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EVALUATION OF WATER QUALITY MODELLING PARAMETERS: TOWARDS THE EVOLVEMENT OF RE-AERATION COEFFICIENT FOR RIVERS IN THE NIGERIAN ENVIRONMENT

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ABSTRACT 
This study was carried out on River Atuwara in Ota, Ogun State, Nigeria with the aim of developing a coefficient of re-aeration model applicable to River Atuwara and other rivers in the Nigerian environment. This was achieved by sourcing for data once every month from 22 sampling locations of interest within a pre-selected segment of the river over a period covering the dry and wet seasons. The data collected include hydraulic data (depth, width, velocity and time of travel) and water quality data such as Dissolved Oxygen (DO) and Biochemical Oxygen Demand (BOD). Excel Spreadsheet and MATLAB were used for data processing. Regression analysis was carried out where stream velocity and depth were the regressors and the re-aeration constant k2 (as a function of BOD, DO and Temperature) was the dependent variable.  A coefficient of re-aeration, k2, (Atuwara re-aeration model) was developed and validated statistically. Its performance was also verified by comparing the model with 10 other internationally recognized models. It was  found that even though Atuwara model performed better than Agunwamba model and most of the other well cited models, both Atuwara model and Agunwamba model could be safely adopted for future water quality modelling researches in the Nigerian environment.  Results of detailed water analysis of samples from River Atuwara shows high level of pollution hence it is unfit for human consumption without adequate treatment. It is recommended that River Atuwara and similar rivers in the country should be regularly monitored for quality control.
TABLE OF CONTENTS      PAGE 
Title Page          i  
Declaration         ii  
Certification         iii 
Dedication          iv 
Acknowledgement        v 
Table of Contents         vii 
List of Figures         x 
List of Tables         xi 
List of Plates         xiv 
Abbreviations and Symbols       xv 
Abstract          xvi 
 
CHAPTER ONE: INTRODUCTION 
1.1  Background Information       1                             
1.2   Water Quality modelling       3 
1.3   Description of Study Location     5 
1.4   Statement of The Problem      6 
1.5   Aim         6 
1.6   Objectives        6 
1.7   Significance of Study       6 
1.8   Scope of Study       7 
 
   CHAPTER TWO: LITERATURE REVIEW 
2.1  Water Quality Modelling as a Field of Study    8 
2.2   Coefficient of Re-aeration, k2      9 
2.2.3  The Indian k2 Model       13 
2.2.4  The Chilean k2 Model       14 
2.2.5  The Nigerian k2 Model     15 
2.3    Water Laws and Standards       15 
2.4    Statistical Analysis       17 
2.4.1  Some Relevant Statistical Operations   17 
2.4.2  Statistical Software     19 
2.4.3  Model Calibration and Validation in Water Quality 
Data       20 
2.4.3.1      Sum of Squares Due to Error  21 
2.4.3.2      R-Square        21 
2.4.3.3      Degrees of Freedom Adjusted R-Square 22 
2.4.3.4      Root Mean Squared Error   22 
 
CHAPTER THREE: METHODOLOGY  
        3.1   Selection of the Study Area       24 
       3.2   Determination of Sampling Stations      27 
       3.3   Field Activities        49 
  3.3.1  Field Observations      31 
  3.3.2  Field Sampling Visits      31 
   3.3.2.1     Rationale for Gathering Data Once Every Month  32 
    3.3.2.2     Activities During the Field Exercises  33 
            3.4     Materials        34 
            3.5     Laboratory Analysis       36 
       3.6     Data Analysis        37 
            3.6.1    Time of Travel       38 
           3.6.2    Re-aeration Coefficient Model     39 
 
CHAPTER FOUR: DATA PRESENTATION AND INTERPRETATION 
  4.1 Data Gathering       40 
   4.1.1   Hydraulic Data      41 
   4.1.2   Physico-Chemical Data     50 
    4.1.3  Monthly Variations in DO, Temperature, Stream Depth       57 
   4.2  Computation of Measured k2                                                              63 
            4.3  Re-arrangement of Sampling Stations    67 
4.3.1  Time of Travel      68 
4.3.2  Hydraulic Radius                 80 
4.3.3  Ultimate BOD and De-oxygenation Rate              80 
4.3.4  Saturation DO and the Upstream and Downstream DO deficits  80
 4.3.5  Determination of k2                 80 
4.3.6  Model Parameters                 80 
4.3.7  The Model                  83 
4.3.8  Comparison with other Selected Models              83 
4.4  Water Use Practices                             103 
 4.5       Pollutants and Public Health Implications              106 
 
