MINISTRY OF EDUCATION MINISTRY OF AGRICULTURE AND TRAINING AND RURAL DEVELOPMENT THUY LOI UNIVERSITY TA DANG THUAN RESEARCH AND DEVELOPMENT OF MATHEMATICAL MODEL TO SIMULATE EUTROPHICATION PROCESS IN SHALLOW STANDING WATER AREAS, APPLIED FOR CU CHINH LAKEHANOI Specialization: Soil and water environment Code number: 44 03 03 SUMMARY OF DOCTORAL DISSERTATION HANOI, 2019 This scientific work has been accomplished at Thuyloi University Supervisor: Assoc Prof Dr Bui Quoc Lap Reviewer No 1: Assoc Prof Dr Tran Lien Ha - Hanoi University of Science and Technology Reviewer No 2: Assoc Prof Dr Duong Thi Thuy - Institute of Environmental Technology Reviewer No 3: Assoc Prof Dr Nguyen Thi Lan Huong - Thuyloi University This Doctoral dissertation will be defended at ………………… ……… on date ….………………………………………………………………………… This dissertation is available at: - The National Library - The Library of Thuyloi University INTRODUCTION The rationale of the research In standing waters (agricultural ponds, natural lakes) due to the lack of water exchange with external water sources and the influence of surface winds, along with the process of nutrients, pollutants from the surrounding area is washed away because the rainwater runoff in the basin is increasingly accumulating in the water areas that degrade the water quality One of the water quality problems that occur in standing water areas is eutrophication, which causes many harms such as excessive growth of algae, and aquatic plants, resulting in cyanobacteria, toxic algae are harmful to humans and creatures When algae bloom, the dead aquatic plants will decompose, reducing the dissolved oxygen (DO) concentration of nitrite (NO 2N) nitrate (NO3-N), causing water poisoning, directly threatening to the life of water animals such as shrimp, fish, In standing waters, shallow lakes with an average depth of fewer than meters are where eutrophication occurs frequently [1] One of the most popular and well-developed research directions is the research, construction and development of mathematical models of lake eutrophication based on the correlation of environmental factors such as water temperature and solar radiation, rain to the growth and development of algae and the exchange of nutrients A mathematical model with many advantages such as the calculation results quickly, cheaply, easily changed to suit the requirements problem Besides, they provide predictive results from which to propose appropriate management measures to improve water quality to meet the target quality of use and sustainable conservation of water quality [2] On the other hand, they overcome difficulties in conducting direct experiments with the natural environment because they are influenced by many factors that work together, interfering with the survey results and in many cases conducting experiments with the natural environment is impossible [3] The process of research and development of lake eutrophication models began in the 1970s, has been applied in practice and obtained remarkable results However, the eutrophication of lakes in the world was built, developed mainly in the natural lakes with large areas and depths in temperate climates but not interested in small and shallow lakes in tropical and subtropical climates Besides, the eutrophication process in the lake is very complicated, associated with specific conditions of each region such as climate and hydrological conditions, geological and soil characteristics as well as the economy and social development activities in the region Therefore, in some specific cases, the application of available models proved inappropriate Moreover, the use of some commercial software in the world is often very expensive and requires many kinds of complex data while limited economic conditions cannot be met If applying that model in conditions in Vietnam lacked or omitted data needed, simulation results and forecasts will not achieve the desired results Hanoi's inner lake plays a very important role in regulating rainwater, creating landscapes, regulating the climate and also the residence of many water plants and animals Most of them are medium, small and relatively shallow, so they have hydrodynamic qualities of other countries with large, deep lakes outside the inner city In recent years, the phenomenon of "blooming" algae has occurred in many urban lakes in Hanoi, negatively affecting the quality of lake water and urban landscape This fact requires in-depth studies of the eutrophication process in Ha Noi lake as a basis for proposing appropriate solutions to support the management and control of eutrophication For the above reasons, the thesis topic "Research and development of a mathematical model to simulate the eutrophication process in shallow standing water areas, applied for Cu Chinh Lake - Hanoi" was selected 2 Research objectives - Developing mathematical modelling tools to simulate the eutrophication process in shallow standing water areas - Application of developing eutrophication model into a shallow natural lake is being affected by eutrophication in Hanoi urban area Research object and scope 3.1 Research object The object of the