# Spatial Forecasting of Dissolved Oxygen Concentration in the Eastern Black Sea Basin, Turkey

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area

^{9}m

^{3}in 2016 [25], the EBS basin is of prime importance, in comparison with a mean annual groundwater potential of 0.49 × 10

^{9}m

^{3}in 2016. The EBS basin comprises the provinces Ordu, Giresun, Trabzon, and Rize, respectively, along the Southeastern Black Sea coast. The Trabzon Province with a total population of 779,379, according to the 2016 census [26] is the biggest city in the basin. There are a lot of streams draining the major agricultural, urban, and industrial areas of the Trabzon Province, where sanitary sewage systems serve 623,503 people, according to the municipal wastewater statistics survey in 2016 [27]. About 73.966 × 10

^{6}m

^{3}per year of wastewater are generated, 3.111 × 10

^{6}m

^{3}of which discharge through the streams to the Black Sea [27]. As a result of this discharge, the stream water quality might be affected negatively. For this reason, the streams that are vital for the province, where the groundwater potential is insignificant, were selected for the water quality monitoring. Considering the modeling studies at a later stage, it was also decided to monitor seven streams, three of which were to the west and three of which were to the east, with reference to the Yomra Stream located in the middle part of the province. In this way, it was possible to represent the study area completely. The streams monitored from west to east were the Foldere, Kalenima, Değirmendere, Yomra, Karadere, Manahoz, and Solaklı, respectively. One monitoring station, where the stream discharges into the Black Sea, was selected for each stream along the coast of Trabzon Province in the basin (Figure 1).

#### 2.2. The Stream Gauging

#### 2.3. Stream Water Quality Monitoring

#### 2.4. Modeling Variables

_{2}

^{−}), nitrate ion (NO

_{3}

^{−}), ammonium ion (NH

_{4}

^{+}), phosphate ion (PO

_{4}

^{3−}), total phosphorus (TP), chemical oxygen demand (COD), sulfate ion (SO

_{4}

^{2−}), sodium ion (Na

^{+}), potassium ion (K

^{+}), calcium ion (Ca

^{2+}), chloride ion (Cl

^{−}), and biochemical oxygen demand (BOD). Taking into account the literature review [29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48], the WT, the EC, and the pH (which are most effective in modeling studies) were selected as the independent variables.

#### 2.5. Multivariate Adaptive Regression Splines (MARS) Method

#### 2.6. Teaching–Learning Based Optimization (TLBO) Algorithm

#### 2.7. Model Development Applications

_{i}) of the independent variables (x

_{i}) [52]. The equations of exponential, power, and linear functions are given below;

_{i}is the monitored value, $\overline{t}$ is the mean of monitored values, td

_{i}is the predicted value, and N is the total number of monitored values [52]. The TLBO algorithm parameters were used for the same values for all functions employed in the study. The number of iterations was 1000, the population size was 50, and the unknown coefficients in the regression equations were used in the range (−5, 5).

## 3. Results and Discussion

#### 3.1. Stream Water-Quality Assessment

#### 3.1.1. Flow Rate

^{3}/s for the Şerifli (Foldere Stream), 2.170 to 42.300 m

^{3}/s for the Öğütlü (Değirmendere Stream), 0.242 to 10.600 m

^{3}/s for the Taşdelen (Yomra Stream), 1.840 to 40.800 m

^{3}/s for the Ağnas (Karadere Stream).

^{2}for the Foldere, 23.2 L/s/km

^{2}for the Değirmendere, 35.4 L/s/km

^{2}for the Yomra, and 23.4 L/s/km

^{2}for the Karadere.

#### 3.1.2. Water Temperature

#### 3.1.3. pH

#### 3.1.4. Luminescent Dissolved Oxygen Concentration

#### 3.1.5. Luminescent Dissolved Oxygen Saturation

#### 3.1.6. Total Dissolved Solids

#### 3.1.7. Electrical Conductivity

#### 3.2. Stream Water-Quality Modeling

#### 3.2.1. MARS Modeling Results

#### 3.2.2. TLBO Algorithm and CRA Modeling Results

#### 3.2.3. Comparison of the MARS, TLBO, and CRA Modeling Results

^{2}. As shown in Figure 4, there was a high correlation between the monitored and predicted values. The R

^{2}value in shown in Figure 4 is an indication of a good fit between the monitored and predicted values. This is an important point that demonstrates the success of the MARS method.

