# Generating Regional Models for Estimating the Peak Flows and Environmental Flows Magnitude for the Bulgarian-Greek Rhodope Mountain Range Torrential Watersheds

^{1}

^{2}

^{*}

## Abstract

**:**

_{env}) are of outmost importance in the context of hydraulic and hydrologic design. In this study, 25 watershed characteristics were linked with the aforementioned recurrence intervals, peak discharge values, as well as Q

_{env}for 15 pristine torrential watersheds with more than 10 years of streamflow records in the Rhodopi mountain range with a view to generating regional relationships for the assessment of discharge annual peaks and environmental flows regarding the ungauged torrential watersheds in the region. The Log-Pearson Type III probability distribution was fitted in the discharge annual peaks time series, so as to predict Q

_{25}, Q

_{50}, and Q

_{100}, whereas the Tennant method was utilised so as to estimate the environmental flows magnitude. Similarly, the Kolmogorov–Smirnov and the Anderson–Darling tests were performed to verify the distribution fitting. The Principal Components Analysis method reduced the explanatory variables number to 14, whilst the stepwise multiple regression analysis indicated that the exponential model is suitable for predicting the Q

_{25}, the power model best forecasted the Q

_{50}and Q

_{100}, whereas the linear model is appropriate for Q

_{env}prognosis. In addition, the reliability of the obtained regression models was evaluated by employing the R

^{2}, the Nash–Sutcliffe efficiency, and the Index of Agreement Statistical Criteria, which were found to range from 0.91–0.96, 0.88–0.95 and 0.97–0.99, respectively, thereby denoting very strong and accurate forecasts by the generated equations. Thus, the developed equations could successfully predict the peak discharge values and environmental flows within the region’s ungauged watersheds with the drainage size not exceeding 330 km

^{2}.

## 1. Introduction

_{env}), and a global review of the environmental flow assessment methodologies present status revealed the existence of around 207 different methods for computing Q

_{env}, which could be categorized into four groups (hydrological, hydraulic rating, habitat simulation, and holistic methodologies) [11]. Among the latter practices, hydrological methods, despite a few disadvantages, are generally considered to be the simplest, valid [12], and most inexpensive. Additionally, unlike other methods, hydrological methods do not require as much fieldwork [13] and they continue to be the most widely used approaches across the world [11].

_{env}estimation value, which is based on 12160/1999 mandate, is computed as the greatest value among 30% of the average daily flow during the summer months (June to August for Mediterranean Countries), 50% of the flow in September and 30 liters per second (l/s) [16]. Meanwhile, in Bulgaria, the Water Act 125 defines Q

_{env}as 10% of the mean multiannual run-off, albeit not less than the minimum average monthly water quantity with 95% availability at the point of each facility for regulating the flow or for water abstraction.

_{env}as well for the torrential watersheds of the Bulgarian–Greek Rhodope mountain range, whereas torrential watersheds are defined as those that vary from 0.1 to about 300 km

^{2}and are prone to generating flash floods and debris flows [17,18], although the torrential watershed size’s upper limit has been shown to be around 100 km

^{2}in other studies [19]. Since the watersheds spanning about 300 km

^{2}in the study area depict the torrential characteristics described by Kotoulas [17] and other researchers [20], a decision was taken to select it for generating regional peak flows and environmental flows models. Additionally, the regional model generation methodology involves four main steps: (a) dependent and explanatory variables calculation; (b) independent variables number reduction through the Principal Component Analysis (PCA) application; (c) the development of regional regression equations between the four dependent variables and the selected independent variables that emerge from the PCA analysis; and, (d) the generated equations evaluation through a set of statistical criteria.

_{env}. On the other hand, the Kolmogorov–Smirnov (K-S) and Anderson–Darling (A-D) tests were utilised for verifying the LP-III distribution fitting [23,24,25] and b) the Q

_{evn}value, which can be determined through the application of the Tennant [26] method. The latter method is probably the best-known hydrological method for environmental flow assessment [27], which was developed to determine the flow that is required for safeguarding the aquatic resources in both warmwater and coldwater streams, due to its ease of application, feasibility of getting results in the short term, and low cost.

_{env}assessment [35]. It is noteworthy that the aforementioned advantages have motivated the authors to select this approach for the regression model development in the area of study.