CHAPTER FIVE: CONCLUSION AND RECOMMENDATION 
5.1  Conclusion                  110 
5.2 Contribution to Knowledge                111 
5.3  Recommendations                 111 
       
REFERENCES                   113 
 
APPENDICES  

Appendix 1: Matlab Code for Beta               121 
Appendix 2: Matlab Model Output                          128 
Appendix 3: Matlab Code and Output for Plot of all Models           132 
Appendix 4: Mix Calculations               140 
Appendix 5: Laboratory Reports               147  
Appendix 6: Procedure for data Analysis              160


LIST OF FIGURES                                           PAGE 

Figure 1.1 - Nigerian Household distribution by source of water supply  2 
Figure 1.2 - Nigerian Household distribution by Toilet Facilities   3 
Figure 1.3 " General Layout of the Study area     5 
Figure 3.1" Field Sampling Stations       28 
Figure 3.2 " Linear representation of Sampling Points    29 
Figure 3.3 - Sampling Cross-section       33 
Figure 4.1 " An 8-month mean stream velocity record    59 
Figure 4.2 " An 8-month mean ambient temperature record    60 
Figure 4.3 " An 8-month mean water temperature record    61 
Figure 4.4 " An 8-month mean stream depth record      61 
Figure 4.5 " DO Fluctuations over an 8-month period    62 
Figure 4.6 - Flowchart showing the progression of the statistical analysis            86 
Figure 4.7 " Plot of 11 models using January data                93 
Figure 4.8 " Plot of measured k2 against computed k2 using January data            94 
Figure 4.9 " Plot of 11 models using March data                96 
Figure 4.10 - Plot of measured k2 against computed k2 using March data            97 
Figure 4.11 " Plot of 11 models using July data                99 
Figure 4.12 - Plot of measured k2 against computed k2 using July data            100 

