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

: The aim of this study was to model, as well as monitor and assess the surface water quality in the Eastern Black Sea (EBS) Basin stream, Turkey. The water-quality indicators monitored monthly for the seven streams were water temperature (WT), pH, total dissolved solids (TDS), and electrical conductivity (EC), as well as luminescent dissolved oxygen (LDO) concentration and saturation. Based on an 18-month data monitoring, the surface water quality variation was spatially and temporally evaluated with reference to the Turkish Surface Water Quality Regulation. First, the teaching–learning based optimization (TLBO) algorithm and conventional regression analysis (CRA) were applied to three di ﬀ erent regression forms, i.e., exponential, power, and linear functions, to predict LDO concentrations. Then, the multivariate adaptive regression splines (MARS) method was employed and three performance measures, namely, mean absolute error (MAE), root means square error (RMSE), and Nash Sutcli ﬀ e coe ﬃ cient of e ﬃ ciency (NSCE) were used to evaluate the performances of the MARS, TLBO, and CRA methods. The monitoring results revealed that all streams showed the same trend in that lower WT values in the winter months resulted in higher LDO concentrations, while higher WT values in summer led to lower LDO concentrations. Similarly, autumn, which presented the higher TDS concentrations brought about higher EC values, while spring, which presented the lower TDS concentrations gave rise to lower EC values. It was concluded that the water quality of the streams in the EBS basin was high-quality water in terms of the parameters monitored in situ, of which the LDO concentration varied from 9.13 to 10.12 mg / L in summer and from 12.31 to 13.26 mg / L in winter. When the prediction accuracies of the three models were compared, it was seen that the MARS method provided more successful results than the other methods. The results of the TLBO and the CRA methods were very close to each other. The RMSE, MAE, and NSCE values were 0.2599 mg / L, 0.2125 mg / L, and 0.9645, respectively, for the best MARS model, while these values were 0.4167 mg / L, 0.3068 mg / L, and 0.9086, respectively, for the best TLBO and CRA models. In general, the LDO concentration could be successfully predicted using the MARS method with various input combinations of WT, EC, and pH variables.


Introduction
Water quality management plays the most important role in the control of surface water pollution and the planning of river basins. The possible pollution of clean water resources by industrial and The paper is structured into four sections. The information about the study area, modeling variables, the techniques used for modeling and the model development applications are introduced in the next section. Then, the water quality monitoring and LDO modeling results are presented in the third section. The summary and some conclusions are then made in the final section of the paper.

Study Area
There are 25 hydrological basins in Turkey. With a mean annual surface water potential of 16.46 × 10 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).

The Stream Gauging
There are a lot of stream gauging stations in the basin, however, many of which are not operational for various reasons. Therefore, it can be asserted that the coastal part of the Trabzon Province is poorly gauged. Nevertheless, there were seven stream gauging stations operated by the 22nd Regional Directorate of General Directorate of State Hydraulic Works in the study area. However, the flow rate data recorded from four stations-the Şerifli station on the Foldere Stream, the Öğütlü station on the Değirmendere Stream, the Taşdelen station on the Yomra Stream, and the

The Stream Gauging
There are a lot of stream gauging stations in the basin, however, many of which are not operational for various reasons. Therefore, it can be asserted that the coastal part of the Trabzon Province is poorly gauged. Nevertheless, there were seven stream gauging stations operated by the 22nd Regional Directorate of General Directorate of State Hydraulic Works in the study area. However, the flow rate data recorded from four stations-theŞerifli station on the Foldere Stream, the Ögütlü station on the Degirmendere Stream, the Taşdelen station on the Yomra Stream, and the Agnas station on the Karadere Stream, respectively, during the study period (March 2015-August 2016). The characteristics of these stations are given in Table 1 [28].

Stream Water Quality Monitoring
We employed two Hach HQ40d portable multi-parameter meters to monitor the stream DO concentration (mg/L) and saturation (%), pH and TDS (mg/L), and EC (µs/cm), simultaneously, since the Hach HQ40d portable multi-parameter meter had only two input channels for simultaneous measurement. The first one was equipped with the conductivity probe (CDC401) and a pH electrode (PHC101), and the second one was equipped with the Luminescent/Optical DO probe (LDO101). The stream WT could be measured by the LDO probe, as well as the pH electrode and the conductivity probe. The stream WT, pH, LDO concentration and saturation, TDS, and EC were automatically measured and recorded in situ for 15 min, at 30 s intervals. The final result was presented as the arithmetic mean of the 30 readings. All measurements were conducted monthly at seven monitoring stations during the study period (March 2015-August 2016).

