**1. Introduction**

Streamflow velocity and discharge rate, water elevation, hydraulic deep, and flow form are the main themes in hydrology and are closely linked to water supply, quality and administration, flood protection, dewatering, irrigation, dam construction, and other related themes [1–3]. The streamflow velocity and discharge rate have a significant effect on water's retention period and quality [2,4,5]. Thus, these variables are typically needed for hydro-systems modelling. Unfortunately, the ongoing streamflow monitoring on a river's cross-section is commonly unfeasible or very costly [2–6]. Fast and accurate discharges calculation is of high importance for a grea<sup>t</sup> number of environmental engineering projects (real-time flood forecasting, water resources administration, etc.) [2,5–7]. The goal of our

**Citation:** Filintas, A.; Panoras, G.; Stamatis, G. Hydrological 2D Modelling of Lithaios River Flows (Greece) Using GIS and Geostatistics for Environmental and Agricultural Water Resources Administration. *Environ. Sci. Proc.* **2023**, *25*, 13. https://doi.org/10.3390/ ECWS-7-14201

Academic Editor: Lampros Vasiliades

Published: 14 March 2023

**Copyright:** © 2023 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 (https:// creativecommons.org/licenses/by/ 4.0/).

research is hydrological 2D streamflow modelling of Lithaios River (Central Greece), using GIS, and geostatistics for studying water velocity and discharge, stage elevation, and hydraulic features (streamflow depth, water flow area, wettable circumference, hydraulic radius and depth, n Manning's coefficient, Chow's composite n, Froude number, etc.).

### **2. Materials and Methods**

#### *2.1. Lithaios River Measurements, Instruments Used, and Specifications*

The study was conducted in Lithaios River (top width = 15 m) at Trikala monitoring station (M-S), in the region of Thessaly in Central Greece. A propeller current flow [7,8] meter (OTT) was employed together with a modern electronic metering system including a flow computer, data logger, and a real-time display monitor, all calibrated by the manufacturer. River flow data were computed by averaging over a 60 + 60 s measured couple. Vertical measurements of water depths and velocities were performed for temporal monitoring of the cross-section's velocity and discharge variation [8].

### *2.2. Hydrological Methodology*

The river's streamflow velocity and the depths and widths of the defined segments were measured and engaged for the estimation of the cross-section's mean discharge of every segmen<sup>t</sup> [2–8]. The overall discharge [2–8] was estimated by the mid-section methodology [5–8]. The features of the cross-section, the water flow velocity of the defined segments and the overall mean flow velocity, were metered, computed, modeled, and depicted in diagrams and GIS maps, respectively, building up a hydrological toolkit for Lithaios River. Water stage elevation and flow measurements were taken monthly for a period of 1 year (January to December). In addition, more measurable variables (streamflow depth, the defined segments' width, overall river width, and water stage elevation) were measured, and more hydraulic features (streamflow depth, water flow area, wettable circumference, hydraulic radius and depth, n Manning's coefficient, Chow's composite n, Froude number, etc.) were computed and depicted in diagrams and saved in the hydrological toolkit. Equation (1) was applied in order to calculate the river flow velocities.

$$V\_{i=1}^{n} = a + (b\_{eq} \times N\_{eq}) \tag{1}$$

where *Vn i*=1 = stream flow velocity (m s<sup>−</sup>1), n is the number of cross-section segments, *a* = the initial speed to overcome mechanical resistance, *beq* = the system's calibration constant, and *Neq* = the equipment's rotations per second.

Equation (2) was used for the river's cross-section total discharge.

$$Q\_T = \sum\_{\mathcal{S}=1}^n V\_{i=1}^n A\_{I=1}^n \tag{2}$$

where *QT* = total discharge (m<sup>3</sup> s<sup>−</sup>1) of the river's cross-section, g = 1 ... n is the number of cross-section segments, *Vn i*=1 = the mean flow velocity of each cross-section segmen<sup>t</sup> (m s<sup>−</sup>1), and *An J*=1 = the wet flow area of each cross-section segmen<sup>t</sup> (m2).

Couples of stage water elevation *h(t)* and discharge *Q(t)* measurements were utilized to develop mathematical relationships between them. Lithaios River rating curves (*h(t)* − *Q(t)*) [2–8] and changes in the riverbed were computed on the basis of the measured variables using various model equations for regression, ANOVA statistical analysis, and the model's fit F test by utilizing the IBM SPSS v.26 statistics software [2,3,9–25].

*2.3. Statistical and Geostatistical Data Analysis, Flow Velocity and Discharge Modelling, and 2D Mapping Methodology*

The data were analyzed through the use of IBM SPSS v.26 [2,9,11,12] statistics software. The results are the observations' averages. ANOVA (analysis of variance) [2,3,9,11–25] was used to assess velocity (*V n <sup>i</sup>*=1), discharge ( *QT*), and hydraulic depth effects. In the present study, we used geostatistics (the Kriging method with power model) [2,11–25] for

modelling and GIS (geographical information system) hydrological 2D mapping of Lithaios River's water velocity and discharge. Furthermore, the validation of *QT* and *Vn i*=1 involves analysis of residual errors, which is the gap between predicted and observed data values and the bias forecast between over- and underestimates. For this purpose, we applied the statistical criteria described by other studies [2,11–16,18–20,22–28], such as the equations for residual sum squares (RSS), standard error (SE), and root mean square error (RMSE).