study is eutrophication and algal biomass, zooplankton and water quality (nutrients of nitrogen, phosphorus, carbon and dissolved oxygen concentrations) in shallow standing water 3.2 Research scope Cu Chinh Lake, a shallow natural lake is being affected by eutrophication in the inner city of Hanoi Research approaches and methods 4.1 The research approaches - Practical and inherited approach The scope of research that the thesis focuses on is that shallow lakes are being affected by eutrophication in the inner city of Hanoi Therefore, the actual survey, collecting information to select suitable objects for research is very important Besides, to study and selectively use the research results of previous researches and projects on lake maintenance related to the research content of the thesis - Multi-disciplinary approach To carry out the thesis, it is necessary to use the general knowledge of many scientific disciplines such as chemistry, biology, and mathematics to clarify the relationship between state variables and the factors affecting the environment in the static lakes are eutrophic Thereby using a computerized programming tool to develop a model of enrichment simulation model suitable for shallow lake conditions in Hanoi urban area 4.2 The research methods The methods implemented in the thesis include: - Methods of analysis, evaluation, synthesis: Overview of research on eutrophication, research and development model simulation of the eutrophication process in the world and Vietnam, applicability and limitations need to overcome Analyzing and evaluating the results obtained based on the survey results of the study area and the results of field measurements, analysis of water samples and algae samples in the laboratory; - Method of field investigation and survey: Conducting field survey and survey of lakes in Hanoi inner city to select suitable research lakes From that, survey specific natural conditions and social conditions in the study area Since the parameters of the lake and the location are determined, the sampling time is appropriate - Mathematical modelling method: Using the numerical solution methods and programming tools to solve mathematical equations into mathematical models Scientific and practical significance 5.1 Scientific significance Developed a mathematical model simulating eutrophication processes in the shallow standing waters based on the addition of nutrients from the atmosphere and rainwater runoff into the lake in the nutrient kinetic equations 5.2 Practical significance Applying a successful development model to Cu Chinh lake located in the inner city of Hanoi Research results of the thesis are scientific documents for training and research in related fields New contributions - A mathematical model developed simulation to model the process of eutrophication in the shallow standing water areas by adding a concentration of nutrients from the atmosphere and rainwater runoff - Applying the developed model for Cu Chinh lake in Hanoi inner city with the corresponding set of parameter values Dissertation structure Apart from the introduction and conclusions, the dissertation consists of three chapters: Chapter 1: Overview of research issues Chapter 2: Developing mathematical models to simulate the eutrophication process in shallow lakes Chapter 3: Results and discussions CHAPTER OVERVIEW OF RESEARCH ISSUES 1.1 Overview of eutrophication Eutrophication is a form of water quality degradation that occurs in lakes and reservoirs because the concentration of nutrients in lakes increases too high, mainly phosphorus [4], causing aquatic plant outbreaks, leading to an increase in the content of suspended substances, organic matter, reducing the amount of dissolved oxygen in the water, especially at the bottom, adversely affecting the quality and ecosystem of water [5] When newly formed, the lakes are in poor nutritional condition, the water is usually quite clear Nutrients to the lake are supplemented by rainwater, silt-bearing flows rich in nutrients, minerals, sediments, decomposition of aquatic plants and animals and their wastes Because the solids and sediments settle down to the bottom of the lake, the strong development of the rooted plants in the coastal area makes the lake more shallow and the surface area becomes more and more narrowed so the natural lake will gradually turn into marshes then becoming grasslands [6] According to many studies, there are many causes of eutrophication but mainly due to the concentration of nutrients in the high water, especially salt maximum amount of nitrogen and phosphorus [9], the water temperature is warm, high levels of solar radiation, high pH values and low CO2 concentrations [10], [11] There are many studies to develop eutrophication and typical methods of evaluation, among them is the method of Hakanson et al (2007) when concentrating on using concentration values of TN, TP and Chlorophyll-a (Chl.a) parameters to divide into nutrient levels Also, the Carlson method of calculating the Carlson nutritional state index with relation to the concentration of TP and Chl.a by TP is a nutrient-limited mainly for the development