Multivariate Adaptive Regression Splines (MARS) Method
The MARS method is a non-parametric, flexible, and rapid regression method, first presented by Freidman [49]. It does not presuppose the functional relationships between input and output variables used in modeling [50,51]. Instead, it attempts to determine the relationship between variables by dividing the data into subsets of data. With this process, the training data set was divided into linear segments called splines. The endpoints of these splines are called knots. Partial curves formed between the two knots are called basic functions [52]. This strategy made the MARS method more advantageous and flexible than the other statistical methods in multivariate modeling studies [53]. More details about the MARS and its implementation can be found in [54][55][56].

Teaching-Learning Based Optimization (TLBO) Algorithm
The TLBO algorithm is a meta-heuristic optimization algorithm developed by [57]. This algorithm is based on the phenomenon of teaching and learning. The TLBO algorithm has some advantages over other population algorithms. One of the most important advantages of the TLBO is that it does not require any parameters setting for the working of the algorithm, making the implementation of TLBO simpler [58]. More detailed information about the TLBO algorithm can be found in the literature [58][59][60].

Model Development Applications
The estimation and forecasting of the major parameters of surface waters are typically performed using various types of artificial intelligence-based techniques that rely on machine learning. This requires training, validation (the latter can be omitted if data are scarce) and test sets [61]. The process of separating data into training, validation, and test data sets can be done in a variety of ways. Csabragi et al. [61] evaluated the process of separating the data into training, validation, and test data sets under three headings. These are as follows-(i) random creation of the respective sets, (ii) assigning the majority of sampling points to the training set and a smaller proportion of sampling points to the test set, and (iii) assigning multiple initial years to the training set and a couple of final years to the test set. In this study, the data were divided into the training and test data sets, taking into account situation (ii). There were a total of 126 measurements, 90 of which were used for training (five streams) and the remaining measurements were reserved for testing (two streams). In this way, the method that gave the best results for the training dataset was tested for whether it gave good results for any stream in the EBS basin. Table 3 shows the division of streams as training and test groups. The general approach to choose a good training data set from the available data is to include all extreme data in the training data set [62]. The minimum (Min), mean, maximum (Max), and standard deviation (SD) values for the water-quality indicators, which were employed for the training and testing data sets, are given in Table 4. In the present study, different input combinations were established to determine the effect of the input variables on the LDO concentration. The input combinations created in the study were WT (Model 1); WT and EC (Model 2); WT and pH (Model 3); and WT, EC, and pH (Model 4), respectively. Following the input combination and modeling process, the MARS method was applied to identify the equations that produced the results closest to the measured LDO concentration, by using the Salford Predictive Modeler 8.0 software. Then, three different regression functions, i.e., exponential, power, and linear, were used for the TLBO and CRA methods, which were chosen to optimize the unknown coefficients (w i ) of the independent variables (x i ) [52]. The equations of exponential, power, and linear functions are given below; The optimization of the extreme values that can be found in the data set can be difficult. To facilitate optimization, minimize the impact of different dimensions, and achieve more effective results, all three input variables and the LDO were normalized using Equation (4) [63][64][65]. Different normalization formulas are also used in water quality modeling studies but there are no fixed rules as to which standardization approach should be used in particular circumstances [19,66]. In this study, "a" and "b" were taken as 0.8 and 0.1, respectively.
In the prediction of the LDO concentration, the aim was to determine the best model for obtaining the monitored values. In this context, three performance measures, i.e., root mean square error (RMSE), mean absolute error (MAE), and Nash Sutcliffe coefficient of efficiency (NSCE), were selected to assess the fitting accuracy and predictability of the MARS, TLBO, and CRA methods. The models with the highest NSCE values, as well as the lowest RMSE and MAE values had more accurate estimates than the other models [67,68]. The RMSE, MAE, and NSCE were calculated as follows: where t i is the monitored value, 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).

