# Generalised Linear Models for Prediction of Dissolved Oxygen in a Waste Stabilisation Pond

^{1}

^{2}

^{*}

## Abstract

**:**

^{−1}in the training period and 0.74–3.54 mg L

^{−1}in the validation period; while SMAPEs were in the range of 2.35–38.70% in the training period and 10.88–71.62% in the validation period. By providing insights into the oxygen-related processes, the findings could be valuable for future pond operation and monitoring.

## 1. Introduction

_{1}, x

_{2},…, x

_{n}; (2) predict Y based on a set of values of x

_{1}, x

_{2},…, x

_{n}; and (3) screen variables x

_{1}, x

_{2},…, x

_{n}, to identify which variables are more important than others to explain the response variable Y, so that the causal relationship could be determined more efficiently and accurately [7]. For prediction purposes, these can sometimes outperform non-linear models, especially in situations with limited numbers of training cases [6]. In short, GLMs find a line that minimize the errors between the line and the experimental data points. There are a number of different definitions of “best fit,” and, therefore, a number of different development methods of GLMs that result in somewhat different fitted lines. By far, the most common is the “ordinary least-squares regression”. The least-squares method minimises the sum of the squares of the deviations of the theoretical data points from the experimental ones [7].

## 2. Materials and Methods

#### 2.1. Study Area

#### 2.2. Sampling Scheme

#### 2.3. Model Construction and Diagnostics

#### 2.3.1. Variables Used to Develop Models

#### 2.3.2. Model Development

#### 2.3.3. Model Diagnostics and Assessment

#### 2.4. Model Comparison

_{i}is the observed value and F

_{i}is the predicted value and n is the number of data points.

#### 2.5. Model Parameters and Their Importance

## 3. Results

#### 3.1. Variability of Physicochemical and Biological Parameters and Climatic Conditions in the Ponds

^{−1}

_{.}The concentration of BOD followed more or less the same pattern as chlorophyll a, except that there was no large variability of BOD concentration between the three different sampling times, which could be appointed to the quite stable BOD removal efficiency of the system. It was also observed that the concentration of BOD decreased from the FPs to MPs by a factor of two, i.e., 33.7 and 18.8 mg L

^{−1}. Water temperature did not change that much between the three sampling times, and fluctuated around 18–19 °C. Additionally, water temperature seemed to be homogenous throughout the water column and between the two pond types. Related to the climatic conditions, only air temperature remained unaltered, i.e., 16.8 ± 2.1 °C, while wind speed and especially solar radiation did change a lot across the three sampling times, i.e., 2.4 ± 1.0 m s

^{−1}and 469.2 ± 223.8 W m

^{−2}, respectively. As DO was in fact influenced by the BOD concentration and the diurnal activity of algae, it also showed a large variability across the three sampling times (Figure 3). Between the two pond types, DO across the three sampling times had a larger variability in FPs than in MPs. There was also a difference of DO between the surface and bottom of both FPs and MPs. Within line 1 of the WSP, there was a decrease of DO from FP 1 to MP 1, in both the surface and the bottom, while in line 2 of the WSP, DO throughout the ponds were more or less the same in both the surface and the bottom layers. From the outlet part of FP1 to MP1 inlet, DO values near the water surface dropped about 70%, i.e., from above 10 mg O

_{2}·L

^{−1}to around 3 mg O

_{2}·L

^{−1}, while the oxygen level remained similar between the two ponds in the upper line.

#### 3.2. Optimal Models for Prediction of Dissolved Oxygen in the Ponds

^{−1}in the training period and 0.74–3.54 mg L

^{−1}in the validation period. To express the predictive accuracy in percentage, SMAPEs were also calculated and it was in the range of 2.35–38.70% in the training period and 10.88–71.62% in the validation period. In general, among the ponds, the model of MPs performed better than those of FPs, and within a pond, the models for the surface performed better than those for the bottom. This was supported by the higher MAEs and SMAPEs values in the optimal models of FPs, compared to those of MPs, and in the optimal models for the bottom compared to those for the surface (Table 1).