## 4. Conclusions

- On a seasonal basis, all streams showed the same trend in that the higher LDO concentrations were observed in the winter months with the coldest WT values, while the lower LDO concentrations appeared in the summer months with the warmest WT values. Interstational correlation coefficients up to R = 0.968 for the stream LDO concentrations and R = 0.992 for the stream WT values supported this trend.
- Autumns, which presented higher TDS concentrations brought about higher EC values, while springs, which presented the lower TDS concentrations gave rise to lower EC values. It was concluded that the higher TDS concentrations were due to the lower flow rates, by taking the negative but strong or moderate correlations into consideration.
- The MARS method produced much better results than the TLBO and CRA methods, for both training and testing the data sets for all models, especially for Model 4, which included all input variables.
- The LDO concentrations predicted by the MARS method were almost near the LDO concentrations measured by a portable field meter. It was concluded that the DO concentration could be successfully predicted by the MARS method in any stream, where WT, pH, and EC, or SC were measured but the DO concentration was not monitored, in case of similar watershed characteristics with the studied streams.
- In the TLBO and CRA methods, lower RMSE and MAE, as well as higher NSCE values were obtained by an exponential function for all models. The LDO concentrations predicted by the TLBO method were almost near the LDO concentrations predicted by the CRA method, that is, the TLBO method could not perform any improvement compared to the CRA method.
- It was concluded that the involvement of the pH variable, which is a parameter commonly used for modeling the DO concentration, the independent variables significantly increased the prediction performance.
- Although the history of the MARS method dates back to the pioneering work of Friedman [49], there is a limited availability of its application in the modeling of DO concentration [44,46]. Therefore, the use of this method is encouraged and recommended for studies related to water resources and environment since the proposed MARS method yielded successful results for this study.
- It is expected that the present study will make a significant contribution to the national literature as part of the stream water-quality monitoring and to the international literature as part of the stream water-quality modeling.
- This study will be continued for one and a half year follow up with a monthly frequency, due to limited economic opportunities. For temporal forecasting, a long-term study covering more frequent monitoring is strongly recommended.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The stream water-quality monitoring stations selected in the Eastern Black Sea Basin, Turkey.

**Figure 3.**The comparison of the monitored LDO concentrations with the modeled LDO concentrations, employing the MARS method for the training set.

**Figure 4.**The comparison of the monitored LDO concentrations with the modeled LDO concentrations by employing the MARS method for the testing set.

Stream | Gauging Station | Coordinates | Drainage Area (km^{2}) | Operating Altitude (m) | Gauging (2015–2016) |
---|---|---|---|---|---|

Foldere | Şerifli | 39°17’06’’ E – 41°00’59’’ N | 181.30 | 60 | Yes |

Kalenima | Doğanköy | 39°28’10’’ E – 40°54’10’’ N | 129.40 | 410 | No |

Değirmendere | Öğütlü | 41°11’00’’ E – 40°51’50’’ N | 728.40 | 160 | Yes |

Yomra | Taşdelen | 39°51’23’’ E – 40°51’14’’ N | 68.85 | 385 | Yes |

Karadere | Ağnas | 40°00’25’’ E – 40°50’58’’ N | 635.70 | 78 | Yes |

Manahoz | Ortaköy | 40°07’00’’ E – 40°51’00’’ N | 174.00 | 150 | No |

Solaklı | Ulucami | 40°15’20’’ E – 40°45’00’’ N | 576.80 | 275 | No |

**Table 2.**The input variables (highlighted cells having asterisk sign) used for dissolved oxygen (DO) modeling in previous studies.

Author(s) | Year | Reference Number | Input Variables | |||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Q | WT | pH | EC | SC | WD | TS | TA | WH | AT | NO_{2}^{−} | NO_{3}^{−} | NH_{4}^{+} | PO_{4}^{3−} | TP | COD | SO_{4}^{2−} | Na^{+} | K^{+} | Ca^{2+} | Cl^{−} | BOD | |||

Diamantopoulou et al. | 2007 | [29] | * | * | * | * | * | * | * | * | * | |||||||||||||

Chen and Li | 2008 | [30] | * | * | * | |||||||||||||||||||

Singh et al. | 2009 | [31] | * | * | * | * | * | * | * | * | * | * | * | |||||||||||

Ay and Kisi | 2011 | [32] | * | * | * | * | ||||||||||||||||||

Wen et al. | 2013 | [33] | * | * | * | * | * | * | * | * | ||||||||||||||

Antanasijevic et al. | 2013 | [34] | * | * | * | * | ||||||||||||||||||

Kisi et al. | 2013 | [35] | * | * | * | * | ||||||||||||||||||

Heddam | 2014 | [36] | * | * | * | * | ||||||||||||||||||

Evrendilek and Karakaya | 2014 | [37] | * | * | * | * | ||||||||||||||||||

Heddam | 2014 | [38] | * | * | * | * | ||||||||||||||||||

Heddam | 2014 | [39] | * | * | * | * | ||||||||||||||||||

Nemati et al. | 2015 | [40] | * | * | * | * | * | * | * | * | ||||||||||||||

Bayram and Kankal | 2015 | [41] | * | * | ||||||||||||||||||||

Kanda et al. | 2016 | [42] | * | * | * | * | ||||||||||||||||||

Olyaie et al. | 2017 | [43] | * | * | * | * | ||||||||||||||||||

Heddam and Kisi | 2018 | [44] | * | * | * | * | ||||||||||||||||||

Elkiran et al. | 2018 | [45] | * | * | * | |||||||||||||||||||

Yaseen et al. | 2018 | [46] | * | * | * | * | ||||||||||||||||||

Csabragi et al. | 2019 | [47] | * | * | * | * | ||||||||||||||||||

Kisi et al. | 2020 | [48] | * | * | * |

**Table 3.**The division of the Eastern Black Sea (EBS) Basin streams used in the luminescent dissolved oxygen (LDO) modeling.