Stream Water-Quality Assessment
The legal documents related to water quality or water pollution in Turkey are published and amended from time to time, such as Turkish Water Pollution Control Regulation (TWPCR) [69], which Water 2020, 12, 1041 8 of 23 comprises quality classifications and are intended for the purposes of aquatic environments. It was published in the official gazette dated 31 December 2004 and numbered 25687. The Article 7, i.e., the intra-continental water resources classification, in the TWPCR [69] was employed by Turkish researchers, who engaged in surface water quality [24,70,71], for a long time. However, Turkish Superficial Water Quality Management Regulation (TSWQMR) was published in the official gazette dated 30 November 2012 and numbered 28483. Several articles, including Article 7, were repealed from the TWPCR [69] based on the Article 21 in the TSWQMR [72]. Moreover, a regulation about the first amendment for the TSWQMR [72] was published in the official gazette dated 15 April 2015, number 29327, and the name of the above-mentioned regulation was amended as Turkish Surface Water Quality Regulation [73]. The second amendment for the TSWQMR [72] was also published in the official gazette dated 10 August 2016, number 29797 [74]. Table 5 shows the upper threshold values [69,72,73,75] in terms of the monitored water-quality indicators.  [73], and Article 7 from TSWQR [75], respectively, for the intra-continental surface water resources classification.

Water-Quality Indicators
Water Quality Classes, TWPCR [69] Water Quality Classes, TSWQMR [72] I II  III  IV  I  II  III  IV WT, • C 25
Taking into account a one-year period from March 2015 to February 2016 and a one-year period from September 2015 to August 2016, Table 6 gives the basic statistics of the water-quality indicators monitored for the surface waters from the EBS basin streams, namely the Foldere (S1), Kalenima (S2), Degirmendere (S3), Yomra (S4), Karadere (S5), Manahoz (S6), and Solaklı (S7), respectively. The Pearson correlation coefficients shown in a half matrix (Table 7) were the results of statistical analyses for the expected relationships between the same water-quality indicators monitored for each stream.  The flow rates from the stream gauging stations are presented in the form of time series in Figure  2. Considering the daily mean values for the days when the stream water monitoring was conducted, the flow rates for each stream fluctuated as follows: 0.275 to 17.900 m 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). Taking into account drainage area for each stream gauging station, the flow rate per unit area was calculated as 29.6 L/s/km 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.

Water Temperature
As would be expected, the maximum and minimum values of the stream WT were measured on 1 August 2015, and 3 January 2016, respectively, for each stream, and the vast majority of the stream WT measurements fell within the range of 5.00 to 25.00 °C, throughout the monitoring. On a stream basis, the Solaklı had a relatively lower WT of 12.55 °C, while the Kalenima had a relatively higher WT of 14.67 °C, considering the annual mean values for the last 12 months from September 2015 to August 2016 (Table 6).
On comparing the average air temperature data records between 1981 and 2010 in the weather station (39°45'40" E and 40°59'55" N) of the Turkish State Meteorological Service in the Trabzon Province, the seasonal trend can be given in increasing order, as follows [27]: 7.87 °C in winter < 12.03 °C in spring < 16.40 °C in autumn < 21.43 °C in summer On a seasonal basis, the same order was being expected as a matter of course for each stream because the temperature of surface waters is naturally determined according to the climate. As would be expected, all streams showed the same trend in that winter presented the coldest stream WT ranging from 6.33 to 7. 53 (Table 6).
On comparing the average air temperature data records between 1981 and 2010 in the weather station (39 • 45'40" E and 40 • 59'55" N) of the Turkish State Meteorological Service in the Trabzon Province, the seasonal trend can be given in increasing order, as follows [27]: 7.87 • C in winter < 12.03 • C in spring < 16.40 • C in autumn < 21.43 • C in summer On a seasonal basis, the same order was being expected as a matter of course for each stream because the temperature of surface waters is naturally determined according to the climate. As would be expected, all streams showed the same trend in that winter presented the coldest stream WT ranging from 6.33 to 7.53 • C, while summer presented the warmest WT values, ranging from 17.98 to 20.49 • C. Interstational correlation coefficients from 0.913 to 0.992 (Table 7) revealed the aforementioned trend.
Based on semimonthly stream WT data records from January 2014 to December 2014, Satilmis [76] reported the seasonal trend for the Degirmendere Stream, in increasing order, as follows: 9.60 • C in winter < 14.24 • C in spring < 16.03 • C in autumn < 24.21 • C in summer In this study, the seasonal trend, which was the same as that reported by Satilmis [76], for the Degirmendere Stream, were as follows: 7.53 • C in winter < 9.50 • C in spring < 17.64 • C in autumn < 18.41 • C in summer No classification for the stream WT was available in the TSWQR [75] but a classification was available in the TSWQR [73]. Based on the annual mean values from 12.70 to 14.72 • C for the first 12 months, and from 12.55 to 14.67 • C for the last 12 months, the waters of the EBS basin streams were classified as high quality [73]. Only for the Degirmendere Stream, where the annual mean values were calculated as 12.89 • C for the first 12 months and 13.27 • C for the last 12 months, Satilmis [76] reported a little higher values of WT, with an annual mean value of 16.02 • C and classified the Degirmendere Stream as high quality [73], too.

