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MINISTRY OF EDUCATION AND TRAINING MINISTRY OF AGRICULTURE AND RURAL DEVELOPMENT THUYLOI UNIVERSITY BUI DINH LAP DEVELOPING ALGORITHMS FOR OPTIMIZING PARAMETERS OF MARINE DISTRIBUTED HYDROLOGICAL MODEL Major: Hydrology Code: 9440224 SUMMARY OF DOCTORAL THESIS IN TECHNICS HA NOI, 2023 The project is completed at Thuyloi University Scientific supervisor 1: Prof Dr Pham Thi Huong Lan, Thuyloi University, Vietnam Scientific supervisor 2: Prof Dr Tran Hong Thai, Vietnam Meteorological and Hydrological Administration Reviewer No 1: Assoc.Prof Dr Tran Ngoc Anh , Hanoi University of Sciences- Vietnam National University, Hanoi Reviewer No 2: Assoc.Prof Dr Hoang Minh Tuyen, Vietnam Institute of Meteorology, Hydrology & Climate Change Reviewer No.3: Prof Dr Huynh Thi Lan Huong, Hanoi University of natural Resources and Environment The thesis will be defended in front of Thesis Evaluation Council at At on .2023 The Thesis can be studied at libraries below: - National Library - Thuyloi University library INTRODUCTION Necessity of the research topic Climate change, fluctuations in water resources, extreme types of natural disasters such as drought, water shortage, saltwater intrusion, storm, flood, inundation has been having many negative impacts on water resource management and natural disaster prevention and control Therefore, it is necessary to have a full assessment, identification and forecast of possible occurrences to proactively respond in all situations, this is a very complex problem, affected by many interdependent inputs, in which the problem of calculating the flow in the basin is always a big challenge for scientists because of the uncertainty of many factors The hydrological mathematical model has always been one of the effective tools in the simulation and forecasting of water sources and is one of the key factors to improve the forecasting quality However, currently in Vietnam, most of the tools and models to support calculation and prediction in this field are still limited The hydrological models describing the process of rain and runoff studied and applied in practice in Vietnam up to the present time are not many and not diverse, The most commonly used hydrological models today are two concentrated hydrological models (the Tank model and the Nam model) Recently, due to computer capacity conditions; spatial data quality (especially satellite data, terrain, land cover); and the quality of ground rain data is getting better and better, hydrological models of distribution parameters are being developed and applied more and more in practice, especially in developed countries with better quality of input data Distributed parameter hydrological models are increasingly being applied in problems related to hydrological forecasting and water resources due to the great advantage of being able to simulate and evaluate fluctuations of water resources in space and time However, most of the hydrological models of distribution parameters are being applied in Vietnam at present, no model has been developed and integrated with optimal parameter control feature, this is a limitation that affects greatly affects the forecast quality and the model's ability to extend the application range to other watersheds, since the parameter detection has to be done manually, which will consume a large amount of time, effort, and heavy burden subjectivity and understanding of the editor With the goal of having a modern hydrological mathematical modeling tool to solve practical problems in the field of hydrology and water resources Within the framework of the doctoral thesis: "Developing algorithms for optimizing parameters of MARINE distributed hydrological model", The author will study in depth the advantages, disadvantages, structure of the optimization algorithms in the field of optimization and the structure of the distributed parameter hydrological models which are highly appreciated in the world in order to proposed a new global, multi-objective optimization algorithm based on the integration of the outstanding advantages of the algorithms being studied by scientists around the world The thesis’s research objectives ✓ Proposing a new global, multi-objective optimization algorithm based on the integration of outstanding advantages of the algorithms being highly appreciated by scientists around the world ✓ Integrate the proposed optimization algorithm into the MARINE distributed hydrological model ✓ Experimental application of the new proposed algorithm for the Nam Mu river basin Objects and scope of the study Research object: Global optimization algorithm, multi-objective; Structure of hydrological model of distribution parameters Research scope: parameter set of MARINE model Methodology To achieve the goal of the thesis, on the basis of documents, research works in the world and in Vietnam in the field of research are collected The author has used the following