LIST OF TABLES                                                                                  PAGE 

 
Table 2.1 " The self-purification factor, f, of different water bodies at 20oC  9 
Table 2.2 " Solubility of Oxygen in water      10 
Table 3.1 - Details of Sampling Stations      30 
Table 3.2 " Parameters Measured with Relevance to study    32 
Table 3.3 " Parameters, equipment and Processes of  parameter determination 
Schedule for field work        34 
Table 4.1 - Sampling dates and conditions      40 
Table 4.2a " Hydraulic Data for January      42 
Table 4.2b " Hydraulic Data for February      43 
Table 4.2c " Hydraulic Data for March      44 
Table 4.2d " Hydraulic Data for April      45 
Table 4.2e " Hydraulic Data for May       46 
Table 4.2f " Hydraulic Data for July       47 
Table 4.2g " Hydraulic Data for August      48 
Table 4.2h " Hydraulic Data for September      49 
Table 4.3a " Physico-Chemical Parameters for January    50 
Table 4.3b " Physico-Chemical Parameters for February    51 
Table 4.3c " Physico-Chemical Parameters for March     52 
Table 4.3d " Physico-Chemical Parameters for April     53 
Table 4.3e " Physico-Chemical Parameters for May      54 
Table 4.3f " Physico-Chemical Parameters for July      55 
Table 4.3g " Physico-Chemical Parameters for August    56 
Table 4.3h" Physico-Chemical Parameters for September    57 
Table 4.4 " Mean Monthly Ambient and Water Temperatures   60 
Table 4.5 " Determination of Reaches for the River      64 
Table 4.6 - Dilution Effects for January      65 
Table 4.7 - Dilution Effects for February      65 
Table 4.8 - Dilution Effects for March      65 
Table 4.9 - Dilution Effects for July       66 
Table 4.10 - Dilution Effects for August      66 
Table 4.11 - Dilution Effects for September      66 
Table 4.12 " Re-arrangement of station numbers      67 
Table 4.13 " Computation of time of travel on Programmed Excel Spreadsheet for January          68 
Table 4.14 " Computation of time of travel on Programmed Excel Spreadsheet for 
February          69 
Table 4.15 " Computation of time of travel on Programmed Excel Spreadsheet for 
March           70 
Table 4.16 " Computation of time of travel on Programmed Excel Spreadsheet for 
July           71 
Table 4.17 " Computation of time of travel on Programmed Excel Spreadsheet for 
August                      72 
Table 4.18 " Computation of time of travel on Programmed Excel Spreadsheet for 
September                     73 
Table 4.19 " Computation of k1 and k2 on Programmed Excel Spreadsheet for JanuaryTable 4.20 " Computation of k1 and k2 on Programmed Excel Spreadsheet for 
February                     75 
Table 4.21 " Computation of k1 and k2 on Programmed Excel Spreadsheet for March
                      76 
Table 4.22" Computation of k1 and k2 on Programmed Excel Spreadsheet for July 
                                          77 
Table 4.23 " Computation of k1 and k2 on Programmed Excel Spreadsheet for August
                                 78 
Table 4.24 " Computation of k1 and k2 on Programmed Excel Spreadsheet for 
September                     79 
Table 4.25" Model fit and goodness of fit Summary for Dry Season              81 
Table 4.26" Model fit and goodness of fit Summary for Rainy Season           82 
Table 4.27 " Selected Models for Model Validation (Test of performance)    84 
Table 4.28" Goodness of fit using January Data                 91 
Table 4.29- Goodness of fit using March Data                 91 
Table 4.30- Goodness of fit using July Data                            92 
Table 4.31: Graphical Goodness of fit using January, March and July Data  102 
Table 4.32 " Order of Composite Goodness of Fit               103 
Table 4.33 " Comprehensive River water and Industrial Effluent Analysis   107 
LIST OF PLATES                                            PAGE 
Plate 3.1 " The industrial effluent flowing along the road down towards the river 25 
Plate 3.2 " the effluent accumulates (left) from where it seeps into the river body 25 
Plate 3.3 " Effluent accumulation beside the river body    26 
Plate 3.4 " Villagers of Iju tapping the river water for domestic use   26 
Plate 3.5 " Sewage being taken near the river for disposal    27 
Plate 3.6 " Field pH meter        35 
Plate 3.7 " Eurolab digital thermometer with sensitive probe   35 
Plate 3.8 - Geopacks Stream flow sensor with its pole and fan-like impeller  36 
Plate 3.9 - Measuring the river width with a tape      36 
Plate 3.10 " the Speedtech Portable Depth Sounder (yellow torchlight shaped 
instrument)          57 
Plate 4.1 " Sampling Station 10 in Rainy season (August)    58 
Plate 4.2 " Sampling Location 10 in Dry season (March)    58 
Plate 4.3 " Human skeleton found in the River               104 
Plate 4.4 " Pollution along the river channel                          104 
Plate 4.5 " The research team could not proceed because of blockage of the river  105 
Plate 4.6 " Water intake station for Ogun State Water Corporation                        105 
Plate 4.7 " Man swimming after the day’s work               106 

ABBREVIATIONS AND SYMBOLS 
1.  DO " Dissolved Oxygen 
2.  BOD -  Biochemical Oxygen Demand 
3.  QUAL " Stream Water Quality models 
4.  CORMIX " Cornell Mixing Zone Expert 
5.  WASP " Watershed Quality Analysis Simulation Programme 
6.  FEPA " Federal Environmental Protection Agency 
7.  USEPA " United States Environmental Protection Agency 
8.  USGS " United States Geological Society 
9.  UNESCO " United Nations Education, Scientific and Cultural Organization 
10. DV " Dependent Variable 
11. IV " Independent Variable 
12. ANOVA " Analysis of Variance 
13. SSE " Error Sum of Squares 
14. SSR " Residual sum of squares 
15. SST " Total sum of squares 
16. R2 " correlation coefficient 
17. Adj. R2" Adjusted Correlation coefficient 
18. RMSE " Root mean square error 
19. APHA - American Public Health Association 
20. SPSS " Statistical Package for Social Sciences 
21. MATLAB " Matrix Laboratory software 
22. GPS " Global Positioning System 
23. k2 " re-aeration coefficient 
24. k1 " de-oxygenation coefficient 
25. f " self purification factor 
26. 2 ^σ  - estimated variance 
27. mg/l " milligram per litre 

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