#### 3.3. Importance of the Predictor Variables

^{−1}), DO increased by 0.713 standard deviation, which was equal to 0.713 × 5.90 = 4.21 mg L

^{−1}(Table 2). Similarly, an increase of one standard deviation of air temperature (2.09 °C) and BOD (7.74 mg L

^{−1}) would result in an increase of 3.69 (0.626 × 5.90) and 1.58 (0.268 × 5.90) mg L

^{−1}DO, respectively. Similar interpretations could be made for the other models, based on the values of the standardised coefficients in the last column of Table 2.

## 4. Discussion

#### 4.1. Variability of the Physicochemical and Biological Parameters and Climatic Conditions in the Ponds

^{−1}, which was considered to be low, according to Mara [1], as the chlorophyll a concentration in “healthy” WSPs is usually in the range of 500–2000 μg L

^{−1}. Therefore, more samplings and long-term data collection should be done to figure out whether this low concentration of chlorophyll a was related to short-term data collection, or this could be a characteristic of a WSP operating at a high altitude [34,35,36,37,38].

#### 4.2. Model Comparison

^{−1}in the training and validation periods, respectively, and the SMAPEs decreased from 2.35 % and 10.88 % to 2.10 % and 9.46 % in the training and validation periods, respectively. Since DO dynamics in the ponds follow diurnal circles [20], timing was expected to have a strong effect on model predictive performance, this was not the case in this study.

#### 4.3. Predictive Accuracy of the Optimal Models

^{−1}and 0.74–1.30 mg L

^{−1}in the training and validation periods, respectively) was lower than that in the FPs (0.29–2.75 mg L

^{−1}and 1.19–3.54 mg L

^{−1}in the training and validation periods, respectively). Similarly, SMAPEs of MPs (2.35–30.61% and 10.88–71.62% in the training and validation periods, respectively) were also lower than those of FPs (11.75–38.70% and 11.01–51.89% in the training and validation periods, respectively).

#### 4.4. Importance of the Predictor Variables in the Optimal Models

#### 4.5. Application and Limitations of the Models

## 5. Conclusions

- There was a large variability of chlorophyll a, DO, and climatic conditions across the three sampling times. Within a pond, higher concentration of chlorophyll a and DO were observed near the surface than near the bottom. Between the two pond types, chlorophyll a and DO in the FPs were higher than those in the MPs. No large variability of BOD within a pond was observed across the three sampling times but there was a decrease of BOD from FPs to MPs.
- Among the 83 models developed based on different data partitioning and cross-validation strategies, the 8 models developed specifically for each pond and each depth were the optimal ones. These optimal models depict varying MAEs of DO in the range of 0.21–2.75 mg L
^{−1}, in the training period and 0.54–3.54 mg L^{−1}in the validation period, and SMAPEs of dissolved oxygen were in the range of 3.18–38.70% in the training period and 7.54–89.24% in the validation period. Among the 8 optimal models, the optimal models of MPs performed better than those of FPs and within a pond, the optimal models for the surface seemed to perform better than those for the bottom. - Among the variables used to predict dissolved oxygen, chlorophyll a and BOD appeared to be representative predictor variables. Additionally, water temperature and climatic conditions also highly influenced DO.
- The effect of the timing variable (expressed at the time points the samples were taken) did not show a strong effect on the prediction of DO.
- The results of this study are valuable in the management of WSP and provide basic insights into oxygen-related processes, which could help in further development of advanced models for WSPs.
- Despite the limitation of the data-driven approach for global extrapolation, it is expected that the data partitioning and cross-validation strategies developed in this study, could be widely applied to identify the optimal models for prediction purposes.

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Layout of the waste stabilisation pond and the sampling locations. The arrows represent the location of the inlets and the outlets of the ponds.

**Figure 2.**Schematic diagram of model development integrating different data partitioning and cross-validation strategies.

**Figure 3.**Variability of dissolved oxygen in the ponds. T1, T2 and T3 represent the mean value of dissolved oxygen of each sampling time; and mean (T1, T2, T3) represents the mean value of dissolved oxygen of the three sampling times. Error bars represent the standard deviation.

**Figure 4.**Mean absolute error of the models with the best predictive performance in different data partitioning and cross-validation strategies. Among seven strategies, only four strategies (S1, S4, S6 and S7) resulted in high predictive performing models, which were pond and depth-specific. FP = Facultative pond; MP = Maturation pond; S = Surface; and B = Bottom.

