Generalised Linear Models for Prediction of Dissolved Oxygen in a Waste Stabilisation Pond
Abstract
:1. Introduction
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
2.5. Model Parameters and Their Importance
3. Results
3.1. Variability of Physicochemical and Biological Parameters and Climatic Conditions in the Ponds
3.2. Optimal Models for Prediction of Dissolved Oxygen in the Ponds
3.3. Importance of the Predictor Variables
4. Discussion
4.1. Variability of the Physicochemical and Biological Parameters and Climatic Conditions in the Ponds
4.2. Model Comparison
4.3. Predictive Accuracy of the Optimal Models
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
References
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Pond | Training Dataset | Validation Dataset | Full Optimal Model | MAE ± sd (mg L−1) | SMAPE ± sd (%) | R2 | ||
---|---|---|---|---|---|---|---|---|
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 |
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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
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 StylePham, 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