15 (mg C OD/(l day)) R 16 (mg DW/(l day)) R 17 (mg O 2 /(l day)) R 18 (mg O 2 /(l day)) f Tk ( ) f Ik ( ) f Nk ( ) K L (m/d) DO sat (mg O 2 /l) F i (mg C j /(l d)) t (day) LVP (log ( m 3 )) LVP (log ( m 3 )) Suffixes U L IN T Release of nitrogen from sediment Release of phosphorus from sediment Release of dissolved organics from sediment Release of detritus from sediment Re-aeration Oxygen consumption by sediment Temperature affecting function for M k Light intensity affecting function for M k Inorganic nutrient concentration affecting function for M k Re-aeration rate constant Saturated dissolved oxygen Changing rate of each state valuable j Time Size of phytoplankton Size of zooplankton Upper layer Lower layer Inflow Total References Jørgensen, S.E., A eutrophication model for a lake. Ecol. Model. 2, Jørgensen, S.E., Validation of prognosis based upon a eutrophication model. Ecol. Model. 32, Jørgensen, S.E., State-of-the art of ecological modeling with emphasis on development of structural dynamic models. Ecol. Model. 120, Jørgensen, S.E., Integration of Ecosystem Theories: A Pattern, 3rd ed. Kluwer Academic Publishers, Dordrecht, p Jørgensen, S.E., Marques, J.C., 2001a. Thermodynamics and ecosystem theory, case studies from hydrobiology. Hydrobiologia 445, Jørgensen, S.E., Bendoriccho, G., 2001b. Fundamentals of Ecological Modelling, 3rd ed. Elsevier, Amsterdam, p Jørgensen, S.E., Mejer, H.F., Friis, M., Examination of a lake model. Ecol. Model. 4, Jørgensen, S.E., Patten, B.C., Straskraba, M., Ecosystems emerging: 4. Growth. Ecol. Model. 126, Jørgensen, S.E., Ray, S., Berec, L., Straskraba, M., Improved calibration of a eutrophication model by use of the size variation due to succession. Ecol. Model. 153 (3), Jørgensen, S.E., Tsuno, Hidaka T, Mahler, H., Santiago, V., PAMOLARE Training Package, Planning and Management of Lakes and Reservoirs: Models for Eutrophication Management. UNEP DTIE IETC and ILEC, 1091 Oroshimo-cho, Kusatsu, Shiga, , Japan. Peters, R.H., The Ecological Implications of Body Size. Cambridge University Press, Cambridge. Xu, F.L., Tao, S., Dawson, R.W., Li, G., Cao, J., Lake ecosystem health assessment: indicators and methods. Water Res. 35 (13), Zhang, J., Jørgensen, S.E., Tan, C.O., Beklioglu, M., 2003a. A structurally dynamic modeling Lake Mogan as a case study. Ecol. Model. 164, Zhang, J., Jørgensen, S.E., Beklioglu, M., Ince, O., 2003b. Hysteresis in vegetation shift Lake Mogan prognoses. Ecol. Model. 164,