of algae and Chl.a is the characteristic value for algae biomass concentration 1.2 Overview of research and development of lake eutrophication model Lake eutrophication models range from simple to complex, words describing several variables to many variables and influential parameters The lake can be assumed to be a homogeneous object, mixed well or divided into different sections horizontally as well as vertically according to the water column and sediment Originally simulated basic nutrients were mainly phosphorus, which was then developed to add nitrogen, carbon and silicon Nutrients are divided into different components but concentrated mainly into the form directly absorbed by phytoplankton and or must be through the process of transformation such as mineralization and hydrolysis to absorb new OK The eutrophication model is usually a one-way or two-way ecological model combined with dynamic processes, chemical and biological interactions The phytoplankton objects concentrate on simulating mainly algae Algae can be considered as a group or divided into typical groups such as blue-green algae, green algae and diatoms etc The study of building models depends on the objectives, objects of the lake and different climatic conditions, etc The rich lake models in the world are built on studies mainly in natural lakes large and deep areas in temperate climates but not interested in small, shallow lakes and tropical and subtropical climates This is also the research direction that the thesis focuses on research The management of the water environment in general and the lake water environment in particular in Vietnam now needs to develop suitable eutrophication models for different lake objects in different regions in Vietnam However, we still have some issues that need to be addressed in the development of lake eutrophication model, namely: In our country, most of the lake eutrophication research models depend on the software or available models of foreign countries The use of such software is available which limits the selection of eutrophication models to suit the conditions of Vietnam The models are mainly black-box models, so it is difficult for users to fully understand the mathematical equations used and are bound to numerical methods when solving simulation models Besides, the lack of simulation models for the eutrophication of lake processes derives from the nature of physical, chemical, biological and hydraulic processes related to eutrophication, leading to a lack of foundation for self-construction building and developing eutrophication models in Vietnam Also, in the lake ecosystem, many different complicated processes are leading to many causes of difficulties in building and developing ecological models, including: - Lakes are objects with heterogeneous habitats linked together (for example, the upper, lower and bottom of the lake have big differences) - In each different nutritional state, the lake ecosystem has some different species that are difficult to describe completely or separately - The interaction between sediment and water column is important for lake ecosystems, especially the diffusion of nutrients from sediments To overcome the limitations and difficulties in the thesis, it will focus on developing lake ecological models with the following main research orientations: - Researching the theoretical basis of modelling eutrophication in sedimentary lakes, thereby developing mathematical equations describing the nutritional relationship to the growth and development process of algae groups - Research and propose suitable and stable algorithms with the equation system to simulate lake eutrophication process - Based on the simulation equation system, algorithm, conduct programming to develop models to simulate the eutrophication process in shallow lakes; - The model application was developed to adjust, verify and simulate the eutrophication process with real data sets measured in a lake in Hanoi 1.3 Overview of the scope of the study Based on the field survey of lakes in Hanoi inner city, the study has selected Cu Chinh lake with characteristics suitable to the research objectives as well as the assumptions of the development of eutrophication model Ho Cu Chinh is a shallow urban lake located in a geographic metropolitan area of 21 o00' north latitude, 105o48' east longitude, in the southwest of Hanoi city centre (indicated in Figure 1.3) According to survey and survey results, Cu Chinh lake is adjacent to Thuong Dinh and Nhan Chinh wards (Thanh Xuan district) The area to catch rainwater has a high population density and many commercial areas and most of the concrete surfaces are rain-proof The area includes the residential area of the population, land for commercial areas, offices, offices, schools and hospitals, the land surface of roads including Quan Nhan road with traffic density high Almost no waste source is discharged directly into the lake due to domestic wastewater from residential areas and stormwater runoff is mostly collected into the city's sewage pipeline system, additional sources from underground water are also very limited due to brick