Stream | Training Group | Testing Group |
---|---|---|

Foldere | ● | |

Kalenima | ● | |

Değirmendere | ▲ | |

Yomra | ● | |

Karadere | ● | |

Manahoz | ▲ | |

Solaklı | ● |

**Table 4.**Basic statistics for the water-quality indicators employed in the training and testing data sets.

Water-Quality Indicators | Training Data Set | Testing Data Set | ||||||
---|---|---|---|---|---|---|---|---|

Min | Mean | Max | SD | Min | Mean | Max | SD | |

LDO, mg/L | 8.25 | 10.89 | 15.08 | 1.38 | 8.98 | 11.08 | 13.97 | 1.20 |

WT, °C | 0.93 | 14.16 | 27.35 | 6.37 | 3.30 | 13.43 | 23.70 | 5.53 |

pH | 7.62 | 8.37 | 9.68 | 0.37 | 7.41 | 8.26 | 8.98 | 0.37 |

EC, µS/cm | 58.11 | 165.34 | 792.53 | 108.42 | 55.71 | 125.97 | 280.60 | 57.43 |

Water-Quality Indicators | Water Quality Classes, TWPCR [69] | Water Quality Classes, TSWQMR [72] | ||||||
---|---|---|---|---|---|---|---|---|

I | II | III | IV | I | II | III | IV | |

WT, °C | 25 | 25 | 30 | >30 | ≤25 | ≤25 | ≤30 | >30 |

pH | 6.5–8.5 | 6.5–8.5 | 6.0–9.0 | <6.0 to >9.0 | 6.5–8.5 | 6.5–8.5 | 6.0–9.0 | <6.0 to >9.0 |

DO, mg/L | 8 | 6 | 3 | <3 | >8 | 6–8 | 3–6 | <3 |

DO, % | 90 | 70 | 40 | <40 | 90 | 70–90 | 40–70 | <40 |

TDS, mg/L | 500 | 1500 | 5000 | >5000 | – | – | – | – |

EC, µS/cm | – | – | – | – | <400 | 400–1000 | 1001–3000 | >3000 |

Water-Quality | Water Quality Classes, TSWQR [73] | Water Quality Classes, TSWQR [75] | ||||||

Indicators | I | II | III | IV | I | II | III | IV |

WT, °C | ≤25 | ≤25 | ≤30 | >30 | – | – | – | – |

pH | 6.5–8.5 | 6.5–8.5 | 6.0–9.0 | <6.0 to >9.0 | 6–9 | 6–9 | 6–9 | 6–9 |

DO, mg/L | >8 | 6 | 3 | <3 | >8 | 6 | 3 | <3 |

DO, % | >90 | 70 | 40 | <40 | – | – | – | – |

TDS, mg/L | – | – | – | – | – | – | – | – |

EC, µS/cm | <400 | 1000 | 3000 | >3000 | <400 | 1000 | 3000 | >3000 |

**I**: High-quality water,

**II**: Slightly polluted water,

**III**: Polluted water, and

**IV**: Highly polluted water.

**Table 6.**Basic statistics of the water-quality indicators monitored in the Eastern Black Sea Basin streams, Turkey (S1: Foldere, S2: Kalenima, S3: Değirmendere, S4: Yomra, S5: Karadere, S6: Manahoz, and S7: Solaklı).

Stations | Water-Quality Indicators (One-year period from March 2015 to February 2016) [81] | |||||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

WT, °C | pH | LDO, mg/L | LDO Saturation, % | TDS, mg/L | EC, µS/cm | |||||||||||||||||||

Min | Mean | Max | SD | Min | Mean | Max | SD | Min | Mean | Max | SD | Min | Mean | Max | SD | Min | Mean | Max | SD | Min | Mean | Max | SD | |

S1 | 2.12 | 13.74 | 27.33 | 7.22 | 8.14 | 8.37 | 9.19 | 0.30 | 8.62 | 11.08 | 14.48 | 1.60 | 99.82 | 104.21 | 113.70 | 4.22 | 67.74 | 104.39 | 164.55 | 37.16 | 105.28 | 178.16 | 352.47 | 92.57 |

S2 | 0.93 | 14.58 | 27.03 | 7.68 | 8.31 | 8.56 | 9.12 | 0.26 | 9.03 | 10.89 | 14.45 | 1.49 | 97.63 | 104.79 | 130.76 | 9.52 | 108.65 | 157.21 | 211.67 | 38.81 | 168.03 | 265.25 | 424.53 | 98.00 |

S3 | 3.79 | 12.89 | 21.20 | 5.46 | 8.33 | 8.48 | 8.63 | 0.10 | 9.08 | 11.16 | 13.54 | 1.18 | 98.68 | 103.91 | 120.68 | 5.71 | 60.55 | 107.47 | 159.35 | 33.21 | 94.92 | 172.40 | 280.60 | 58.94 |