scientific research methods to carry out the research contents of the thesis: i) Method of analysis and synthesis of theory; ii) Inheritance method; iii) Expert method; iv) System analysis method GIS techniques and programming techniques are used by the thesis to analyze and process spatial data, test the optimal algorithm and realize the research results achieved by the Thesis Scientific and practical significance ▪ Scientific significance Contributing to completing the MARINE distributed hydrological model There is a new global, multi-objective optimization algorithm based on the integration of the outstanding advantages of the algorithms being highly appreciated by scientists around the world The new proposed algorithm has improved three existing problems of previous studies in the field of hydrology and water resources, including: 1) the calibration time is still very large (especially when applying used for hydrological modeling of distribution parameters); 2) the problem tends to converge quickly (pseudoconvergence) when the number of parameters to be searched is large or the objective functions are highly correlated; 3) algorithms are often not very efficient when the number of objective functions to be calibrated is large ▪ Practical significance The development model uses modern techniques, integrates the ability to effectively exploit existing data sources on the hydrometeorological monitoring network of Vietnam and multi-objective parameter correction techniques, so it is applicable highly practical, helping to improve the quality of solving problems in the field of hydrology and water resources After developing and testing the model, it can be deployed in service at the National Center for Hydrometeorological Forecasting; The development model is designed in accordance with the conditions of data and topographical characteristics in the river basins in the territory of Vietnam, so it can be easily deployed to other river basins (besides the experimental basin of thesis) Structure of the thesis In addition to the introduction, conclusion and recommendations, the thesis is presented in chapters: Chapter 1: Overview of studies on hydrological models of distributed parameters and parameter estimation problems in nonlinear systems; Chapter 2: Scientific basis for proposing optimization algorithm for MARINE distributed hydrological model; Chapter 3: Experimental Research Results and Discussion CHAPTER 1: OVERVIEW OF STUDIES ON HYDROLOGICAL MODELS OF DISTRIBUTED PARAMETERS AND PARAMETER ESTIMATION PROBLEMS IN NONLINEAR SYSTEMS 1.1 Overview of the structure and mathematical basis in the system of simulating the process of rain, the flow of distributed parameters in use in the world Distributed parameter hydrological models are being developed and applied in practice more and more, especially in developed countries with better input data quality Most of the major universities in the world have researched and developed hydrological models of distribution parameters to serve research and teaching, some well-structured and algorithmic models have been deployed into practical application To achieve the research goal of the thesis, in this content the thesis has focused on analyzing the overview of the physical-mathematical structure (in cross section) of 12 typical model systems with high applicability, currently being used in many countries around the world, including Vietnam to serve the purpose of developing mathematical models and solving the multi-objective optimal control problem of the thesis The results of the review showed that: - In the structure of the system of distributed hydrological models, the components in the system are usually represented by partial differential equations, containing both space and time variables - To set up the system, the system developer usually divides the basin into grid cells, each grid cell is considered as the structure of a miniature centralized hydrological model 1.2 Overview of parameters in the hydrological model of the distribution parameters In this content, the thesis conducts an overview analysis of the parameters commonly used to calibrate and test the system and analyze their role based on the documents of 12 systems to guide the selection of the methodology to achieve the research objectives of the thesis The analysis results show that: the number of parameters to be determined in the system is very large, the magnitude depends on the resolution of the grid, to determine the parameters in the system requires the computer to have large computing power, but most of the parameters in the system are related to vegetation cover and soil structure, so this problem can also be improved if this rule is found 1.3 Overview of parameter estimation methods in nonlinear systems In this content, the thesis has analyzed the results obtained on the method of parameter estimation in nonlinear systems from research work that has been carried out over