Nghiên cứu phát triển mô hình toán mô phỏng quá trình phú dưỡng ở các vùng nước tĩnh nông, ứng dụng cho hồ cự chính hà nội tt tiếng anh

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: 9 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
1. 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 5 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].

1


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


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.
3. 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.
4. 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

3


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.
5. 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.

4


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.
6. 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.
7. 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 1 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.
5


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.
6


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.

7


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
8


around the lake. Only the amount of rainwater falls on the surface of the lake
and some of the water overflows in the lake's grounds.
Cu Chinh lake

Aquarium

Figure 1.3 Map of the study area
The lake has a circumference of about 250 m, the water surface is
approximately 4000m2. The largest length is about 75m, the largest width is
about 65m, the average depth of the lake ranges from 1.5-1.7 m and the average
water volume is about 4600m3. The main purpose of Ho Cu Chinh is to regulate
microclimate, rainwater and entertainment place of people in the area. The

campus of an area of about 1500 m2 is used as a parking lot and a sports gym
area for people with concrete surfaces. Because it is a small lake, the ability to
mix nutrients in the lake is better than that of large lakes.
1.4 Summary of chapter 1
Eutrophication is one of the typical water quality problems in the world,
especially in shallow waters. Their main harm is to be able to disrupt the
internal balance that leads to gradual damage and degradation of the functions
of the water ecosystem.
There are many directions of research on eutrophication and one of them is to
build and develop models to simulate special eutrophication process in the lake.
Initially, the models were built and developed mainly as an experimental model
when the nutrients used in the model were phosphorus and the simulation
process focused on calculating the load as well as predicting the concentration
9


of nutrients. nutrition and level of eutrophication in the lake.
However, these models only apply in case of lack of data and low reliability.
The centralized equilibrium model describes inputs and outputs to predict longterm trends, mainly total phosphorus. To overcome that, in addition to
developing the kinetic models of phosphorus, additional nutrients, such as
nitrogen and carbon, need to be added. Currently, the popular research direction
that eutrophication models aim at is the ecological model in which the focus is
on describing the relationship between nutrient concentrations with
phytoplankton biomass and zooplankton.
In fact, in Vietnam in general and in Hanoi in particular, shallow natural lakes
have been seriously affected by water pollution, especially the eutrophication
process. Some of the shallow lakes in Hanoi city have successfully controlled
the concentrated wastewater sources flowing into the lake but the nutrients from
the dispersed sources such as overflow on the basin surface as well as
additional sources from the atmosphere.

It also contributes to organic pollution in the lake. In some recent studies, some
reservoirs, although they have controlled concentrated waste sources, continue
to pollute organic matter causing eutrophication when maintaining the level of
eutrophication, even super eutrophication. Among them, Cu Chinh lake has
characteristics suitable to the research objectives as well as the hypothesis of
model development problem when being a shallow lake in Hanoi urban area,
with few concentrated sewage sources joining and being affected by
eutrophication.
CHAPTER 2: DEVELOPING MATHEMATICAL MODELS TO
SIMULATE EUTROPHICATION IN SHALLOW STANDING LAKES
2.1 Steps to develop a simulation model of eutrophication of the lake
The steps to develop a mathematical model to simulate eutrophication in
shallow water are shown in Figure 2.1 below:

10


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 3 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), 2 organic
variables (DOC, TOC), 2 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 1 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 1. Green algae biomass, 2. Blue-green algae biomass, 3.
Diatom algae biomass; 4. 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.
1

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:
1
K
(2-8)
Fitness =
 RMSE
K

k =1

k

Conditions for optimal fitness function when:
1
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 <± 25% for
the value of the state variables.
Table 2.3 Evaluation criteria for the quality indicators for model [122]
Classification
NSE
RSR
PBIAS (%)
Very good
0,75 < NSE ≤ 1
0 ≤ RSR ≤ 0,5
PBIAS < ± 10
Good
0,65 < NSE ≤ 0,75 0,5 ≤ RSR ≤ 0,6 ±10 ≤ PBIAS < ±15
Satisfactory
0,5 < NSE ≤ 0,65 0,6 ≤ RSR ≤ 0,7 ±15 ≤ PBIAS < ±25
Unsatisfactory
NSE ≤ 0,5
RSR > 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 3 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 6 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 2
The content of chapter 2 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 2 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 3 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 2 groups: Group 1 is 42 parameters
with constant values, shown in detail in Table 3.6 and Group 2 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 và 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 3
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 4 and 5 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
1. 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 4 and order 5 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.
2. 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.
3. 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