S4 | 3.14 | 14.72 | 26.05 | 7.09 | 8.09 | 8.54 | 9.50 | 0.40 | 8.25 | 10.43 | 13.53 | 1.60 | 97.46 | 100.18 | 102.79 | 1.84 | 50.11 | 78.56 | 134.68 | 25.06 | 87.21 | 136.03 | 268.93 | 61.75 |

S5 | 3.09 | 13.66 | 24.09 | 6.91 | 8.08 | 8.39 | 8.86 | 0.27 | 8.91 | 11.19 | 15.08 | 1.65 | 98.26 | 105.25 | 122.74 | 6.62 | 44.97 | 113.02 | 420.07 | 101.86 | 68.78 | 194.80 | 792.53 | 201.36 |

S6 | 3.30 | 13.45 | 23.70 | 6.64 | 7.74 | 8.21 | 8.98 | 0.40 | 8.98 | 11.16 | 13.97 | 1.38 | 98.74 | 104.79 | 117.93 | 5.57 | 36.03 | 54.67 | 82.58 | 14.72 | 55.71 | 91.48 | 157.87 | 34.82 |

S7 | 3.39 | 12.70 | 22.21 | 5.86 | 7.74 | 8.30 | 8.71 | 0.27 | 9.42 | 11.14 | 14.00 | 1.33 | 96.14 | 102.91 | 110.03 | 3.89 | 41.01 | 71.22 | 97.70 | 17.86 | 67.85 | 115.31 | 184.05 | 37.43 |

Stations | Water-Quality Indicators (One-year period from September 2015 to August 2016) | |||||||||||||||||||||||

WT, °C | pH | LDO, mg/L | LDO Saturation, % | TDS, mg/L | EC, µS/cm | |||||||||||||||||||

Min | Mean | Max | SD | Min | Mean | Mean | SD | Min | Mean | Max | SD | Min | Mean | Max | SD | Min | Mean | Max | SD | Min | Mean | Max | SD | |

S1 | 2.12 | 13.74 | 27.35 | 7.22 | 7.65 | 8.29 | 8.29 | 0.47 | 9.64 | 11.32 | 14.48 | 1.41 | 101.39 | 106.90 | 130.44 | 8.09 | 39.59 | 97.44 | 164.55 | 37.44 | 65.42 | 165.18 | 317.00 | 85.74 |

S2 | 0.93 | 14.67 | 26.81 | 7.72 | 7.94 | 8.49 | 8.49 | 0.32 | 8.84 | 11.01 | 14.45 | 1.47 | 99.97 | 105.95 | 130.76 | 8.56 | 50.70 | 149.90 | 211.67 | 46.08 | 83.43 | 253.67 | 424.53 | 104.53 |

S3 | 3.79 | 13.27 | 21.20 | 5.79 | 7.96 | 8.39 | 8.39 | 0.26 | 9.07 | 11.16 | 13.54 | 1.33 | 100.43 | 104.54 | 120.68 | 5.40 | 60.55 | 107.47 | 159.35 | 31.10 | 96.35 | 174.44 | 280.60 | 57.84 |

S4 | 3.14 | 14.48 | 26.05 | 7.06 | 7.69 | 8.56 | 8.56 | 0.59 | 8.25 | 10.65 | 13.53 | 1.58 | 99.39 | 101.71 | 102.89 | 1.79 | 56.63 | 75.16 | 134.68 | 23.38 | 87.21 | 128.90 | 268.93 | 56.61 |

S5 | 3.09 | 13.37 | 24.09 | 6.77 | 7.76 | 8.34 | 8.34 | 0.36 | 9.70 | 11.45 | 15.08 | 1.63 | 100.41 | 106.92 | 122.74 | 6.01 | 57.87 | 110.25 | 420.07 | 100.03 | 69.60 | 187.82 | 792.53 | 195.86 |

S6 | 3.30 | 13.14 | 22.53 | 6.39 | 7.41 | 7.98 | 7.98 | 0.39 | 8.98 | 11.27 | 13.97 | 1.44 | 100.91 | 104.93 | 115.03 | 4.23 | 39.83 | 55.40 | 82.58 | 14.98 | 56.76 | 91.94 | 157.87 | 34.14 |

S7 | 3.39 | 12.55 | 20.20 | 5.95 | 7.62 | 8.19 | 8.19 | 0.30 | 9.56 | 11.33 | 14.00 | 1.43 | 100.99 | 104.23 | 110.03 | 2.85 | 38.54 | 69.06 | 97.70 | 16.25 | 58.11 | 111.50 | 184.05 | 34.97 |

**Table 7.**Interstational correlation matrices for water-quality indicators monitored in the Eastern Black Sea Basin streams, Turkey (highlighted cells show the correlation being significant at the 0.01 level).