the past decades The analytical results show that there are still many problems that need to be further researched and perfected to further improve the efficiency of the algorithm such as: The correction time is still very large (especially when applied to hydrological model of distribution parameters); The problem tends to converge quickly (pseudo-convergence) when the number of parameters to be searched is large or the objective functions are highly correlated; Algorithms are often not very efficient when the number of correction targets is large;… 1.4 Overview of domestic studies on the problem of parameter estimation in hydrological modeling systems 1.4.1 Overview of the current status of research projects with application of optimal techniques to solve problems in the field of hydrology and water resources In Vietnam, optimization techniques have been researched and applied by many scientists to solve various problems in the field of hydrology and water resources, in which special focus is on optimization problems in calculation and operation of the inter-reservoir system in the basin Typical research works in the past two decades can be mentioned as: Tran Hong Thai (2005) [1]; Ha Van Khoi, Le Bao Trung (2003) [2]; Nguyen The Hung, Le Hung (2009) [3]; Ngo Le Long, Henrik Madsen, Dan Rosbjerg (2007) [4]; Nguyen Lan Chau et al (2010) [5]; Hoang Thanh Tung, Ha Van Khoi, Nguyen Thanh Hai (2013) [6]; Nguyen Huu Khai, Le Xuan Cau (2009) [7] It can be seen that the optimal methods used to solve problems in the field of hydrology and water resources in our country today are mostly two-dimensional dynamic programming methods, complex shuffled evolution algorithms SCE, and a few optimization tools built from foreign researches, most of the methods used today use single-objective optimization techniques to solve the problem (a few studies have research has considered, argued to convert the remaining objectives into the constraints of the problem) Most of the current solutions are implemented based on optimization techniques proposed before 2008 1.4.2 Overview of domestic studies on the problem of optimal parameter estimation in hydrological model system There are not many research works applying optimization techniques to solve parameter estimation problems in hydrological modeling systems found in domestic journals Case studies in the past two decades to address this issue can be mentioned by author Tran Hong Thai (2009) [8] From the research results published in scientific journals, it is shown that hydrological models describing the process of rain and runoff have been studied and applied in practice in Vietnam not many, and are widely used today are concentrated parameters hydrological models NAM (especially DHI's MikeNAM model) and Japan's TANK model, both of which have built-in automatic parameter detection feature Recently, the computer capacity conditions; satellite data quality (especially topographic data, land cover); and the quality of ground rain data is getting better and better, some hydrological models of distribution parameters have been studied and applied in VietNam such as MARINE, WETSPA, WEB-DHM, DIMOSOP, SWAT, IFAS models , however, most of these hydrological models of distribution parameters have not been developed and integrated with optimal control of parameters 1.5 Research direction of the thesis From the general research results, the author finds that the research proposes a new optimal algorithm based on the integration of the outstanding advantages of the algorithms being evaluated high by scientists around the world, suitable for solving problems in the field of hydrology and water resources, especially solving the problem of optimal parameter estimation in a distributed hydrological model system containing nonlinear mathematical equations is necessary and also the research direction of the author in this thesis 1.6 Conclusion Chapter - The optimal methods used to solve problems in the field of hydrology and water resources in our country today, mostly two-dimensional dynamic programming method, complex shuffle evolutionary algorithm SCE, and Some optimization tools are built from foreign researches Most of the current solutions are made based on the optimization techniques proposed before 2008 - In the world, the proposed optimal algorithms to calibrate hydrological models still have many problems that need to be further researched and perfected such as: The correction time is still very large (especially when applying for the hydrological model of the distribution parameters); The problem tends to converge quickly (pseudo-convergence) when the number of parameters to be searched is large or the objective functions are highly correlated; Algorithms are often not very efficient when the number of correction targets is large - Based on the limitations pointed out in the overview, the author has oriented the research direction of the thesis to improve the above