pH
The vast majority of the stream water pH measurements fell within the range of 7.50 to 9.00, and the values greater than 9.00 were rarely monitored. On a stream basis, Yomra had a relatively higher water pH of 8.53, while Manahoz had a relatively lower water pH of 8.11.
On a seasonal basis, there was no distinct trend in terms of water pH, contrary to the similar trends observed in the WTs, LDO concentrations, and conductivities of the EBS basin streams. Interstational correlation coefficients, which were rarely significant at the 0.01 level (Table 7), revealed this reality.
With reference to the pH range of 6.0-9.0 [75], the waters of the EBS basin streams were classified as high quality. Only for the Degirmendere Stream, where the annual mean values were calculated as 8.48 for the first 12 months and 8.39 for the last 12 months, Satilmis [76] reported similar values of pH, with an annual mean value of 8.35, and also classified the Degirmendere Stream as high quality, too.

Luminescent Dissolved Oxygen Concentration
The vast majority of the stream water LDO measurements fell within the range of 9.00 to 13.00 mg/L, throughout the study, and the values greater than 13.00 mg/L were only monitored on 3 January 2017, when the stream water measurements were in the range of 0.93 to 3.79 • C. On a stream basis, Karadere had a relatively higher LDO concentration of 11.19 mg/L, while Yomra had a relatively lower LDO concentration of 10.43 mg/L, based on the annual mean values for the first 12 months.
On a seasonal basis, all streams showed the same trend, in that, the winter presented the coldest stream temperatures brought about by higher LDO concentrations that varied from 12.31 to 13.26 mg/L, while the summer presented the warmest WT values, which gave rise to lower LDO concentrations that varied from 9.13 to 10.12 mg/L. Interstational correlation coefficients up to R = 0.968 (Table 7) revealed the aforementioned trend.
Based on semimonthly LDO data records from January 2014 to December 2014, Satilmis [76] reported the seasonal trend for the Degirmendere Stream, in increasing order, as follows: 8.68 mg/L in summer < 10.17 mg/L in autumn < 10.46 mg/L in spring < 11.19 mg/L in winter. In this study, the seasonal trend (which was the same as that reported by Satilmis [76]) for the Degirmendere Stream were as follows: 9.63 mg/L in summer < 10.55 mg/L in autumn < 12.03 mg/L in spring < 12.44 mg/L in winter. Based on the average LDO concentrations from 10.43 to 11.14 mg/L, the waters of the EBS basin streams were classified as high quality [75]. Only for the Degirmendere Stream, where the annual mean values were calculated to be 11.16 mg/L for the first 12 months and 11.16 mg/L for the last 12 months, Satilmis [76] reported a little lower concentration of LDO, with an annual mean value of 10.18 mg/L, and also classified the Degirmendere Stream as high quality.

Luminescent Dissolved Oxygen Saturation
The stream water LDO saturation values were generally greater than 100%. On a stream basis, Karadere had a relatively higher LDO saturation of 105.25%, while Yomra had a relatively lower LDO saturation of 100.18%, based on the annual mean values for the first 12 months.
As such in the stream water LDO concentration, there was no definite seasonal trend in the stream water LDO saturation, since higher values were monitored during summer for the Foldere, Yomra, and Manahoz streams, but during autumn values were monitored for the Kalenima, Degirmendere, Karadere, and Solaklı streams. Nevertheless, it was clear that the springtime LDO saturation values were relatively lower.
No classification for the stream water LDO saturation was available in the TSWQR [75] but a classification was available in the TSWQR [73]. Based on the annual mean values from 100.18% to 105.25% for the first 12 months and 101.71% to 106.92% for the last 12 months, the waters of the EBS basin streams could be classified as high quality [73]. Only for the Degirmendere Stream, where the annual mean values were calculated to be 103.91% for the first 12 months and 104.54% for the last 12 months, Satilmis [76] reported a little lower saturation of LDO, with an annual mean value of 101.42%, and also classified the Degirmendere Stream as high quality.