Stations | Water Temperature, °C | pH | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

S2 | S3 | S4 | S5 | S6 | S7 | S2 | S3 | S4 | S5 | S6 | S7 | |

S1 | 0.989 ^{b}0.000 | 0.944 ^{b}0.000 | 0.949 ^{b}0.000 | 0.922 ^{b}0.000 | 0.948 ^{b}0.000 | 0.913 ^{b}0.000 | 0.824 ^{b}0.000 | 0.219 0.383 | 0.300 0.227 | 0.309 0.211 | 0.725 ^{b}0.001 | 0.472 ^{a}0.048 |

S2 | 0.954 ^{b}0.000 | 0.970 ^{b}0.000 | 0.935 ^{b}0.000 | 0.951 ^{b}0.000 | 0.920 ^{b}0.000 | − | 0.003 0.990 | 0.584 ^{a}0.011 | 0.202 0.421 | 0.542 ^{a}0.020 | 0.346 0.159 | |

S3 | 0.961 ^{b}0.000 | 0.979 ^{b}0.000 | 0.980 ^{b}0.000 | 0.970 ^{b}0.000 | − | 0.121 0.633 | 0.550 ^{a}0.018 | 0.498 ^{a}0.035 | 0.556 ^{a}0.014 | |||

S4 | 0.971 ^{b}0.000 | 0.973 ^{b}0.000 | 0.935 ^{b}0.000 | 0.117 0.643 | 0.130 0.608 | 0.165 0.513 | ||||||

S5 | 0.992 ^{b}0.000 | 0.986 ^{b}0.000 | 0.432 0.074 | 0.758 ^{b}0.000 | ||||||||

S6 | 0.981 ^{b}0.000 | 0.500 ^{a}0.035 | ||||||||||

Stations | Luminescent dissolved oxygen, mg/L | Luminescent dissolved oxygen, % | ||||||||||

S2 | S3 | S4 | S5 | S6 | S7 | S2 | S3 | S4 | S5 | S6 | S7 | |

S1 | 0.935 ^{b}0.000 | 0.883 ^{b}0.000 | 0.933 ^{b}0.000 | 0.933 ^{b}0.000 | 0.911 ^{b}0.000 | 0.896 ^{b}0.000 | 0.588 ^{a}0.010 | 0.206 0.411 | 0.289 0.245 | 0.433 0.073 | 0.695 ^{b}0.001 | 0.689 ^{b}0.002 |

S2 | 0.894 ^{b}0.000 | 0.914 ^{b}0.000 | 0.885 ^{b}0.000 | 0.863 ^{b}0.000 | 0.837 ^{b}0.000 | 0.716 ^{b}0.001 | 0.312 0.208 | 0.441 0.067 | 0.612 ^{b}0.007 | 0.736 ^{b}0.000 | ||

S3 | 0.882 ^{b}0.000 | 0.922 ^{b}0.000 | 0.906 ^{b}0.000 | 0.937 ^{b}0.000 | 0.307 0.215 | 0.338 0.170 | 0.205 0.414 | 0.527 ^{a}0.025 | ||||

S4 | 0.891 ^{b}0.000 | 0.908 ^{b}0.000 | 0.873 ^{b}0.000 | 0.286 0.250 | 0.178 0.480 | 0.428 0.077 | ||||||

S5 | 0.839 ^{b}0.000 | 0.967 ^{b}0.000 | 0.340 0.167 | 0.650 ^{b}0.004 | ||||||||

S6 | 0.968 ^{b}0.000 | 0.812 ^{b}0.000 | ||||||||||

Stations | Total dissolved solids, mg/L | Electrical conductivity, µS/cm | ||||||||||

S2 | S3 | S4 | S5 | S6 | S7 | S2 | S3 | S4 | S5 | S6 | S7 | |

S1 | 0.882 ^{b}0.000 | 0.670 ^{b}0.002 | 0.875 ^{b}0.000 | 0.595 ^{b}0.009 | 0.624 ^{b}0.006 | 0.610 ^{b}0.007 | 0.964 ^{b}0.000 | 0.791 ^{b}0.000 | 0.941 ^{b}0.000 | 0.658 ^{b}0.003 | 0.791 ^{b}0.000 | 0.765 ^{b}0.000 |

S2 | 0.755 ^{b}0.000 | 0.745 ^{b}0.000 | 0.405 0.095 | 0.435 0.071 | 0.579 ^{a}0.012 | 0.788 ^{b}0.000 | 0.887 ^{b}0.000 | 0.578 ^{a}0.012 | 0.672 ^{b}0.002 | 0.689 ^{b}0.002 | ||

S3 | 0.601 ^{b}0.008 | 0.536 ^{a}0.022 | 0.623 ^{b}0.006 | 0.910 ^{b}0.000 | 0.749 ^{b}0.000 | 0.707 ^{b}0.001 | 0.731 ^{b}0.001 | 0.907 ^{b}0.000 | ||||

S4 | 0.798 ^{b}0.000 | 0.767 ^{b}0.000 | 0.602 ^{b}0.008 | 0.816 ^{b}0.000 | 0.855 ^{b}0.000 | 0.762 ^{b}0.000 | ||||||

S5 | 0.741 ^{b}0.000 | 0.662 ^{b}0.003 | 0.777 ^{b}0.000 | 0.782 ^{b}0.000 | ||||||||

S6 | 0.740 ^{b}0.000 | 0.856 ^{b}0.000 |

^{a}correlation is significant at the 0.05 level (two-tailed);

^{b}correlation is significant at the 0.01 level (two-tailed).