embankments and strong steel fences Figure 2.1 Steps to develop a simulation model of eutrophication of the lake 2.2 Theoretical basis for developing the eutrophication model In this section, the theoretical basis of the thesis will be presented in detail to develop eutrophic simulation models in shallow lakes, which include influencing factors, assumptions, mathematical equations and variables status, exogenous variables, constants and influential parameters as well as model development, evaluation and application The main factors affecting water eutrophication include (1) High concentrations of TN, TP; (2) slow flow velocity; (3) high temperature and other favourable environmental factors and (4) microbial activity and biodiversity Phytoplankton can occur faster when all environmental conditions are favourable To minimize the complexity but still ensure the simulation of eutrophication process in the lake reasonably in the thesis, some assumptions are given as follows: The shallow pond, there is no flow in, out and no impacted by surface wind; The simulated object is to tie water in a tank in a fully blended mode (considering the exchange of organic matter between the water column and sediment surface); Selecting the dominant algae groups in the lake is the phytoplankton object to simulate; Zooplankton in the lake is simply described 11 as a single group; The selected nutrients are nitrogen, phosphorus and organic carbon; There is no direct discharge of wastewater into the lake The natural nutrient supplement to the lake is deposited from the atmosphere and stormwater runoff in the basin In this hypothesis, the nutrient diffusion coefficient from the atmosphere to the water column and the concentration of nutrients in stormwater runoff are constant for the duration of the simulation With the assumption on a eutrophication model developed based on the combination of kinetic processes of biomass concentration of dominant algae groups, zooplankton and biochemical processes including The following state variables: Biomass concentration of algae groups (blue-green algae, green algae and diatoms), zooplankton, dissolved inorganic nitrogen concentration (NH4-N, NO3-N, NO2-N) ; Dissolved inorganic phosphates (PO4-P), organic variables (DOC, TOC), total nutrient variables (TN, TP) and dissolved oxygen concentrations (DO) The seasonal change in the temperature of the water column, the intensity of light radiation and the deposition of atmospheric influences on the biochemical process in the lake is described as exogenous variables Overview of lake eutrophication model is presented in Figure 2.2, describing the interaction between state variables Figure 2.2 Diagram of simulation eutrophication models in the standing, shallow lake 12 As mentioned above, in addition to the equations inherited from previous studies, the thesis proposes to improve the equations describing nutrient dynamics when adding nutrients of organic carbon and phosphorus and nitrogen from the atmosphere including diffusion from the air, rain and stormwater runoff specifically as follows: WPOC V = A × kaPOC + X × A × CRPOC +  × X × F × COPOC A×Z+X×A+×X×F (2-1) WDOC V = A × kaDOC + X × A × CRDOC +  × X × F × CODOC V (2-2) WDIP V W NH4 V W NO2 V W NO3 V = A × kaDIP + CrDIP × X × A+  × X × F × CODIP V k aNH4 = aNO2 × X × A +  × X × F ×C ONH4 × A+C rNO2 × X × A +  × X × F ×C ONO2 V k = rNH4 V k = ×A+C aNO3 ×A+C rNO3 (2-3) (2-4) (2-5) ×X×A+×X×F×C ONO3 V (2-6) The system of ordinary differential equations describes the eutrophication process in standing shallow lakes including equations 2-1 to 2-13 with the component values detailed in Appendix from equation PL1-1 to PL1- 31 and the nutrient supplement composition into the lake is shown in equations from 226 to 2-31 In summary, we have a model of rich eutrophication with 14 state variables including Green algae biomass, Blue-green algae biomass, Diatom algae biomass; Zooplankton biomass, 5.TOC, 6.TP, 7.TN, 8.DO, 9.POC, 10.DOC, 11.PO4-P, 12.NH4-N, 13.NO2-N, 14.NO3-N and 95 model parameters 2.3 Method of solving equations The Runge-Kutta method incorporates the 4th and 5th order is the numerical method chosen to solve the ODE simultaneously and the concentration value of the state variables over time Using the built-in MATLAB programming language, there are modules, for numerical solutions of ODE equations 13 Using RSME indicates the average magnitude of the error T RMSEk = √T ∑t=1(Ot,k − Pt,k )2 (2-7) So in the thesis, genetic algorithms automatically adjust through fitness function values to determine the value of the parameters of the model, described through the following formula: K (2-8) Fitness =  RMSE K k =1 k Conditions for optimal fitness function when: K Fitness = min(  k =1 RMSE k ) K (2-9) Where Fitness is the value of the objective function, k is the order of state variables In addition to using the error of RMSE, the study used three error values including the Nash-Sutcliffe Efficiency (NSE), RMSE -observations standard deviation ratio (RSR) and Percent BIAS percentage index (PBIAS) are used to assess the appropriateness between simulated values and actual measured