_{env}assessment introduced in the Rhodopi region through the assessment of four different types of regression models (linear, power, exponential, and the logarithmic models) in order to obtain the best model for estimating flood discharges. In contrast, most other studies [7,29,40,41] have only examined the power model. Additionally, these previous studies did not generate a regional model for Q

_{env}.

## 2. Study Area and Datasets Description

^{2}between longitudes 23°40′ E–26°40′ E and latitudes 40

^{o}50′ N–42°15′ N, out of which the 83% is located in Southern Bulgaria, and the remainder 17% in Northern Greece. They are characterised by high-mountainous relief in the western part and low-mountainous and hilly relief in the east/south varying from 0–2191 m with an average elevation of around 630 m. It is notable that the region climate is influenced by both the humid continental climate from the north and by the Mediterranean climate from the south. Furthermore, the average annual temperature varies from 5 to 10 °C in the western part to 13 °C in the eastern and southern parts, whereas the average annual precipitation ranges between 600–1100 mm [42]. The Rhodope Mountain Range is famous for the largest coniferous woods in the Balkans. It includes a number of Bulgarian and Greek Natura 2000 protected sites, whereas a significant part of Bulgaria’s hydropower resources are also located there.

^{3}/s, for a time period of at least 10 years of measurement, whereas Figure 1 shows the location of the measuring stations. Moreover, the discharge records were retrieved from hydrological directories that contain data for all gauging stations Bulgaria’s territories, mainly after 1950 [43].

^{3}/s (Yugovo gauge). Moreover, while seven gauging stations with drainage area ranging between 452–4947 km

^{2}are located in the area, these streams cannot be considered as torrential streams that typically vary from 0.1 to 100 km

^{2}[19] or about 300 km

^{2}, according to other studies [17,18]. For this reason, the latter watersheds were excluded from any further analysis.

_{env}regional models. To the best of the authors’ knowledge, among them, the length of the straight line from the source to gauging-station (L), the Total stream length (Tl), the circulatory ratio (Rc), the elongation ratio (Re), and the lemniscate ratio (R

_{l}) [44] have been considered for the first time for such purposes, whereas the remaining 20 characteristics have been used in previous regional flood frequency studies and they include the following: Drainage area (A) [1,7,41,45,46,47], Main-channel length (Ls) and Main channel slope (S), [1,7,41,46], Basin length (BL) [7,41,45], Mean basin slope (BS) [46,47], Mean basin elevation (E) [1,7,45,47], Basin Perimeter (B) [41], Mean basin width (BW), Form factor (Rf), Curve factor (Cr), or main-channel sinuosity, accounting the main rivers meandering, gaging-station latitude (GLT) and longitude (GLN) [7], Drainage density (D) [45,47], Compactness ratio (CR), Maximum basin elevation (E

_{max}), Minimum basin elevation (E

_{min}) and Relative basin relief (RH) [47], Basin Relief (H) [45], Basin centroid elevation (CE) [46], and gaging-station elevation (GE) [1].

^{2}, with basin perimeters from 17.8 to 107.9 km, whereas the main stream length was found to vary between 6 and 50.1 km. The average elevation of all watersheds is above 1000 m, with the average slope exceeding 20%. This, in turn, determines the steep slope of the main channels (from 15.6 to 120.5 m/km). Table 1 summarises the calculated watershed characteristics that were referred to in this study.

## 3. Materials and Methods

#### 3.1. Peak Flow and Environmental Flow Assessment

^{2}and D are calculated for the A-D and the K-S tests, respectively. In case the latter statistics are less than the critical value of each test at a chosen significance level, respectively, it can be inferred that the LP-III distribution is suitable for representing the annual daily maximum streamflow distribution in the study area [51]. Additionally, the Weibull plotting position method was only used to graphically illustrate the fitting between the observed and predicted LP-III distribution annual peak discharges [51].

#### 3.2. Peak Flow and Environmental Flow Regional Models’ Generation

_{i}denote the dependent variable, x

_{i}signifies the explanatory variables, a is constant, b

_{i}, b

_{2}... b

_{i}are the regression coefficients for each independent variable, and i represents the number of explanatory variables. While making use of appropriate mathematic transformation techniques, it is possible to shift the power, the exponential, and the logarithmic models into multiple linear models, and their explanatory coefficients values can be subsequently computed by applying stepwise multiple regression analysis [45,61]. Moreover, the latter MLR models can be retransformed to their original prediction equation form by using similar mathematic transformation techniques [1].