**Table 8.**Basic functions and equations for the multivariate adaptive regression splines (MARS) models.

MARS Model 1 | MARS Model 2 | MARS Model 3 | MARS Model 4 | ||||
---|---|---|---|---|---|---|---|

Basic | Equations | Basic | Equations | Basic | Equations | Basic | Equations |

Functions | Functions | Functions | Functions | ||||

BF02 | max (0.501816 − WT) | BF02 | max (0.501816 − WT) | BF01 | max (WT − 0.501816) | BF01 | max (WT − 0.501816) |

BF03 | max (WT − 0.890111) | BF04 | max (0.315742 − WT) | BF02 | max (0.501816 − WT) | BF02 | max (0.501816 − WT) |

BF04 | max (0.890111 − WT) | BF06 | max (0.595661 − WT) | BF03 | max (pH − 0.724264) × BF01 | BF03 | max (pH − 0.724264) × BF01 |

BF06 | max (0.326452 − WT) | BF08 | max (0.463269 − WT) | BF05 | max (pH − 0.613074) × BF01 | BF04 | max (0.724264 − pH) × BF01 |

BF08 | max (0.595661 − WT) | BF10 | max (0.441271 − WT) | BF07 | max (pH − 0.500589) × BF02 | BF05 | max (pH − 0.613074) × BF01 |

BF09 | max (WT − 0.16559) | BF12 | max (0.762159 − WT) | BF09 | max (pH − 0.70212) × BF01 | BF07 | max (pH − 0.500589) × BF02 |

BF10 | max (0.16559 − WT) | BF13 | max (WT − 0.828759) | BF11 | max (pH − 0.538634) × BF01 | BF08 | max (0.500589 − pH) × BF02 |

BF11 | max (WT − 0.828759) | BF14 | max (0.828759 − WT) | BF12 | max (0.538634 − PH) × BF01 | BF09 | max (pH − 0.70212) × BF01 |

BF14 | max (0.79445 − WT) | BF16 | max (0.791625 − WT) | BF13 | max (pH − 0.590224) × BF01 | BF11 | max (pH − 0.538634) × BF01 |

BF16 | max (0.860646 − WT) | BF18 | max (0.677397 − WT) | BF15 | max (pH − 0.600353) × BF01 | BF13 | max (pH − 0.590224) × BF01 |

BF18 | max (0.801312 − WT) | BF19 | max (WT − 0.284057) | BF17 | max (WT − 0.321796) | BF15 | max (pH − 0.600353) × BF01 |

BF20 | max (0.791625 − WT) | BF20 | max (0.284057 − WT) | BF18 | max (0.321796 − WT) | BF17 | max (WT − 0.321796) |

BF22 | max (0.466095 − WT) | BF21 | max (WT − 0.374672) | BF19 | max (pH − 0.581743) × BF18 | BF18 | max (0.321796 − WT) |

BF24 | max (0.340767 − WT) | BF24 | max (0.650151 − WT) | BF20 | max (0.581743 − pH) × BF18 | BF19 | max (pH − 0.581743) × BF18 |

BF26 | max (0.671342 − WT) | BF26 | max (0.622906 − WT) | BF25 | max (pH − 0.175147) × BF17 | BF20 | max (0.581743 − pH) × BF18 |

BF28 | max (0.444299 − WT) | BF28 | max (0.694753 − WT) | BF21 | max (pH − 0.437102) × BF01 | ||

BF30 | max (0.431181 − WT) | BF30 | max (0.716347 − WT) | BF33 | max (pH − 0.551355) × BF01 | ||

BF34 | max (0.650151 − WT) | BF31 | max (WT − 0.417053) | ||||

BF36 | max (0.630575 − WT) | BF32 | max (0.417053 − WT) | ||||

BF38 | max (0.615439 − WT) | BF34 | max (0.340767 − WT) | ||||

BF40 | max (0.683451 − WT) | BF36 | max (0.55449 − WT) | ||||

BF38 | max (EC − 0.252423) | ||||||

BF39 | max (0.252423 − EC) | ||||||

LDO _{Model 1} = | 0.254679 + 0.0886742 × BF02 + 2.15867 × BF03 + 0.0444198 × BF04 + 0.165892 × BF06 + 0.0705814 × BF08 − 0.0450666 × BF09 − 0.0228572 × BF10 − 0.257149 × BF11 + 0.0483375 × BF14 + 0.0454513 × BF16 + 0.0475508 × BF18 + 0.0485729 × BF20 + 0.0990403 × BF22 + 0.148585 × BF24 + 0.0579245 × BF26 + 0.103979 × BF28 + 0.108156 × BF30 + 0.0612519 × BF34 + 0.0641136 × BF36 + 0.0669608 × BF38 + 0.0565882 × BF40 | ||||||

LDO _{Model 2} = | 0.284243 + 0.0871611 × BF02 + 0.161665 × BF04 + 0.0680995 × BF06 + 0.0992744 × BF08 + 0.104501 × BF10 + 0.0476524 × BF12 − 0.162201 × BF13 + 0.0423067 × BF14 + 0.0453071 × BF16 + 0.0542304 × BF18 − 0.0407528 × BF19 + 0.177219 × BF20 − 0.0414545 × BF21 + 0.0584495 × BF24 + 0.0628739 × BF26 + 0.0526291 × BF28 + 0.0508015 × BF30 − 0.0426374 × BF31 + 0.111746 × BF32 + 0.141249 × BF34 + 0.0754296 × BF36 + 0.0194781 × BF38 + 0.065239 × BF39 | ||||||