values Quality assessment criteria for error indicators are presented in Table 2.3 The model can be rated as "pass" if NSE ≥ 0,5, RSR ≤0,7 and PBIAS 0,7 PBIAS ≥ ±25 2.4 Sampling, experimental measurement Water sampling time taken from April 2017 to March 2018 is divided between the rainy season (from May to October) and the dry season (from November to April) Sample 1-2 times a month Conduct a representative sample of mixed 14 samples from points in the lake to a depth of about 20 cm below the water level (Figure 1) and filtered with GF/F filter paper The portion of filtered water is stored separately in plastic bottles for nutrient analysis A certain volume of water is collected and fixed by Lugol solution to determine the density of floating plant cells 2.5 Application of development eutrophication model at Cu Chinh Lake – Hanoi To set up the simulation process, the input and output data of the model are presented in Figure 2.6 The initial value of state variables, exogenous variables, nutrient supplement sources is the input database for the model Exogenous variable values including water temperature values and daily average solar radiation intensity are calculated based on the air temperature data and the number of sunshine hours per day Real day rainfall measured at meteorological station Lang accompanied by weekly average rainfall quality The average depth value of lake Z = 1.6 m and lake water area is 4000 m2 Figure 2.6 Overview of input data, the output of lake eutrophication model The time to select the model is from April 4, 2017, to September 30, 2017, with a series of nine data collected for each state variable Time to select the model 15 test from 19.10.2017 to 8.3.2018 with real measurements for each state variable Through the evaluation results of the error of the simulation of parameters in the process of adjusting and verifying models, for the required parameters with the evaluation criteria selected for the enrichment model to develop Use corrected parameter set values to simulate some technical scenarios that can occur in practice, including aeration, sediment dredging and algae removal 2.6 Summary of chapter The content of chapter presents the theoretical basis of the mathematical equations that the model chooses to apply, including the kinetic equations of algae, zooplankton, nutrients and dissolved oxygen concentrations In the equations of nutrients kinetics, the thesis proposes to improve when adding nutrient components deposited from the atmosphere and stormwater runoff Besides, chapter also introduces research methods and equipment for research In which Matlab software is integrated with the 4th and 5th order Runge-Kutta numerical solution to solve the system of mathematical equations and is also a convenient environment for programming and developing models The actual observation and measurement time at Cu Chinh Lake is divided into two phases: the adjustment time (from April 4, 2017, to September 30, 2017) and the model verification (from October 19, 2017, to March 8, 2018) From the results of calibration and verification of the model, the thesis proposes some measures to minimize lake eutrophication through some simulation scenarios CHAPTER RESULTS AND DISCUSSION 3.1 Results of water quality analysis and eutrophication assessment - The assessment of water quality is compared with national standards for surface water quality level A2-QCVN 08:2015/BTNMT, 2015 - Assessing the level of eutrophication: Based on the ratio of TN/TP, comparing with the standards of the World Health Organization [12] consider which nutrients are limiting factors to the development of algae Compare TP, TN and 16 Chl.a parameters with Hakanson's nutritional classification [21] Calculation of trophic status index Carlson with TSI (TP), TSI (Chl.a) and TSI (TN) [23] From the data of water quality analysis, floating plants some conclusions were drawn about enrichment in Cu Chinh lake as follows: 1- The quality of water in Cu Chinh lake only suitable for low water standards is not suitable for conserving aquatic plants and animals DO, BOD5 concentration some time is not suitable for QCVN 08–2015, BTNMT level A2 The concentration of NH4-N, NO2-N, PO4-P parameters is higher than the permissible standards, not suitable for the conservation of water plants and animals and has seasonal changes, mainly increasing in the rainy season and reducing about the dry season 2- The results of eutrophication assessment showed that phosphorus is mainly a nutrient that limits the development of algae while nitrogen only has some time in the rainy season Eutrophication status of the reservoir was assessed according to the TSI (TN), TSI (TP), TSI (Chl.a) and TN and TP levels, which showed that the eutrophication level in the lake was always maintained in the state of super eutrophication except for the concentration of Chl.a, the lake is at a nutrient level This proves that the lake is at very high levels of organic pollution 3- Plants float in the lake dominated by green algae and cyanobacteria with typical genera as biological indicators of organic pollution like Scenedesmus and blooming in water like