Total Dissolved Solids
The vast majority of the stream water TDS measurements were lower than 200 mg/L. On a stream basis, the Kalenima Stream had a higher TDS value of 157.21 mg/L, while the Manahoz Stream had a lower EC value of 54.67 mg/L, based on the annual mean values for the first 12 months. On a seasonal basis, all streams, except for the Kalenima and the Degirmendere, showed the same trend, in that, autumn presented higher TDS concentrations, while spring presented lower TDS concentrations. It was thought that lower TDS concentrations were due to higher flow rates. In other words, higher TDS concentrations were due to lower flow rates. The Pearson correlation analysis revealed that the stream TDS concentration was negatively but strongly correlated with the stream flow rate in the Degirmendere and the Yomra (R = −0.858 and −0.640, respectively). The stream TDS concentration was also negatively but moderately correlated with the stream flow rate in the Foldere and the Karadere (R = −0.606 and −0.430, respectively).
As stated by Bayram [11], no classification for TDS is available in the TSWQR [75]. No health-based guideline value is proposed for TDS nationally [77] and internationally [78,79], except for the US EPA [80], in which the allowable concentration is 500 mg/L.

Electrical Conductivity
The vast majority of the stream water EC measurements were lower than 400 µS/cm, which was only exceeded three times in the Kalenima Stream during the period August-October 2016 and one time during August 2016 in the Karadere Stream. As such, in the stream TDS concentration, the Kalenima Stream had a higher EC value of 265.25 µS/cm, while the Manahoz Stream had a lower EC value of 91.48 µS/cm, based on the annual mean values for the first 12 months. As in the stream TDS concentration, it was also thought that the lower EC values were due to higher flow rates. In other words, higher EC values were due to lower flow rates. The Pearson correlation analysis revealed that the stream EC value was negatively but strongly correlated with the stream flow rate in the Degirmendere and the Foldere (R = −0.831 and −0.625, respectively). The stream EC value was also negatively but moderately correlated with the stream flow rate in the Yomra and the Karadere (R = −0.527 and −0.412, respectively).
On a seasonal basis, all streams showed the same trend, in that, autumns that presented higher TDS concentrations brought about higher EC values from 122.26 to 375.12 µS/cm, while springs that presented lower TDS concentrations gave rise to lower EC values from 60.66 to 200.39 µS/cm. Interstational correlation coefficients up to 0.964 (Table 7) revealed the aforementioned trend.
With reference to the upper threshold value of 400 µS/cm for EC [75], the waters of the EBS basin streams were classified as high quality. Moreover, the permissible EC value was 2500 µS/cm at 20 • C, according to TS 266 [77]. The whole measurement results were well below the threshold value. Only for the Degirmendere Stream, where the annual mean values were calculated as 172.40 µS/cm for the first 12 months and 174.44 µS/cm for the last 12 months, Satilmis [76] reported similar conductivity values, with an annual mean SC value of 212.26 µS/cm, corresponding to an EC value of 176.53 µS/cm, calculated by using the stream WT and SC data, and also classified the Degirmendere Stream as high quality.

MARS Modeling Results
In this part of the study, a model developed with training data using the stream WT, EC, and pH as the inputs, and the stream LDO concentration as the output. The data from the streams Degirmendere and Manahoz were used to test the developed model. When modeling with the MARS method, it should be noted that the model was influenced by various parameters such as the number of basic functions, the maximum degree of self-interaction, and penalty per knot, etc. These parameters were determined by trial and error. The predicted coefficients and basic functions for the best model were recorded and presented in Table 8 for all models.  The MARS models predicting the LDO concentration involved a total of 21 basic functions for the first one, 23 basic functions for the second one, 15 basic functions for the third one, and 17 basic functions for the last one. The MARS equation for the LDO concentration, which was a function of WT, EC, and pH, could be generated considering Table 8.

TLBO Algorithm and CRA Modeling Results
In this part of the study, the aim was to predict the LDO concentration by employing the TLBO and CRA methods, for all input combinations. Exponential, power, and linear functions were used as a regression function for each method. The best-fit coefficients of the regression functions obtained by the TLBO and CRA methods are given in Table 9, in which the coefficients obtained by each method were very close to each other. Table 9. Coefficients obtained from the teaching-learning based optimization (TLBO) and conventional regression analysis (CRA) methods. The ability of the MARS method to predict LDO concentration was evaluated by comparing the results of the MARS model with those of the TLBO and CRA methods. The comparisons were made using the RMSE, MAE, and NSCE criteria given in Table 10.