^{2}), the Root mean square error (RMSE), the prediction error (PE), or the Mean Absolute Percent Error (MAPE), the Nash–Sutcliffe efficiency (NSE), as well as the index of agreement (d), which have also been used in similar studies [40,41,62,63]. Meanwhile, the relevant equations are, respectively, expressed, as follows:

_{i}and P

_{i}are the measured and predicted values, respectively, of the under study variable at time i, $\overline{O}$ and $\overline{P}$ denote the mean values of the observed and predicted variable, whilst n signifies the number of records. The closest the values of the R

^{2}, NSE, and d to 1, the better the association between measured and predicted variables. On the other hand, an NSE value of lower than zero indicates that the mean value of the observed time series would have been a better predictor than the model [64]. Moreover, the closer the values of the RMSE and PE statistics are to zero, the better the model’s predictions fits the observations. Finally, the multiple regional models’ development was conducted through the use of IBM SPSS Version 23 software, whereas the computation of five statistical evaluation measurers was performed while utilising an online calculator tool [65].

## 4. Results and Discussion

#### 4.1. Peak Flow and Environmental Flow Computation

^{3}/year).

_{25}, Q

_{50}, and Q

_{100}values computed by the LP-III distribution differ a little. Meanwhile in similar studies, such as in the Minab river at Iran [66] or the Mahi river in India [49], a similar small difference has been observed, which could be attributed to the fact that the discharge might be dominated by groundwater flows or the rain shadow effect. The observed and the predicted LP-III distribution annual peak discharges for all cases were observed to be fairly close to most of the data points. For this reason, the predicted discharge values are likely to be quite reliable [49]. Figure 2 illustrates a reasonable fit between the observed and predicted LP-III distribution annual peak discharges for a random gauge, Velingrad. Moreover, the statistic values for the K-S and A-D goodness of fit tests were computed based on [50] guidelines, whilst the critical value at a 95% confidence level for the K-S test were found to range between 0.257 and 0.410, while the critical value was 2.502 for the A-D test. It can be inferred that the LP-III distribution is appropriate enough to represent the annual daily maximum streamflow distribution, since it can be seen from Table 3 that the maximum value of the K-S and the A-D statistics were calculated equal to 0.21 and 0.76 respectively, which is less than the aforementioned critical values.

_{env}assessment that was based on Tennant’s [26] method, the MAF for the 15 under study catchments were initially computed, whereas the river ecological condition corresponding to “Poor or minimum” habitat conditions was selected as the desired ecosystem condition for this study. Under the latter habitat condition, a 10% proportion of the MAF, which corresponds to a minimum river depth and minimum average flow velocity of 0.3 m must be 0.25 m/s, respectively [27], is allocated in the river during the entire year to sustain short-term aquatic life. The 10% percentage of the MAF that is necessary for maintaining the minimum ecosystem attributes constituted the Q

_{env}variable. Table 3 summarises the results that were derived from the application of this method. The Q

_{env}magnitude was found to range from 18.55 hm

^{3}/year for the Yugovo watershed to 0.61 hm

^{3}/year for the Dabnitsa watershed in order to maintain minimum habitat conditions in the study area. The latter values correspond to 50,811 and 1,665 m

^{3}/day, respectively.

#### 4.2. Hydrologic and Sediment Yield Modeling

_{25}. Q

_{50}, Q

_{100}, and Q

_{env}) with the 14 explanatory variables derived from the PCA analysis (B, L, Ls, BL, A, Tl, Emax, BW, S, E, BS, CE, GE, and Emin) for the four different model types were calculated through application of the stepwise multiple regression analysis, [40,46], which reduces the number of explanatory variables to those significant at the 95% confidence level [35]; Table 5 illustrates the relevant results, where it can be observed that that the linear models and logarithmic models exhibit the worst and the second worst prediction efficiency, respectively, for the peak discharge values prognosis concerning the selected recurrence intervals with low R

^{2}and high PE, in comparison to the power or exponential models. Although the power and exponential model yielded similar results for the Q

_{25}forecast in terms of the R

^{2}, RMSE, NSE, and d statistical measures, the exponential model was found to have a smaller PE value, and it should be selected for the discharge value with 25 years recurrence interval assessment. However, the power models clearly outperformed all other types of models for the Q

_{50}and Q

_{100}prediction, since they depicted not only the highest R

^{2}, d, and NSE values, but also the smaller PE and RMSE values. Finally, although the linear and power models illustrated the same fit for the Q

_{env}prediction, the linear model has a slightly better prediction than the power model, since it depicts larger NSE and d and smaller RMSE values.