### **3. Results and Discussion**

The streamflow velocity 2D modelling [2,27] results of the Lithaios River crosssection for the year's maximum (March) and minimum (August) water discharges and the univariate velocity model output statistics are depicted in Figure 1a–d. Lithaios River mean water flow velocity (*V n <sup>i</sup>*=1) of the cross-section segments for the year's maximum (March) and minimum (August) water discharge results show that *Vn <sup>i</sup>*=1(max) ranged 0.199–0.329 (m s<sup>−</sup>1) and *Vn <sup>i</sup>*=1(min) ranged 0.098–0.177 (m<sup>3</sup> s<sup>−</sup>1).

**Figure 1.** (**a**) Streamflow velocity 2D modelling results on a digital 2D *Vn i*=1 map of the Lithaios River cross-section (Trikala M-S) for the year's maximum discharge (March), (**b**) univariate velocity model (Vmax) statistics, (**c**) streamflow velocity 2D modelling results on a digital 2D *Vn i*=1 map of the Lithaios River cross-section (Trikala M-S) for the year's minimum discharges (August), and (**d**) univariate velocity model (Vmin) statistics.

The flow velocity (*V n <sup>i</sup>*=1) statistics [− *x* (mean), median, geometric mean, coefficient of variation (CV), s2 (variance), and s (standard deviation)] for the year's maximum discharges (March) are presented in Figure 1b and the year's minimum discharges (August) are presented in Figure 1d. Velocity fluctuation of a river's cross-section can be specified by means of descriptive statistics [2,3,9,27–29], and of all the descriptive statistics, the coefficient of variation (CV) is the most important measure. [2,9]. The results for both CVs' of the cross-sections velocity variability for the year's maximum (March) (CV = 0.302) and minimum (August) (CV = 0.307) discharges were classified as moderate variability *Vn i*=1. The resulting spatial distribution of water flow velocities obtained using river cross-section measurements was best fitted using the Kriging with power model, which resulted in minimum residual sum squares (RSS = 0.0001694), and the RSS used as one of the criteria to choose the greatest model. The other criteria used included the standard error (SE) and root mean square error (RMSE), as in other studies. [2,27]. The best SE for March's velocity modelling was the one using the Kriging with power model (SE = 0.0002236) and for August, it was also the same model (SE = 0.0008328). The RMSE using the Kriging with

power model for March's velocity modelling was found to be the best, RMSE = 0.0406329, and for August, it was found to be the best, RMSE = 0.1431426. These results are acceptable since the SE and RMSE scores should be close to zero for accurate prediction and they classified the Kriging with power model as the best model. The abovementioned outcomes, prove the validity and accuracy of the generated 2D digital velocity maps (Figure 1a,c). The relationships between the n Manning's coefficient [2,3,5,7], the Chow's composite n coefficient [5], and the river's water discharges modelling (power model) resulted in high coefficients of determination (R2) [2,9,12,13,16] for the 12-month measurement study period (Figure 2a,b). The diagrams of the discharges power model (which resulted in being the best model), the Darcy–Weisbach f coefficient multinomial model, and the shear linear model for year's maximum (March) and minimum (August) water discharges are depicted in Figure 2c,d. The R-squared gives a measure of how accurately the observable outputs are reproduced by the model based on the percentage of the total variance that is explained by the model [2,9].

**Figure 2.** (**a**) Diagram of n Manning's coefficient vs. discharge, (**b**) diagram of Chow's composite n coefficient vs. discharge, (**c**) diagram of the discharge power model, the Darcy–Weisbach f coefficient multinomial model, and the shear linear model for year's maximum QT (March), and (**d**) the diagram of discharge power model, the Darcy–Weisbach f coefficient multinomial model, and the shear linear model for the year's minimum QT (August).

The R squared output results for the n Manning's coefficient vs. discharge showed a high R<sup>2</sup> = 0.8576 and the Chow's composite n coefficient vs. discharge also resulted in a high R<sup>2</sup> = 0.8927. The n Manning's coefficient and the Chow's composite n coefficient results show a high degree of correlation with the river's water discharges, with the Chow's composite n coefficient found to have a higher correlation. These results indicate that Chow's composite n [5]—which is built on the hypothesis that the overall force resisting the streamflow in the cross-section is equivalent to the summation of the resisting forces of streamflow in each of the defined segment's regions [2,5]—more accurately approximates the force resisting water flow in Lithaios River. Finally, the statistical results showed that the Froude number during the study period was Fr < 1, showing that the Lithaios streamflow is classified as subcritical [2,3,5].