**Figure 5.**Symmetric mean absolute percentage error of the models with the best predictive performance in different data partitioning and cross-validation strategies. Among seven strategies, only four strategies (S1, S4, S6 and S7) resulted in high predictive performing models, which were pond and depth-specific. FP = Facultative pond; MP = Maturation pond; S = Surface; and B = Bottom.

Pond | Training Dataset | Validation Dataset | Full Optimal Model | MAE ± sd (mg L^{−1}) | SMAPE ± sd (%) | R^{2} | ||
---|---|---|---|---|---|---|---|---|

Training | Validation | Training | Validation | |||||

FP1_Surface | T2T3 FP1_Surface | T1 FP1_Surface | DO = −43.718 + 0.039Chl + 0.204BOD + 1.772AT | 1.59 ± 0.73 | 3.06 ± 2.74 | 11.75 ± 14.17 | 11.01 ± 10.03 | 0.909 |

FP1_Bottom | T2T3 FP1_Bottom | T1 FP1_Bottom | DO = −9.550 + 0.447BOD | 2.75 ± 2.20 | 3.52 ± 3.00 | 38.70 ± 31.49 | 20.08 ± 24.08 | 0.540 |

MP1_Surface | T1T2 MP1_Surface | T3 MP1_Surface | DO = −2.024 + 0.012Chl + 0.007SR | 0.54 ± 0.46 | 0.74 ± 0.43 | 17.50 ± 21.64 | 17.64 ± 10.07 | 0.854 |

MP1_Bottom | T1T2 MP1_Bottom | T3 MP1_Bottom | DO = 7.470 − 0.445WT + 0.095AT | 0.22 ± 0.18 | 0.79 ± 0.46 | 30.61 ± 17.28 | 49.19 ± 30.84 | 0.391 |

FP2_Surface | T1T3 FP2_Surface | T2 FP2_Surface | DO = −40.463 + 0.014Chl + 0.201BOD + 1.448WT + 0.496AT | 1.07 ± 0.67 | 3.54 ± 2.62 | 12.66 ± 9.47 | 20.91 ± 10.35 | 0.752 |

FP2_Bottom | T1T3 FP2_Bottom | T2 FP2_Bottom | DO = −2.494 + 0.119BOD | 0.29 ± 0.22 | 1.19 ± 1.10 | 25.29 ± 13.71 | 51.89 ± 25.79 | 0.424 |

MP2_Surface | T1T2 MP2_Surface | T3 MP2_Surface | DO = −15.016 + 0.016Chl + 1.952WT+ 0.004SR − 0.947WS − 0.969AT | 0.32 ± 0.27 | 1.14 ± 0.77 | 2.35 ± 2.00 | 10.88 ± 6.42 | 0.885 |

MP2_Bottom | T1T2 MP2_Bottom | T3 MP2_Bottom | DO = −5.773 + 0.018Chl + 0.407BOD | 0.55 ± 0.32 | 1.30 ± 1.35 | 13.51 ± 12.82 | 71.62 ± 33.56 | 0.624 |

Model | Model Parameter | Mean | Standard Deviation | Unstandardised Coefficient | Standardised Coefficient | 95% Confidence Interval for Coefficient | Change of DO by Change of Each Variable † | ||
---|---|---|---|---|---|---|---|---|---|

Coefficient | Standard Error | Lower Bound | Upper Bound | ||||||

FP1 Surface | DO | 11.28 | 5.90 | ||||||

Constant | −43.718 | 5.975 | −56.533 | −30.904 | |||||

Chlorophyll a | 430.22 | 109.10 | 0.039 | 0.005 | 0.713* | 0.028 | 0.049 | 4.21 | |

BOD | 41.67 | 7.74 | 0.204 | 0.068 | 0.268* | 0.058 | 0.351 | 1.58 | |

Air temperature | 16.87 | 2.09 | 1.772 | 0.238 | 0.626* | 1.263 | 2.282 | 3.69 | |

FP1 Bottom | DO | 5.17 | 5.31 | ||||||

Constant | −9.550 | 4.050 | −18.375 | −0.725 | |||||

BOD | 32.93 | 8.72 | 0.447 | 0.119 | 0.735* | 0.187 | 0.707 | 3.90 | |

MP1 Surface | DO | 2.46 | 1.89 | ||||||

Constant | −2.024 | 0.511 | −3.113 | −0.935 | |||||

Chlorophyll a | 245.73 | 108.63 | 0.012 | 0.002 | 0.678* | 0.008 | 0.016 | 1.28 | |