_{25}and Q

_{100}prediction is also premised on the latter variables plus the drainage area (A). The length (L) of the main river course from the divide of the basin to the measuring station and the drainage area (A) has also been indicated in similar peak flow regression analysis studies, as determinant explanatory variables in order to compute peak discharge values for different return periods [7,32,41]. However, to the best of the authors’ knowledge, it is the first time that the gauge station elevation (GE) is found to be a significant determinant, despite having been assessed by [1]. Moreover, this research highlighted the total stream length (TI) as a determinant factor for environmental flow estimation that has not been assessed in similar regression analysis studies for environmental flows computation at ungauged basins [35,60].

^{2}, the NSE, and the d were found to range from 0.91–0.96, 0.88–0.95, and 0.97–0.99, respectively. Mimikou [40] also reported R

^{2}values that were equal to 0.96 and 0.98 for the maximum observed floodflows for the western and north western region of Greece, respectively, whereas Selvanathan et al. [46] developed regression equations that relate peak discharges to basin and climate characteristics with an accuracy reaching an R

^{2}values equal to 0.86 for certain regions of the U.S. El-Jabi and Caissie [69] developed regional models for mean, median, high, as well as low flows of different recurrence intervals in New Brunswick with high R

^{2}values ranging between 0.799 and 0.989. On the other hand, Zhang et al. [35] developed a regression equation for computing environmental flow with an adjusted R

^{2}value of 0.96. Moreover, the emerging equations for the Q

_{25}, Q

_{50}, Q

_{100}, and Q

_{env}projection in this study illustrate a prediction error (PE) between 24.20 and 39%, which is in alignment with the findings of similar studies, such as Topaloúlu [41], who reported PE values between 20.24–34.07 or Antonopoulos et al. [60], who found MAPE values that ranged between 23.8 and 43.8. Finally, since many regions of the world are experiencing more intense rainfall as well as more frequent flooding/drought with each passing decade due to global climate change methods such as this, it can be inferred that stationarity should only be used as a guideline.

## 5. Conclusions

_{env}magnitude was assessed by the Tennant method and it represented the model dependent variables.

_{env}. The exponential model was found most suitable for predicting Q

_{25}, the power model was deemed most feasible for forecasting Q

_{50}and Q

_{100}, whereas the linear model was found to prognose Q

_{env}in the best possible manner. Furthermore, four statistical evaluation measures revealed the emerged models’ high accuracy of the obtained models. The developed regional peak-flow and environmental flows models could be employed in an ungauged unregulated watershed within broader regions in the Rothope Mountain Range to calculate the peak discharge magnitude with 25, 50, and 100 year return periods, respectively and the Q

_{env}by determining the required watershed characteristics to apply the equations obtained. However, these watershed characteristics should be within the range of characteristics that were initially used to develop the regional models.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Table 1.**Morphometric and hydrographic characteristics for study watersheds that are commonly used in regional regression analysis.

Characteristics | Watershed Number | ||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | |

A (km^{2}) | 22.60 | 23.63 | 85.66 | 18.06 | 31.54 | 326.14 | 86.18 | 241.72 | 16.00 | 106.30 | 24.17 | 35.21 | 236.69 | 108.42 | 175.75 |

B (km) | 25.85 | 19.75 | 42.12 | 19.02 | 27.15 | 89.61 | 45.41 | 93.61 | 17.76 | 46.72 | 22.79 | 31.98 | 107.90 | 60.82 | 86.28 |

BL (km) | 8.78 | 7.34 | 11.18 | 5.03 | 7.23 | 23.16 | 16.5 | 30 | 5.5 | 17 | 8.2 | 13.37 | 42.07 | 20.94 | 8.9 |

BW (km) | 2.57 | 3.22 | 7.66 | 3.59 | 4.36 | 14.08 | 5.22 | 8.06 | 2.91 | 6.25 | 2.95 | 2.63 | 5.63 | 5.18 | 19.75 |