Microcystis, Anabaena The density of algae cells in the lake has a large fluctuation with higher value in the rainy season Moreover, the cell density of cyanobacteria, especially Microcystis, Anabaena during the monitoring period showed that the risk of producing neurotoxins and hepatotoxins affects plants and animals in the lake 3.2 Development results of the simulation model of the eutrophication process The parameters of the model are divided into groups: Group is 42 parameters with constant values, shown in detail in Table 3.6 and Group are 53 parameters whose values are determined based on the range value The process 17 of modifying the model uses genetic algorithms (GA) to optimize the parameter value of the model through the objective function as the mean of the root-meansquare error (RMSE) The sequence of execution steps is shown in Figure 3.13 The study has developed a simulation model of eutrophication in standing, shallow lakes with a suitable level of simulated value and acceptable real measured value The results of the value optimization process of the 15 parameters with the most influence levels related to algae groups showed maximum growth rates, optimum temperature of algae groups at the smallest value On the contrary, the value of the parameter causes alleviation of algae biomass such as respiratory coefficient, non-predatory mortality rate fluctuates at the maximum value The study has narrowed the range of values for 15 parameters, helping to improve the reliability and accuracy of the simulation of the eutrophication process Figure 3.13 Optimization process of a eutrophication model The optimization process by GA with the smallest objective function value indicates the reliability to find the optimal parameters of the model Simulation 18 results and actual measurements of biomass concentration, nutrient uptake of algae groups tend to change relatively appropriate and have low RMSE value Table 3.13 The RMSE, NSE, RSR PBIAS value comparison between the optimization of the 15 parameters before and after adjustment Observation set Green algae biomas Blue-green algae biomas Diatom algae biomas Zooplakton biomas TOC TP TN DO POC DOC PO4–P NH4-N NO2-N NO3-N The value of 15 parameters before adjustment RMSE PBIAS NSE RSR (mg/l) (%) The value of 15 parameters after adjustment RMSE PBIAS NSE RSR (mg/l) (%) 0,072 0,89 0,502 -29,4 0,006 1,00 0,044 -2,5 0,103 0,65 0,338 -52,8 0,055 0,95 0,18 -23,3 0,005 0,93 0,163 -23,7 0,004 0,95 0,15 -20,7 9E-06 0,95 0,38 -20,0 1E-05 0,94 0,254 -19,9 0,578 0,144 2E-04 0,417 0,037 0,275 0,157 0,03 0,0002 0,06 0,94 -3,29 1,00 0,87 0,99 0,96 -53,2 0,94 1,00 0,65 0,37 0,78 0,001 0,54 0,049 0,247 2,93 0,19 0,0015 0,33 -22,6 -184,0 0,0 -32,5 7,4 -17,1 -654,8 21,1 -0,2 52,7 0,315 0,046 0,012 0,238 0,066 0,261 0,002 0,046 0,035 0,043 0,96 0,91 0,97 0,96 0,98 0,97 0,99 0,95 0,96 0,83 0,2 0,25 0,03 0,31 0,088 0,233 0,037 0,29 0,264 0,238 -12,3 5,6 3,6 18,5 13,4 -16,3 9,1 22,9 22,6 38,5 The results of the model calibration show some relatively reasonable results between the trend of changes as well as the error value between the simulated and measured values of the state variables The results of the NSE, RSR and PBIAS indicators show the efficiency in the simulation process for the biomass concentration parameters of green algae, blue-green algae and diatom algae, soluble inorganic nutrient concentrations, DO and TOC type from level to very good Only the NO3-N concentration value of PBIAS25% is not satisfactory when the simulation value and the measured value at some time have a big difference The results of the model validation show that the majority of the parameters with the simulation process are relatively consistent with the measured value results The values of NSE, RSR and PBIAS showed that for biomass 19 concentration, biomass of zooplankton, TOC, TP, TN, DO, DOC and NO3-N, simulation results of the model from good to very good, PO4-P, NH4-N and NO2-N with RSR met requirements but NSE and PBIAS indexes with large errors did not meet the requirements and POC parameters did not meet all requirements This result partly shows that the value of the lake enrichment model parameter is reliable With satisfactory parameters when evaluating error values, the model can use parameter set values to forecast and simulate scenarios in Cu Chinh lake The results of model calibration and validation have proved the correctness that the proposed mathematical equations mentioned above are applied in practice in a metropolitan Hanoi lake Results of calibration and verification showed that for biomass concentration parameters of algae groups, the biomass of zooplankton, TOC, TP, TN, DO, DOC and NO3-N were simulated effectively by the model evaluated Through the values of NSE, RSR and PBIAS errors ranged from satisfactory to very good levels 3.3 Calculation results according to the scenario model simulation Results of comparison between algae biomass concentration, dissolved oxygen concentration and DIP in the initial state with simulation scenarios are shown in Table 3.14 The results of the simulation scenario show that with the use of measures such as sediment