Solar radiation | 228.86 | 121.67 | 0.007 | 0.002 | 0.448* | 0.004 | 0.010 | 0.85 | |

MP1 Bottom | DO | 0.402 | 0.369 | ||||||

Constant | 7.470 | 2.299 | 2.571 | 12.370 | |||||

Water temperature | 18.59 | 0.86 | −0.445 | 0.143 | −1.035* | −0.750 | −0.139 | −0.38 | |

Air temperature | 12.60 | 3.25 | 0.095 | 0.038 | 0.833* | 0.014 | 0.176 | 0.31 | |

FP2 Surface | DO | 4.92 | 2.58 | ||||||

Constant | −40.463 | 10.646 | −63.462 | −17.463 | |||||

Chlorophyll a | 343.74 | 128.96 | 0.014 | 0.003 | 0.691* | 0.006 | 0.021 | 1.78 | |

BOD | 31.67 | 6.87 | 0.201 | 0.061 | 0.536* | 0.070 | 0.333 | 1.38 | |

Water temperature | 18.21 | 0.66 | 1.448 | 0.659 | 0.371* | 0.025 | 2.871 | 0.96 | |

Air temperature | 15.88 | 2.06 | 0.496 | 0.216 | 0.396* | 0.029 | 0.962 | 1.02 | |

FP2 Bottom | DO | 0.60 | 0.49 | ||||||

Constant | −2.494 | 1.046 | −4.773 | −0.215 | |||||

BOD | 25.93 | 2.70 | 0.119 | 0.040 | 0.651* | 0.032 | 0.207 | 0.32 | |

MP2 Surface | DO | 6.87 | 1.14 | ||||||

Constant | −15.016 | 12.656 | −42.590 | 12.558 | |||||

Chlorophyll a | 242.92 | 63.72 | 0.016 | 0.002 | 0.910* | 0.011 | 0.021 | 1.04 | |

Water temperature | 19.32 | 0.23 | 1.952 | 0.688 | 0.387* | 0.453 | 3.451 | 0.44 | |

Solar radiation | 568.57 | 193.24 | 0.004 | 0.001 | 0.604* | 0.001 | 0.006 | 0.69 | |

Wind speed | 3.73 | 1.05 | −0.947 | 0.174 | −0.871* | −1.326 | −0.558 | −0.99 | |

Air temperature | 18.89 | 0.46 | −0.969 | 0.376 | −0.386* | −1.787 | −0.151 | −0.44 | |

MP2 Bottom | DO | 2.51 | 1.05 | ||||||

Constant | −5.773 | 1.723 | −9.446 | −2.100 | |||||

Chlorophyll a | 67.04 | 33.85 | 0.018 | 0.006 | 0.592* | 0.005 | 0.032 | 0.62 | |

BOD | 17.33 | 2.63 | 0.407 | 0.082 | 1.016* | 0.233 | 0.581 | 1.07 |

^{−1}) when there was a change of one standard deviation of a variable while the effects of all other variables were kept constant.

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**MDPI and ACS Style**

Pham, D.T.; Ho, L.; Espinoza-Palacios, J.; Arevalo-Durazno, M.; Van Echelpoel, W.; Goethals, P.
Generalised Linear Models for Prediction of Dissolved Oxygen in a Waste Stabilisation Pond. *Water* **2020**, *12*, 1930.
https://doi.org/10.3390/w12071930

**AMA Style**

Pham DT, Ho L, Espinoza-Palacios J, Arevalo-Durazno M, Van Echelpoel W, Goethals P.
Generalised Linear Models for Prediction of Dissolved Oxygen in a Waste Stabilisation Pond. *Water*. 2020; 12(7):1930.
https://doi.org/10.3390/w12071930

**Chicago/Turabian Style**

Pham, Duy Tan, Long Ho, Juan Espinoza-Palacios, Maria Arevalo-Durazno, Wout Van Echelpoel, and Peter Goethals.
2020. "Generalised Linear Models for Prediction of Dissolved Oxygen in a Waste Stabilisation Pond" *Water* 12, no. 7: 1930.
https://doi.org/10.3390/w12071930