Ls (km) | 11.54 | 8.49 | 16.51 | 7.01 | 9.92 | 29.69 | 18.75 | 37.98 | 5.98 | 19.30 | 10.19 | 13.84 | 50.11 | 25.87 | 33.42 |

L (km) | 7.15 | 7.04 | 10.2 | 6.05 | 7.6 | 22.6 | 15.3 | 27.5 | 4.9 | 16.2 | 7.4 | 12.5 | 41.02 | 20 | 21.25 |

Tl (km) | 20.64 | 27.02 | 87.44 | 21.82 | 24.74 | 519.27 | 158.95 | 360.07 | 30.19 | 132.68 | 26.38 | 40.52 | 253.44 | 118.51 | 214.40 |

Rc (dimensionless) | 0.42 | 0.76 | 0.61 | 0.63 | 0.54 | 0.51 | 0.52 | 0.35 | 0.64 | 0.61 | 0.58 | 0.43 | 0.26 | 0.37 | 0.30 |

Re (dimensionless) | 0.61 | 0.75 | 0.93 | 0.95 | 0.88 | 0.88 | 0.64 | 0.58 | 0.82 | 0.68 | 0.68 | 0.50 | 0.41 | 0.56 | 1.68 |

Rf (dimensionless) | 0.29 | 0.44 | 0.69 | 0.71 | 0.60 | 0.61 | 0.32 | 0.27 | 0.53 | 0.37 | 0.36 | 0.20 | 0.13 | 0.25 | 2.22 |

Rl (dimensionless) | 0.85 | 0.57 | 0.36 | 0.35 | 0.41 | 0.41 | 0.79 | 0.93 | 0.47 | 0.68 | 0.70 | 1.27 | 1.87 | 1.01 | 0.11 |

Cr (dimensionless) | 1.61 | 1.21 | 1.62 | 1.16 | 1.30 | 1.31 | 1.23 | 1.38 | 1.22 | 1.19 | 1.38 | 1.11 | 1.22 | 1.29 | 1.57 |

D (km/km^{2}) | 0.91 | 1.14 | 1.02 | 1.21 | 0.78 | 1.59 | 1.84 | 1.49 | 1.89 | 1.25 | 1.09 | 1.15 | 1.07 | 1.09 | 1.22 |

CR (dimensionless) | 3.38 | 6.06 | 4.83 | 4.99 | 4.28 | 4.06 | 4.18 | 2.76 | 5.07 | 4.87 | 4.65 | 3.44 | 2.03 | 2.93 | 2.36 |

E (m) | 1645.0 | 1365.3 | 1703.9 | 1671.2 | 1638.2 | 1220.8 | 1158.1 | 1257.9 | 996.5 | 1299.4 | 1559.0 | 1031.5 | 1422.1 | 1513.9 | 1339.2 |

E_{max} (m) | 2021 | 1710 | 2102 | 1799 | 1951 | 1997 | 1822 | 2121 | 1348 | 1709 | 1932 | 1517 | 1915 | 1796 | 1636 |

E_{min} (m) | 1443 | 1012 | 1471 | 1517 | 1407 | 516 | 685 | 668 | 628 | 749 | 1254 | 490 | 1133 | 1208 | 1075 |

CE (m) | 1582 | 1347 | 1775 | 1603 | 1501 | 862 | 1214 | 1104 | 853 | 1132 | 1428 | 861 | 1248 | 1493 | 1402 |

H (m) | 578 | 698 | 631 | 282 | 544 | 1481 | 1137 | 1453 | 720 | 960 | 678 | 1027 | 782 | 588 | 561 |

RH (dimensionless) | 0.35 | 0.51 | 0.37 | 0.55 | 0.42 | 0.48 | 0.42 | 0.41 | 0.51 | 0.57 | 0.45 | 0.53 | 0.37 | 0.52 | 0.47 |

S (m/km) | 50.07 | 82.19 | 38.21 | 40.26 | 54.86 | 49.89 | 60.64 | 38.26 | 120.45 | 49.75 | 66.52 | 74.22 | 15.60 | 22.73 | 16.79 |

BS (%) | 25.54 | 26.51 | 22.63 | 21.28 | 26.26 | 45.13 | 38.67 | 39.04 | 49.07 | 32.60 | 29.66 | 27.83 | 25.66 | 24.35 | 27.23 |