limitations CHAPTER 2: SCIENTIFIC BASIS FOR PROPOSING OPTIMIZATION ALGORITHM FOR MARINE DISTRIBUTED HYDROLOGICAL MODEL 2.1 Research and propose new multi-objective global optimization algorithm for automatic parameter calibration problem in hydrological model If the solution method is classified according to the adjusted objective function F(X), the optimization problem can be divided into three main classes, including: 1) The single-objective parameter optimization problem; 2) The multi-objective parameter optimization problem is aggregated to single-objectives; 3) Multiobjective parameter optimization problem solved directly In the third way, the multi-objective optimization problem (MOP) is expressed as follows: (2-3) Min 𝐹(𝑥) = (𝑓1 (𝑥), … , 𝑓𝑚 (𝑥))𝑇 𝑔𝑗 (𝑥) ≥ 0, 𝑗 = 1, … , 𝐽 𝑆𝑢𝑏𝑗𝑒𝑐𝑡 𝑡𝑜: { ℎ𝑘 = 0, 𝑘 = 1, … , 𝐾 𝑥 ∈ Ω where: ▪ J K are the numbers of inequality and equality constraints, respectively ▪ 𝛀 ⊆ ℝ𝒏 is the parameter (decision variable) space, ▪ 𝒙 = (𝒙𝟏 , … , 𝒙𝒏 )𝑻 ∈ 𝛀 is the parameter vector ▪ F: Ω -> Rm consists of m real-valued objective functions ▪ Rm is the objective space Currently, the best option to solve the above problem is to develop algorithms towards multi-objective evolution (MOEAs), combined with the concept of Pareto optimization From the results of synthesis, analyze the advantages and disadvantages of domestic and foreign studies, analyze the advantages and disadvantages of different solutions The thesis chooses the approach of solving the problem in the 3rd way "Solve the multi-objective optimization problem directly" to build an algorithm to achieve the research goal of the thesis The new multi-objective optimization algorithm of the thesis is built on the basis of combining the achievements of the single-objective optimization algorithm in the field of hydrology and water resources SCE_UA and the multi-objective optimization algorithm SPEA/R [9] Specifically, the new proposed optimization algorithm of the thesis will be built on the application of the following concepts: o A deterministic, random combination approach o Complex evolution o Competitive evolution o Complex shuffle o Spatial decay based on reference direction o Evaluate the individual based on the reference direction ▪ The new multi-objective optimization algorithm MSCE_UA The algorithm MSCE_UA is designed to be able to find the optimal solution (in the space of possible solutions) on the Pareto optimal set through the set of participating solutions Unlike the original algorithm SCE_UA, the multiobjective optimization technique will be used by the thesis to evolve the sample instead of the single-objective optimization technique of the original algorithm Algorithm structure MSCE_UA is designed similar to algorithm SCE_UA [10], techniques for individual evaluation, sample sorting of SCE_UA and CCE algorithms are replaced by improved SPEA/R [11] algorithm Overall structure of the algorithm MSCE_UA 1: Input: S (starter pattern) 2: Ouput: approximated Pareto-optimal front and proposed set of optimal parameters 3: Start the algorithm, load the configuration file containing the algorithm control information into the variable Start the algorithm, load the configuration file containing the algorithm control information into the variable 𝑗 4: Create s sample points vectơ 𝜃𝑖 = (𝜃11 , … , 𝜃𝑠𝑛 ) với i=1, …, s and j=1, …, n in the feasible space 𝛺 𝜖 𝑅 𝑛 and store in set X, define the corresponding target function vector set 𝐹(𝜃𝑖 ) = (𝑓1 (𝜃𝑖 ), … , 𝑓𝑀 (𝜃𝑖 ) at each point 𝜃𝑖 and and store in variable Xf[𝑓j , … , 𝑓𝑀 , fitness), where j = ÷ M, M is the number of the target function indexes are less than 0.8 IGD and HV index tend to be better than NSGA-II, NSGA-II+SDE, MOEA/D, MOEA/IGD-NS on the same test problem[55], on problem ZDT1 NSGA's HV index -II is 6.6054e-1, MOEA/D is 6.6035e-1, MOEA/IGD-NS is 6.6085e-1 while the proposed algorithm is 7.1880e-1, MOEA/D IGD index is 4.9935e -3 while the proposed algorithm is 4.9621e-3, Table 2.1: Result of rating index the efficiency of algorithms achieved IGD, HV (mean and standard deviation) through the test problems ZDT1 ZDT6 DTLZ1 DTLZ5 IGD HV IGD HV IGD HV IGD HV 4.9621e-3 7.1880e-1 6.9891e-2 3.1083e-1 4.6169e-2 7.6382e-1 2.9604e-2 7.6382e-1 (4.33e-4) (7.32e-4) (5.30e-2) (6.19e-2) (2.31e-2) (8.01e-2) (4.50e-3) (8.01e-2) ▪ Building a new proposed multi-objective, global parameter optimization program MSCE_UA There are 25 functional functions and about 4500 command lines coded by the thesis on C++ programming language to perform steps and in the overall algorithm MSCE_UA based on the inheritance of the SPEA/R theoretical basis and algorithm (for details of the algorithm's source code, see the main report appendix) The program is designed to operate according to the steps proposed in the thesis's algorithm Steps 3, and 7, 8, 9, 10 are integrated directly on the object (model) to be optimized, steps 5, operate in parallel with the optimal object After each evolutionary cycle, the