dredging and algae-killing chemicals, there is a significant impact to reduce the introduction of algae biomass while the aeration method has a more limited effect Meanwhile, for DO concentration, the sediment dredging method has the biggest improvement, then the aeration method also uses algaekilling chemicals to reduce the decomposition of more algae of the algae, but the reduction is negligible For DIP concentrations, sediment dredging measures significantly reduce their concentration, contributing to limiting algae growth and development Although the use of chemicals is cost-effective, there are still concerns about the lake ecosystem when applying this method 20 Table 3.1 Impact, advantages and disadvantages of the simulation scenario to algae biomass concentration, average dissolved oxygen and average DIP in Cu Chinh lake Scenario Variability (%) Algae DO DIP biomass Enriched with oxygen - 0,1 + 24,9 + 0,01 Dredging sediment -11,35 + 27,8 - 61,07 Chemical kill algae - 16,45 - 3,24 3,8 Advantages Significant improvement in DO concentration in the lake Helps reduce relatively large DIP levels, algae biomass and improve DO in the lake Relatively large reduction of algae biomass concentration Disadvantages The effect was negligible for algae biomass and DIP in the lake Costly, difficult to apply regularly compared to some other techniques Smell, taste and poison can still exist in the water; May cause changes to other processes in the lake In fact in Hanoi, the measures are widely applied to many lakes as aeration measures and use of chemicals kill algae The measures, although there are some limitations, have obtained quite positive results, contributing to improving lake water quality in general and eutrophication in particular The sediment dredging method is used less because it is expensive and difficult to implement in practice Therefore, in each specific case, we choose different measures to suit the objectives 3.4 Summary of chapter The results of the analysis of water quality and eutrophication in Ho Cu Chinh indicate that the lake is being polluted organically and the main cause is nitrogen and phosphorus The level of eutrophication in the lake is quite high when maintained in eutrophication state even super-nutrition Three of the algae groups with dominant cell density in the lake are green algae, blue-green algae, diatoms and they are closely related to nutrient concentrations, environmental factors such as water temperature and solar radiation level The research results in the thesis have successfully developed a mathematical model that simulates eutrophication process in shallow water areas and applied 21 in Cu Chinh lake, shallow lake eutrophication is in the inner city of Hanoi is monitored for a period of 12 months - The model has improved the kinetic equation of organic carbon, phosphorus and nitrogen by adding sources from the atmosphere and rainwater runoff and actively use the Runge-Kutta method order and to solve the ODE system - The process of model calibration in the period from 4.5.2017 to 30.9.2017 has identified the optimal parameter set of the model through genetic algorithms integrated into Matlab with the value of the objective function (RMSE) as small as 0.0791 The values of NSE, RSR and PBIAS indicators show the simulation process for biomass concentration parameters of green algae, blue-green algae and diatom algae, soluble inorganic nutrient concentrations, DO and TOC are graded from good to very good level Only the NO3-N parameter of PBIAS value   25% is unsatisfactory when the simulation value and the real value measured at some time have a large difference - The process of model validation found that most of the state variables have relatively simulated results following the measured results The values of NSE, RSR and PBIAS showed that for algae biomass concentration, the biomass of zooplankton, TOC, TP, TN, DO, DOC and NO3-N parameters for simulation results rated from satisfactory to very good levels, PO4-P and NO2-N parameters have satisfactory RSR but NSE and PBIAS index values are not satisfactory From the model calibration and validation results, algae biomass concentration parameters and DO were selected to evaluate the change from the initial state with the technical simulation scenarios The results show that scenarios of algae use and sediment dredging are highly effective in reducing algae biomass while the aeration and sedimentation scenarios increase DO levels in the lake CONCLUSIONS AND SUGGESTIONS Conclusions of the dissertation - Successfully developed a mathematical model to simulate the eutrophication process for standing shallow lakes, applied to Cu Chinh Lake - Hanoi: 22 + Set up the equation system of eutrophication process to describe the dynamical processes of algae groups, the concentration of nutrients and DO under the influence of exogenous variables including water temperature, the solar radiation intensity is expressed by 12 ODEs with 14 state variables and 95 parameters + Improving the kinetic equation of nutrient concentration when adding the number of nutrients deposited from the atmosphere and rainwater runoff