GE (m) | 1460 | 1028 | 1491 | 1531 | 1421 | 533 | 689 | 677 | 636 | 762 | 1257 | 515 | 1134 | 1229 | 1079 |

GLT (decimal degrees) | 41.87 | 41.99 | 41.83 | 41.80 | 41.82 | 41.88 | 41.48 | 41.56 | 41.42 | 41.87 | 41.73 | 41.57 | 41.64 | 41.64 | 41.60 |

GLN (decimal degrees) | 23.93 | 23.84 | 24.13 | 24.07 | 24.17 | 24.81 | 24.85 | 24.87 | 24.98 | 23.62 | 23.90 | 23.83 | 24.16 | 24.23 | 24.18 |

**Table 2.**Recommended Q

_{env}magnitudes that must be allocated so as to maintain predefined ecosystem attributes.

Description of Flow | April–September | Octomber–Mach. |
---|---|---|

Flushing flow (from 48–96 hours) | 200% | |

Optimum range of flow | 60–100% | |

Outstanding habitat | 60% | 40% |

Excellent habitat | 50% | 30% |

Good habitat | 40% | 20% |

Fair or degrading habitat | 30% | 10% |

Poor or minimum habitat | 10% | |

Severe degradation | <10% |

**Table 3.**Estimated discharges in m

^{3}/sec based on LP-III distribution, LP-III goodness of fit tests, and Q

_{env}magnitude in hm

^{3}/year.

S.No. | Station | Q_{25} | Q_{50} | Q_{100} | K-S Statistic | A-D Statistic | Q_{env} |
---|---|---|---|---|---|---|---|

1 | Chehliovo | 11.72 | 16.43 | 22.70 | 0.14 | 0.36 | 1.15 |

2 | Tsvetino | 19.00 | 21.27 | 23.29 | 0.16 | 0.28 | 2.13 |

3 | Devinska | 4.03 | 4.07 | 4.10 | 0.13 | 0.76 | 2.94 |

4 | Sarayar | 4.99 | 5.37 | 5.71 | 0.12 | 0.26 | 1.16 |

5 | Toplika | 7.62 | 8.19 | 8.66 | 0.11 | 0.34 | 1.22 |

6 | Yugovo | 271.02 | 331.80 | 397.53 | 0.13 | 0.48 | 18.55 |

7 | Rudozem | 137.79 | 178.58 | 228.28 | 0.05 | 0.21 | 8.04 |

8 | Taran | 179.54 | 200.37 | 220.55 | 0.11 | 0.24 | 14.94 |

9 | Erma_reka | 59.57 | 61.12 | 62.10 | 0.06 | 0.13 | 1.32 |

10 | Eleshnitsa | 74.64 | 102.84 | 138.11 | 0.06 | 0.19 | 2.27 |

11 | Beslet | 29.72 | 35.99 | 42.68 | 0.10 | 0.49 | 2.74 |

12 | Dabnitsa | 143.69 | 367.19 | 889.06 | 0.21 | 0.41 | 0.61 |

13 | Dospat | 77.66 | 79.01 | 79.63 | 0.09 | 0.25 | 11.08 |

14 | Zmeitsa | 49.18 | 67.30 | 92.02 | 0.16 | 0.50 | 5.72 |

15 | Barutin | 50.28 | 55.25 | 60.09 | 0.14 | 0.33 | 9.15 |

B | L | Ls | BL | A | Tl | Emax | BW | S | Rc | E | BS | CE | GE | Emin | GLN | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

PC1 | 0.96 | 0.95 | 0.95 | 0.94 | 0.94 | 0.93 | 0.89 | 0.88 | −0.76 | −0.68 | ||||||

PC2 | 0.92 | −0.90 | 0.85 | 0.83 | 0.82 | −0.67 |

Equations | R^{2} | RMSE | PE (%) | NSE | d | |
---|---|---|---|---|---|---|

Q_{25} | $=150.338+0.295\cdot TI-0.114\cdot E\mathrm{min}$ | 0.91 | 22.85 | 83.80 | 0.91 | 0.98 |

$={10}^{8.246}\cdot G{E}^{-2.545}\cdot {L}^{0.860}$ | 0.96 | 18.32 | 31.50 | 0.94 | 0.99 | |