new set of individuals will be moved to step 5, for evaluation and classification, the individuals after determining their position in the population will be transferred to step to continue evolution cycle until the convergence condition in step 10 is satisfied The program is capable of parallel operation on multiple Servers operating in the Linux operating system environment and the high-performance computer operating system Cray XC 40 Series ▪ Integrating the algorithm into the Marine model The MARINE model (Modelisation de lAnticipation du Ruissellement at des Inondations pour des événements Extrêmes) was developed by the French Institute of Fluid Mechanics Toulouse (IMFT -Institut de Mecanique de Fluides de Toulouse) The model is developed based on the conservation of mass equation and the Green Ampt permeation method 11 In this content, the thesis has directly integrated the algorithm into the MARINE distributed hydrological model as a part of the mathematical model, using Fortran and C++ programming languages The model is designed to run parallel tests on 02 servers using Linux operating system (Red Hat Enterprise Linux Server, 18 Processor: Intel CPU @ 2.6 GHZ) There are main functional modules added to the Marine model for the purpose of integrating the algorithm into the model and implementing steps 3, and 7, 8, 9, 10 in the new proposed algorithm MSCE_UA (detailed source code see the main report appendix) 2.3 Conclusion Chapter In this chapter, the thesis: 1) A new global, multi-objective optimization algorithm MSCE_UA has been proposed and built to solve optimization problems in the field of hydrology and water resources The program can operate on Linux operating system environment (running in parallel on many Servers) or operating on Cray XC Series system (high-performance supercomputer system); 2) Successfully integrated the new algorithm into the MARINE distributed hydrological model to serve the problem of automatic model parameter calibration and verification when considering the results evaluation criteria at the same time The new proposed algorithm MSCE_UA is made based on the hybridization between the two algorithms SCE_UA and SPEA/R, on the basis of integrating the outstanding advantages of these two algorithms, in order to improve the efficiency and quality of the Parameter calibration problem in hydrological model distribution parameters and applications to solve other optimization problems in the field of hydrology and water resources CHAPTER 3: EXPERIMENTAL RESEARCH RESULTS AND DISCUSSION To evaluate the applicability of the new proposed algorithm MSCE_UA in practice, the thesis chose to integrate both: the original algorithm SCE_UA and the proposed algorithm MSCE_UA into the MARINE distributed hydrological model The basin selected to test the algorithm is the Nam Mu river basin (to Ban Chat reservoir) on the Da river 3.1 Marine model application for test basin 3.1.1 Divisional basin division In the process of implementing the model application, in order to minimize the 12 spatial impact of inputs such as soil composition, cover composition and variation of spatial rain distribution , most Modern hydrological mathematical models, all require the division of large basins into smaller sub-basins, before hydrological simulations can be performed But, how to divide the basin like? and how many sub-basins is reasonable? There are still difficult questions and problems when implementing applications in practice Figure 3-10: Description of the basin numbering process in the ARC/INFO environment for the Ban Chat reservoir basin The unreasonable division of the basin will lead to difficulties in calibrating the model parameters and the process of collecting water to calculate the flood in the river, thereby leading to the quality of the flood simulation in the basin also being degraded To solve this problem, the thesis has researched and selected the Pfafstetter basin numbering system to perform the task of sub-basin division for the test basin [14] The AML language (ARC/INFO Macro Language) and the Fortran programming language are the two main tools used to realize the Pfafstetter watershed numbering method and its application to the Ban Chat reservoir Figure 3-10 is the result of the application of the Pfafstetter basin numbering system to the Ban Chat reservoir, whereby basins from the large basin have been numbered and separated so that the Marine model can be applied to the calculation runoff from rain 13 3.1.2 Set up the rain~flow calculation diagram for the Marine model Figure 3-11: Diagram of the rain~flow calculation for Ban Chat reservoir basin The rainfall~flow calculation diagram on the basin is built mainly based on the analysis of the current situation: the network of rivers and streams; small and medium hydropower reservoir systems; terrain distribution; and the existing infrastructure of rain and flood monitoring stations in the basin Figure 3.11 is the result