Methods Functions Coefficients
As seen in Table 10, the best results for both the training and testing data sets were obtained from the MARS method, for all models. In other words, the MARS method yielded the least RMSE and highest NSCE values for all models, and the least MAE values for the Models 3 and 4. The best results for each data set were also obtained from Model 4. The results showed that the accuracy of predictions increases with the addition of independent variables. For the TLBO and CRA methods, the exponential function provided the best results despite the fact that the lowest error values were obtained from the MARS method for all models. Moreover, when the TLBO and CRA methods were compared, it was seen that the results for each method were very close to each other. Contrary to the initial expectations, it was seen that the employment of the stream EC, together with the stream WT as an input variable was of no use, considering that the performance measure values were close to each other for Models 1 and 2.
From the performance measures, the RMSE and MAE values for the MARS method ranged from 0.2599 to 0.4123 mg/L and 0.2125 to 0.3069 mg/L, respectively, for training and 0.2709 to 0.3718 mg/L and 0.2126 to 0.2844 mg/L, respectively, during testing, as seen in Table 10. The NSCE values ranged from 0.9106 to 0.9645 for training and 0.9033 to 0.9487 for testing. These values meant that the performance of the MARS method was satisfactory. The MARS model with three inputs had the best accuracy in the training and testing periods. In the training data set, the RMSE values for Model 4 were approximately 37% lower than the Models 1 and 2, and approximately 24% lower than Model 3, for the MARS method. Generally, the addition of the EC and pH variables as input variables increased the accuracy of predictions for each method. In particular, the contribution of pH to model performance was greater than that of EC. For the training set, the most suitable results for each model are presented in the form of time-series in Figure 3, in which the stream LDO concentrations modeled by the MARS method are shown as compared to the monitored concentrations.
were approximately 37% lower than the Models 1 and 2, and approximately 24% lower than Model 3, for the MARS method. Generally, the addition of the EC and pH variables as input variables increased the accuracy of predictions for each method. In particular, the contribution of pH to model performance was greater than that of EC. For the training set, the most suitable results for each model are presented in the form of time-series in Figure 3, in which the stream LDO concentrations modeled by the MARS method are shown as compared to the monitored concentrations. For the testing set, the most suitable results for each model are presented in the form of time series and scatter plots in Figure 4, in which the stream LDO concentrations modeled by the MARS method are shown, as compared to the monitored concentrations.  For the testing set, the most suitable results for each model are presented in the form of time series and scatter plots in Figure 4, in which the stream LDO concentrations modeled by the MARS method are shown, as compared to the monitored concentrations. Figures 3 and 4 show that the stream LDO concentrations modeled by the MARS method for both the training and testing data sets were almost the same as the monitored concentrations. Especially Model 4 gave very satisfactory results at maximum values and minimum values. Additionally, the goodness-of-fit of MARS was evaluated employing R 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. Water 2020, 12, x FOR PEER REVIEW 4 of 23 Additionally, the goodness-of-fit of MARS was evaluated employing R 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

Conclusions
This study consists of two parts. The first, is the monitoring and assessment of the stream water quality in the Eastern Black Sea (EBS) Basin, Turkey, in terms of six water-quality indicators, i.e., water temperature (WT), pH, total dissolved solids (TDS), and electrical conductivity (EC), as well as luminescent dissolved oxygen (LDO) concentration and saturation. The second one is the spatial forecasting of the stream LDO concentration employing different methods, i.e., multivariate adaptive regression splines (MARS), teaching-learning based optimization (TLBO) algorithm, and conventional regression analysis (CRA), and for different regression functions, i.e., exponential, power, and linear, with different input combination, i.e., WT (Model 1); WT and EC (Model 2); WT and pH (Model 3); WT, EC, and pH (Model 4). In consequence of the monitoring and modeling studies, the following conclusions come into prominence: • 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.

•
Based on 18-month observations, the waters of the EBS basin streams were classified as high quality, in terms of the monitored water-quality indicators, with reference to the national regulations, being in force in TSWQR [75] and repealed in TSWQR [73].

•
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.

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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.

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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.