$={\mathit{e}}^{\mathbf{5.933}}\cdot {\mathit{e}}^{-\mathbf{0.003}\cdot \mathit{G}\mathit{E}}\cdot {\mathit{e}}^{\mathbf{0.047}\cdot \mathit{L}}$ | 0.95 | 19.10 | 24.20 | 0.93 | 0.98 | |

$\begin{array}{l}=-285-318.3\cdot LnGE+432.2\cdot LnE\mathrm{max}\\ -117.6\cdot LnS-88.3\cdot LnLS\end{array}$ | 0.97 | 13.79 | 51.90 | 0.97 | 0.99 | |

Q_{50} | $=368.056-0.261\cdot E\mathrm{min}$ | 0.68 | 64.10 | 147.80 | 0.68 | 0.89 |

$={\mathbf{10}}^{\mathbf{9.481}}\cdot \mathit{G}{\mathit{E}}^{-\mathbf{2.887}}\cdot {\mathit{L}}^{\mathbf{2.032}}\cdot {\mathit{A}}^{-\mathbf{0.784}}$ | 0.91 | 38.33 | 31.30 | 0.88 | 0.97 | |

$={e}^{8.871}\cdot {e}^{-0.004\cdot GE}\cdot {e}^{-0.017\cdot S}$ | 0.90 | 36.30 | 38.10 | 0.90 | 0.97 | |

$\begin{array}{l}=824.3-557.3\cdot Ln(E\mathrm{min})+516.1\cdot LnE\\ -185.2\cdot LnBS\end{array}$ | 0.91 | 33.95 | 87.80 | 0.91 | 0.98 | |

Q_{100} | $=1605.119+0.804\cdot E\mathrm{min}-20.653\cdot BS$ | 0.71 | 121.34 | 353.20 | 0.71 | 0.91 |

$={\mathbf{10}}^{\mathbf{10.489}}\cdot \mathit{G}{\mathit{E}}^{-\mathbf{3.174}}\cdot {\mathit{L}}^{\mathbf{2.480}}\cdot {\mathit{A}}^{-\mathbf{01.095}}$ | 0.96 | 49.59 | 38.70 | 0.95 | 0.99 | |

$={e}^{9.280}\cdot {e}^{-0.004\cdot \cdot E\mathrm{min}}\cdot {e}^{-0.017\cdot S}$ | 0.61 | 139.30 | 74.40 | 0.61 | 0.86 | |

$=8651-843.2\cdot LnE\mathrm{min}-800.6\cdot LnBS$ | 0.86 | 85.05 | 214.50 | 0.86 | 0.96 | |

Q_{env} | $=\mathbf{0.475}+\mathbf{0.037}\cdot \mathit{T}\mathit{I}$ | 0.95 | 1.23 | 39.00 | 0.95 | 0.99 |

$={10}^{-1.07}\cdot T{I}^{0.862}$ | 0.95 | 1.44 | 38.50 | 0.93 | 0.98 | |

$={e}^{0.216}\cdot {e}^{0.01\cdot A}$ | 0.82 | 3.97 | 43.40 | 0.47 | 0.91 | |

$=-14+4.492\cdot LnTI$ | 0.80 | 2.42 | 82.10 | 0.80 | 0.94 |

_{25}, Q

_{50}, Q

_{100}and Q

_{env}are marked in bold.

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Myronidis, D.; Ivanova, E.
Generating Regional Models for Estimating the Peak Flows and Environmental Flows Magnitude for the Bulgarian-Greek Rhodope Mountain Range Torrential Watersheds. *Water* **2020**, *12*, 784.
https://doi.org/10.3390/w12030784

**AMA Style**

Myronidis D, Ivanova E.
Generating Regional Models for Estimating the Peak Flows and Environmental Flows Magnitude for the Bulgarian-Greek Rhodope Mountain Range Torrential Watersheds. *Water*. 2020; 12(3):784.
https://doi.org/10.3390/w12030784

**Chicago/Turabian Style**

Myronidis, Dimitrios, and Ekaterina Ivanova.
2020. "Generating Regional Models for Estimating the Peak Flows and Environmental Flows Magnitude for the Bulgarian-Greek Rhodope Mountain Range Torrential Watersheds" *Water* 12, no. 3: 784.
https://doi.org/10.3390/w12030784