of setting up the rain~flow calculation diagram for the basin water collection service on the system from the Marine model, with a total of subbasins, 12 water collection nodes and segments directly involved in the process flow calculation to Ban Chat reservoir 3.2 Data, parameters and objective function participating in the experiment 3.2.1 Data for experiment The thesis uses 19 years (2001-2019) of observing data taken from the data 14 source provided by the National Center for Hydrometeorological Forecasting to evaluate the performance and efficiency of the algorithm Using flood data corresponding to the flood season in the typical years of large flood, medium flood and small flood in the basin to calibrate model parameters, including the years 1969, 1971, 1999, 2001 2009, 2012 2019 (June 15 - October 15) The years before 2009 used flow data at Ban Cung station to verify and calibration parameters, years after 2012 directly used flow data to Ban Chat reservoir to verify and calibrate parameters 3.2.2 Parameters and objective function participating in the experiment The thesis selects 04 parameters to test the proposed optimal algorithm MSCE_UA for the Marine model, including: parameter of surface resistance 𝐾𝑚 ; soil porosity; 𝛹 capillary water column of wet side (mm); 𝐾 Hydraulic conductivity (mm/hr) Other parameters are fixed or calculated interpolated from the DEM map data, see Table 3.7 Table 3.7: Optimal parameters and their boundary limits in the Marine model Optimal parameters Variable symbol Lower Upper 𝑲𝒎 var4_ODS 0.01 0.3 var1_ETA 0.25 0.5 𝜳 (mm) var2_SF 20 520 𝑲 (mm/hr) var3_KGA 0.3 120 This study selects 03 objective functions with high conflict to participate simultaneously in the optimization problem, the objective functions are shown in Table 3.8 Table 3.8: List of objective functions participating in the test problem Objective function name Variable symbol Nash–Sutcliffe Measure NASH Math formula 1− ∑𝑛𝑡=1(𝑂𝑡 − 𝑆𝑡 (𝜃))2 ∑𝑛𝑡=1(𝑂𝑡 − 𝑂̅)2 𝑀𝑙 Root Mean Squared Error RMSE Absolute Peak Difference APD 𝑛𝑗 1 ∑ √ ∑ (𝑂𝑖 − 𝑆𝑖 (𝜃))2 𝑀𝑙 𝑛𝑗 𝑖=1 𝑗=1 | max {𝑂𝑡 } − max {𝑆𝑡 (𝜃)}| 1≤𝑡≤𝑛 15 1≤𝑡≤𝑛 where: 𝑂𝑡 is the actual measured flow at the time of observing t (t=1, …, n); 𝑀𝑙 is the number of low flow events, 𝑛𝑗 is the number of steps in each event; 𝑆𝑡 (𝜃) the simulated flow value achieved by the Marine model at time t; 𝑂̅ is the average value of actual measured flow of the monitoring series 3.3 Analyze test results 3.3.1 The results of testing the new proposed algorithm MSCE UA calibration parameters for the Marine model Figure 3-22: The normalized parameter space, the bold line is the solution found by the algorithm MSCE_UA suitable for the flood season of many years Figure 3-23: Standardized objective space, bold lines are the three simultaneous optimal objectives of the algorithm corresponding to the parameters found 16 Table 3.13: Results of evaluation of simulation criteria of flood season in years through discharge to Ban Chat reservoir Years Qin Ban Chat 2001 S/ 0.65 Nash 0.58 2002 0.56 0.69 2003 0.57 0.68 2004 0.57 0.68 2005 0.67 0.55 2006 0.54 0.71 2007 0.51 0.74 2008 0.64 0.59 2009 0.54 0.71 Average 0.58 0.66 Max 0.67 0.74 Min 0.51 0.55 (*) The above table is calculated in terms of discharge to Ban Chat reservoir interpolated from Ban Cung station according to area ratio ▪ Analyze the results Figure 3-24: Process line between calculated and actual (interpolated) discharge to Ban Chat reservoir in 2009 The results obtained in Table 3.13, Figure 3-24 show that the new proposed algorithm MSCE_UA applying parameter correction test to the Marine model gives quite good results, the quality criterion S/ and the Nash criterion both 17 achieved allowable criteria, which shows that the proposed algorithm can be applied to optimize the parameters for the Marine model 3.3.2 Comparison results between the new proposed algorithm MSCE_UA and the original algorithm SCE_UA in the Marine model parameter calibration problem In this test, the thesis is mainly interested in the degree of convergence of the optimal parameters and the simulation ability of the distributed parameter hydrological model on the basis of the application of the new algorithm MSCE_UA compared with the the original algorithm SCE_UA, other aspects of the SCE_UA algorithm and the SPEA/R algorithm can be found in [10], [11] ▪ Analysis of optimal parameters The optimal solutions of the four parameters in the MARINE model on different flood events show that the convergence areas of both methods tend to be similar (shown in Figure 3-25) However, the parameter var2_SF (the wetting front soil suction head) and parameter var4_ODS (surface resistance) of SCE_UA method have a wider range and less convergence than new method MSCE_UA Figure 3-25: The distribution of convergence points in the normalized space of parameter 18 Table 3.14 shows that the Nash-Sutcliffe index of the SCE_UA method is larger, but their convergence region fluctuates