LDO _{Model 3} = | 0.433206 + 0.534022 × BF02 − 5.03225 × BF03 + 1.63042 × BF05 + 2.18339 × BF07 + 2.44452 × BF20 − 0.46187 × BF25 − 3.45894 × BF09 − 0.166635 × BF11 − 1.8866 × BF12 + 1.39271 × BF13 + 1.48764 × BF15 − 0.263369 × BF17 + 0.474985 × BF18 + 24.5231 × BF19 | ||||||

LDO _{Model 4} = | 0.31183 − 1.13213 × BF01 + 1.2448 × BF02 + 4.33683 × BF03+ 0.730011 × BF04 + 22.2679 × BF05 + 0.783317 × BF07 + 0.3346 × BF08 − 19.1624 × BF09 − 33.0927 × BF11 + 41.9666 × BF13 − 47.8018 × BF15 + 0.253183 × BF17 + 29.2467 × BF19 + 0.706642 × BF20 + 6.09 × BF21 + 19.8123 × BF23 | ||||||

**Table 9.**Coefficients obtained from the teaching–learning based optimization (TLBO) and conventional regression analysis (CRA) methods.

Models | Methods | Functions | Coefficients | ||||
---|---|---|---|---|---|---|---|

${\mathit{w}}_{\mathbf{0}}$ | ${\mathit{w}}_{\mathbf{1}}$ | ${\mathit{w}}_{\mathbf{2}}$ | ${\mathit{w}}_{\mathbf{3}}$ | ${\mathit{w}}_{\mathbf{4}}$ | |||

Model 1 | TLBO | ${y}_{EF={W}_{0}+exp\left({W}_{1}+{W}_{2}*WT\right)}$ | 0.0848 | 0.0683 | −2.6255 | ||

CRA | 0.0848 | 0.0683 | −2.6255 | ||||

TLBO | ${y}_{PF={W}_{0}*W{T}^{{W}_{1}}}$ | 0.2357 | −0.6627 | ||||

CRA | 0.2357 | −0.6627 | |||||

TLBO | ${y}_{LF={W}_{0}+{W}_{1}*WT}$ | 0.7912 | −0.7633 | ||||

CRA | 0.7912 | −0.7633 | |||||

Model 2 | TLBO | ${y}_{EF={W}_{0}+exp\left({W}_{1}+{W}_{2}*WT+{W}_{3}*EC\right)}$ | 0.0941 | 0.0844 | −2.6933 | −0.0895 | |

CRA | 0.0938 | 0.0841 | −2.6912 | −0.0883 | |||

TLBO | ${y}_{PF={W}_{0}*W{T}^{{W}_{1}}*E{C}^{{W}_{2}}}$ | 0.1681 | −0.6621 | −0.1991 | |||

CRA | 0.1681 | −0.6621 | −0.1991 | ||||

TLBO | ${y}_{LF={W}_{0}+{W}_{1}*WT+{W}_{2}*EC}$ | 0.7808 | −0.8414 | 0.2261 | |||

CRA | 0.7808 | −0.8414 | 0.2261 | ||||

Model 3 | TLBO | ${y}_{EF={W}_{0}+exp\left({W}_{1}+{W}_{2}*WT+{W}_{3}*pH\right)}$ | 0.0781 | 0.0362 | −2.5699 | 0.0697 | |

CRA | 0.0780 | 0.0360 | −2.5700 | −0.0700 | |||

TLBO | ${y}_{PF={W}_{0}*W{T}^{{W}_{1}}*p{H}^{{W}_{2}}}$ | 0.2210 | −0.6639 | −0.0711 | |||

CRA | 0.2210 | −0.6640 | −0.0710 | ||||

TLBO | ${y}_{PF={W}_{0}*W{T}^{{W}_{1}}*p{H}^{{W}_{2}}}$ | 0.7323 | −0.8097 | 0.1869 | |||

CRA | 0.7320 | −0.8100 | 0.1870 | ||||

Model 4 | TLBO | ${y}_{EF={W}_{0}+exp\left({W}_{1}+{W}_{2}*WT+{W}_{3}*EC+{W}_{4}*pH\right)}$ | 0.0886 | 0.0512 | −2.6432 | −0.0997 | 0.0747 |

CRA | 0.0886 | 0.0512 | 0.6432 | −0.0997 | 0.0747 | ||

TLBO | ${y}_{PF={W}_{0}*W{T}^{{W}_{1}}*E{C}^{{W}_{2}}*p{H}^{{W}_{3}}}$ | 0.1695 | −0.6606 | −0.2135 | 0.0351 | ||

CRA | 0.1695 | −0.6605 | 0.2135 | 0.0351 | |||

TLBO | ${y}_{LF={W}_{0}+{W}_{1}*WT+{W}_{2}*EC+{W}_{3}*pH}$ | 0.7365 | −0.8600 | 0.1737 | 0.1481 | ||

CRA | 0.7365 | −0.8600 | 0.1737 | 0.1481 |

**Table 10.**The comparison of the performance measures of the models and methods for the training and testing phases.

Models | Methods | Functions | Training | Testing | ||||
---|---|---|---|---|---|---|---|---|