into the lake in the area + Using the Runge - Kutta method to combine order and order to solve the numerical value of state variables in ODEs and programmed with Matlab version 2016a + The results of model calibration and validation show the model's state variables such as biomass concentrations of algae groups, the biomass of zooplankton, DO and some nutrient indicators with good simulation results This suggests that it is possible to use the model parameter value of the model to predict water quality developments as well as algal blooms - The results of simulation scenarios showing measures to reduce algal biomass as well as increasing DO concentration in water shows that sediment dredging measures have significant impacts on the quality of the lake water following the use of algae-killing chemicals Meanwhile, the aeration method helps to replenish quite well the DO concentration but has negligible impact to prevent algal blooms in the lake Based on the evaluation of solutions, it is possible to consider and choose the appropriate application method in practice New contributions of the dissertation - A mathematical model developed simulation to model the process of eutrophication in the shallow standing water areas by adding a concentration of nutrients from the atmosphere and rainwater runoff - Applying the developed model for Cu Chinh lake in Hanoi inner city with the corresponding set of parameter values Limitation and future research The thesis focuses on simulating the eutrophication process in shallow lakes with the assumption that the lake is completely mixed and there is no source of 23 concentrated wastewater Additional sources of nutrients for the lake are deposition from the atmosphere and overflow due to rain Due to the limitation of the total research time as well as the implementation budget, the thesis focuses on the application of the eutrophication model in Cu Chinh lake To overcome these limitations, the study proposes some further research orientations: - For algae groups, it is necessary to supplement from studies to assess the impact of meteorological factors when extreme weather events occur such as prolonged hot sunshine or short-term local heavy rain At the same time, increase the number of sampling times especially during periods where meteorological factors have a large change to assess the reaction level of state variables to environmental conditions - The correction time can be seasonally adjusted so that the value of the parameter of the model with the characteristic value can be increased to increase the accuracy of the model forecast - Need to measure water quality in many more lakes in Hanoi city to have a more diverse database to better serve the model calibration and verification process Recommendations Based on the research findings and issues that need further research and application for lakes in Hanoi urban area, the author of the thesis has the following recommendations: - The development of lake eutrophication models in Hanoi inner city should continue to be implemented to create more useful tools in eutrophication research - In addition to Cu Chinh lake, the research results can be applied to lakes with similar characteristics to Cu Chinh lake to predict the development of algae biomass in the lake and propose technical measures suitable for controlling eutrophication 24 PUBLICATIONS Ta Dang Thuan, Bui Quoc Lap, Analysis of seasonal variation of factors affecting algae growth in a lake of the inner Hanoi city by using a eutrophication model, Journal of water resources & environmental engineering, 64, 60-68, 2019 ISSN 1859-3941 Thuan Dang Ta, Lap Quoc Bui, Thanh Dang Binh Nguyen, Tri Quang Doan, Jaya Kandasamy, Application of a Genetic Algorithm for the Calibration of Eutrophication model in an Urban Lake, International Journal of Earth Sciences and Engineering (H-index: 10 (2017), Vol 12(1), pp 1-15, February 2019 ISSN 0974-5904 (SCOPUS DOI:10.21276/ijee.2019.12.0101 Ta Dang Thuan, Bui Quoc Lap, The eutrophication status of Hanoi Lakes and a case study of a shallow lake in the inner city, Hanoi Forum 2018: Towards Sustainable Development, pp 164, 2018 Ta Dang Thuan, Bui Quoc Lap, Some characteristics of eutrophication in a shallow lake in Hanoi, Journal of water resources & environmental engineering, 61, 52-61, 2018 ISSN 1859-3941 Ta Dang Thuan, Bui Quoc Lap, Survey and initial assessment of the state of eutrophication in a lake in Hanoi, Proceedings of the annual conference of Thuyloi university 2017, pp 409-411, 2017 ISBN: 978-604-82-2274-1 ... increase in the content of suspended substances, organic matter, reducing the amount of dissolved oxygen in the water, especially at the bottom, adversely affecting the quality and ecosystem of water... decomposition of aquatic plants and animals and their wastes Because the solids and sediments settle down to the bottom of the lake, the strong development of the rooted plants in the coastal area makes... model parameters 2.3 Method of solving equations The Runge-Kutta method incorporates the 4th and 5th order is the numerical method chosen to solve the ODE simultaneously and the concentration