more greatly than that of the MSCE_UA method This can be explained by the fact that the MSCE_UA method has to balance between highly conflicting goals while the SCE_UA method only searches the optimal area based on the Nash-Sutcliffe index Table 3.14: Fluctuations of optimal solutions between methods MSCE-UA and SCE_UA var1_ETA MSCE_ SCE_ UA UA 0.996 0.947 0.995 0.097 0.997 0.995 0.664 0.013 0.892 0.942 0.254 0.551 0.378 0.629 0.615 0.494 0.378 0.028 var2_SF MSCE_ SCE_ UA UA 0.996 0.995 0.361 0.522 0.998 0.99 0.614 0.012 0.996 0.995 0.617 0.998 0.948 0.947 0.41 0.324 0.948 0.899 var3_KGA MSCE_ SCE_ UA UA 0.981 0.995 0.995 0.984 0.996 0.997 0.478 0.272 0.997 0.993 0.997 0.996 0.906 0.996 0.996 0.919 0.906 0.995 var4_ODS MSCE_ SCE_ UA UA 0.995 0.995 0.944 0.99 0.013 0.076 0.023 0.046 0.014 0.021 0.578 0.997 0.763 0.084 0.927 0.995 0.763 0.997 Average Nash MSCE_ SCE_ UA UA 0.68 0.57 0.68 0.63 0.5 0.69 0.69 0.77 0.48 0.75 0.6 0.85 0.53 0.69 0.63 0.74 0.58 0.74 0.60 0.71 The standardized parameter graph of the MARINE model (using the NashSutcliffe calibration objective function and SCE_UA algorithm) in Figure 3-26 and the standardized parameter graph of the MARINE model (using simultaneous calibration of objective functions (Nash-Sutcliffe, RMSE, APD) and MSCE_UA algorithm) in Figure 3-27 also show that the convergence region of the calibration parameter set in the parameter space of the MSCE_UA algorithm tends to converge better than SCE_UA algorithm Figure 3-26: The standardized parameter graph of the MARINE model (using the Nash-Sutcliffe calibration objective function and SCE_UA algorithm) 19 Figure 3-27: The standardized parameter graph of the MARINE model (using the objective functions Nash-Sutcliffe, RMSE, APD and MSCE_UA algorithm) ▪ Estimated parameter test Validating the performance of a hydrological model against independent data sets is an important procedure to evaluate the applicability of the identified parameter set In this study, the flood events from 2015 to 2019 were used to validate the model parameters Results in Table 3.15 show that the quality simulation of the system with the found parameter set from the MSCE_UA method is better than the SCE_UA method in both flood peaks and Nash-Sutcliffe statistical index Table 3.15: Results performed by different optimal solutions Difference ms Peak Nash Event Thực đo MSCE_UA SCE_UA MSCE_UA SCE_UA MSCE_UA SCE_UA 20-30/6/2019 1543 838 673 -705 -870 0.65 0.62 22/7-01/8/2019 1038 826 679 -212 -359 0.64 0.63 29/8-8/9/2019 543 550 551 0.68 0.64 20/6-30/6/2018 4995 3393 2249 -1602 -2746 0.52 0.5 0.62 0.6 Average 20 Finally, the two simulated curves obtained from the two algorithms are compared with the actual measured process (Figure 3-28) Figure 3-28: Flow simulations using MSCE_UA algorithm and the SCE_UA original algorithm In which the bold line is the actual process, the dotted line is the simulation obtained from the SCE_UA method, the long dashed line is the MSCE_UA The simulation results show that the simulation curve MSCE_UA is also more suitable with the real measurement than the SCE_UA method 3.4 Conclusion Chapter The experimental results show that the new proposed algorithm MSCE_UA applies the parameter calibration to the Marine model with good results The comparison test results between the new proposed algorithm MSCE_UA and the original algorithm SCE_UA in the Marine model parameter calibration problem show that: 1) the convergence area of the set of parameters to be calibrated in the parameter space of the algorithm MSCE_UA tends to converge better than the SCE_UA algorithm; 2) the system simulation quality of the MSCE_UA method with test data is more consistent with reality than that of the SCE_UA method 21 CONCLUSIONS AND RECOMMENDATIONS Conclusion The thesis has built a scientific basis, optimal algorithms and optimal programs to solve problems in the field of hydrology and water resources The new proposed algorithm of the MSCE_UA thesis is made based on the hybridization between the two algorithms SCE_UA and SPEA/R, on the basis of integrating the outstanding advantages of the two algorithms The technique of decomposing the target space into independent small regions based on the reference-oriented set and the individual evaluation technique of the SPEA/R algorithm has been researched and applied by the thesis to improve the original SCE_UA algorithm, This approach has improved the SCE_UA algorithm from single-objective optimization to multi-objective optimization, making the new algorithm capable of searching the entire POF (Pareto optimal front) and ensuring the diversity of samples in target space On the basis of the new proposed optimization algorithm, the thesis has successfully built a new multi-objective optimization program MSCE_UA using C++ and Fortran programming languages with the support of MATLAB tools The program is designed and built to be able to operate on the Linux operating system environment and run