RMSE | MAE | NSCE | RMSE | MAE | NSCE | |||

MARS | 0.4109 | 0.3056 | 0.9111 | 0.3718 | 0.2844 | 0.9033 | ||

TLBO | Exponential | 0.4177 | 0.3038 | 0.9082 | 0.3770 | 0.2834 | 0.9005 | |

TLBO | Power | 0.5736 | 0.4460 | 0.8269 | 0.4634 | 0.3840 | 0.8497 | |

Model 1 | TLBO | Linear | 0.5703 | 0.4042 | 0.8289 | 0.4418 | 0.3391 | 0.8634 |

CRA | Exponential | 0.4177 | 0.3038 | 0.9082 | 0.3770 | 0.2834 | 0.9005 | |

CRA | Power | 0.5736 | 0.4460 | 0.8269 | 0.4636 | 0.3843 | 0.8496 | |

CRA | Linear | 0.5703 | 0.4041 | 0.8289 | 0.4418 | 0.3391 | 0.8634 | |

MARS | 0.4123 | 0.3069 | 0.9106 | 0.3686 | 0.2813 | 0.9049 | ||

TLBO | Exponential | 0.4175 | 0.3051 | 0.9083 | 0.3747 | 0.2805 | 0.9017 | |

TLBO | Power | 0.5188 | 0.4110 | 0.8584 | 0.4362 | 0.3563 | 0.8668 | |

Model 2 | TLBO | Linear | 0.5387 | 0.3772 | 0.8473 | 0.4534 | 0.3316 | 0.8561 |

CRA | Exponential | 0.4175 | 0.3050 | 0.9083 | 0.3748 | 0.2805 | 0.9017 | |

CRA | Power | 0.5188 | 0.4110 | 0.8584 | 0.4362 | 0.3563 | 0.8669 | |

CRA | Linear | 0.5387 | 0.3771 | 0.8473 | 0.4535 | 0.3316 | 0.8560 | |

MARS | 0.3134 | 0.2475 | 0.9483 | 0.3382 | 0.2637 | 0.9199 | ||

TLBO | Exponential | 0.4170 | 0.3059 | 0.9085 | 0.3783 | 0.2884 | 0.8998 | |

TLBO | Power | 0.5684 | 0.4375 | 0.8300 | 0.4533 | 0.3774 | 0.8562 | |

Model 3 | TLBO | Linear | 0.5360 | 0.3862 | 0.8488 | 0.4397 | 0.3432 | 0.8647 |

CRA | Exponential | 0.4170 | 0.3060 | 0.9085 | 0.3787 | 0.2888 | 0.8996 | |

CRA | Power | 0.5684 | 0.4375 | 0.8300 | 0.4533 | 0.3773 | 0.8562 | |

CRA | Linear | 0.5361 | 0.3863 | 0.8488 | 0.4405 | 0.3434 | 0.8642 | |

MARS | 0.2599 | 0.2125 | 0.9645 | 0.2709 | 0.2126 | 0.9487 | ||

TLBO | Exponential | 0.4167 | 0.3068 | 0.9086 | 0.3753 | 0.2845 | 0.9014 | |

TLBO | Power | 0.5176 | 0.4135 | 0.8590 | 0.4322 | 0.3540 | 0.8693 | |

Model 4 | TLBO | Linear | 0.5180 | 0.3799 | 0.8588 | 0.4561 | 0.3609 | 0.8544 |

CRA | Exponential | 0.4167 | 0.3068 | 0.9086 | 0.3753 | 0.2845 | 0.9014 | |

CRA | Power | 0.5176 | 0.4135 | 0.8590 | 0.4322 | 0.3540 | 0.8693 | |

CRA | Linear | 0.5180 | 0.3799 | 0.8588 | 0.4561 | 0.3609 | 0.8544 |

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## Share and Cite

**MDPI and ACS Style**

Nacar, S.; Bayram, A.; Baki, O.T.; Kankal, M.; Aras, E.
Spatial Forecasting of Dissolved Oxygen Concentration in the Eastern Black Sea Basin, Turkey. *Water* **2020**, *12*, 1041.
https://doi.org/10.3390/w12041041

**AMA Style**

Nacar S, Bayram A, Baki OT, Kankal M, Aras E.
Spatial Forecasting of Dissolved Oxygen Concentration in the Eastern Black Sea Basin, Turkey. *Water*. 2020; 12(4):1041.
https://doi.org/10.3390/w12041041

**Chicago/Turabian Style**

Nacar, Sinan, Adem Bayram, Osman Tugrul Baki, Murat Kankal, and Egemen Aras.
2020. "Spatial Forecasting of Dissolved Oxygen Concentration in the Eastern Black Sea Basin, Turkey" *Water* 12, no. 4: 1041.
https://doi.org/10.3390/w12041041