in parallel on many Servers or on a highperformance supercomputer system The new proposed optimization algorithm has been successfully applied by the thesis to solve the "parameter optimization problem for distributed parameter hydrology model" By testing the algorithm on the Marine model and applying it to the Da river basin (to Ban Chat lake) with 03 highly conflicting objective functions participating in the optimization problem simultaneously (NASH, RMSE, APD) With 19 years (2001-2019) observed data were used to experimentally evaluate the performance and efficiency of the algorithm and compare it with the original SCE_UA algorithm The experimental results show that the new proposed algorithm MSCE_UA applies the parameter correction test to the Marine model with good results The convergence area of the set of correction parameters in the parameter space of the new algorithm MSCE_UA tends to converge better than that of the SCE_UA algorithm, the system simulation quality of the MSCE_UA method with test data also gives the same results The results are more in line with reality than the SCE_UA method 22 MARINE model has been successfully researched and developed by the thesis and has become a modern computational tool to solve problems in the field of water resource management such as: 1) The problem of near-real-time flood control through through the inter-reservoir system on the basin; 2) The problem of flood forecasting of extremely short duration; 3) The problem of monitoring and warning flash floods; The multi-objective parameter optimization function and other new functions added to the MARINE model have greatly reduced the time and effort of the model adjuster (from 1500 hours to hours) for basins > 3000 km2), eliminating the subjectivity of the calibrator by trial and error, improving the quality of system simulation and easily deploying the application on Vietnam's river basins because it has been integrate features suitable to our country's data structure and infrastructure New Contributions 1) Proposing and building a new global, multi-objective optimization algorithm MSCE_UA to solve optimization problems in the field of hydrology and water resources The program can operate on Linux operating system environment (running in parallel on many Servers) or operating on Cray XC Series system (high-performance supercomputer system) 2) Successfully integrated the new algorithm into the MARINE distributed hydrological model to serve the problem of automatic model parameters calibration and verification when considering the results evaluation criteria at the same time 3) Initially, successfully applied the algorithm to automatically calibrate the MARINE distributed hydrological model for the Nam Mu river basin, Vietnam Help improve the efficiency of using MARINE distributed hydrological model in flow simulation to Ban Chat reservoir in forecasting service at the National Center for Hydrometeorological Forecasting Development direction and recommendations of the thesis The results achieved in the thesis are the results achieved after a long time of research efforts of the author, despite many efforts, the authors found that this is only the initial achievement in the career Scientific research of the author The proposed optimization algorithm of the thesis has only been tested on the "parameter optimization problem for distributed parameter hydrology model" on 23 a MARINE distributional parameter hydrology model and on a test basin Algorithm application studies need to be further expanded on different problems in the field of hydrology and water resources, in order to more deeply and objectively evaluate the performance and effectiveness of the algorithm The improved MARINE model product of the thesis needs to be researched and applied to other river basins in Vietnam to improve the application efficiency 24 LIST OF WORKS RELATED TO THE THESIS HAS BEEN PUBLISHED [1] Bui DinhLap, Tran Hong Thai, Pham Thi Huong Lan, "Development of a multi-objectives optimization method in the field of hydrology and water resources, application test for automatic parameter estimation problem in a fully distributed hydrological model", Collection of reports from the National Scientific Conference on Hydrometeorology, Environment and Climate Change, 2022 [2] Bui DinhLap, Tran Hong Thai, Pham Thi Huong Lan, " Development of the distributed hydrological model MARINE in flood forecasting problem, pilot application for Nam Mu river basin ", VietNam Journal of Hydro Meteorology no 723, 2021 [3] Bui DinhLap, Tran Hong Thai, Pham Thi Huong Lan, "Application of objectives space decomposition technique solve the parameter estimation problem in the distributed hydrological model", Journal of Water Resources & Environmental Engineering no 72, 2021 [4] Bui DinhLap, "Applying Remote Sensing Technology in flood forecasting and warning systems in Viet Nam", Workshop on SMART Informatics for Sustainability, Thailand 2018 25