Environmental Quality Management through Parshall Flume Aeration Efficiency Modelling

The dissolved oxygen content in surface waters is one of the vital indicators for human water quality usage as well as the aquatic plant and animal environmental life sustainability. Parshall flumes are one of the important ejector devices that are successfully used for oxygen requirement satisfying in various irrigation, wastewater, and ecosys - tems. However, the present study aimed to manage and improve various waterworks aeration efficiency through integrated modeling of experimental and analytical analysis as well as their operation conditional parameters for the Parshall flumes configuration. On the basis of the experiment work data sets run results, the principal com - ponent regression (PCR), partial least squares (PLS), and ridge regression (RR) techniques are used to develop the required aeration efficiency prediction models for such aerators by interrelating the impact of Parshall flumes characteristics and configurations, as well as various water flow rates on aeration efficiency. The predictive mod - els developed in the study were statistically compared to the experimental data. The comparison confirms a good reliability and high accuracy. Considering the proposed aeration models, the optimum design of the new Parshall flumes can be successfully facilitated.


INTRODUCTION
Parshall flumes are usually fabricated from three parts: The first part represents the followed by the throat part that consequently discharge the water to the third diverging part, Figure 1. Hamed (2022) conducted experimental work to investigate the influence of venturi system properties on aeration performance. He proposed mathematical equations for prediction venturi system aeration efficiency. Al Ba'ba'a et al. (2017) conducted experimental work to determine the optimum aeration efficiency of a lab-scale airdiffused system. They investigated the influence of the orifice characteristics and configurations on the aeration efficiency. Therefore, in this study, integration regression-based techniques of the principal component regression (PCR), partial least squares (PLS), and ridge regression (RR) techniques were used to develop the target Parshall flume aeration efficiency prediction models.

AERATION MECHANISM
The oxygen transfer effi ciency (aeration efficiency), A E may be defi ned as: (1) where: u and d -the subscripts that indicate the upstream and downstream locations, respectively; Cs and C -the saturation concentration of oxygen in water at prevailing ambient conditions and the actual concentration of oxygen in the water.
The aeration effi ciency is generally normalized to a 20 °C standard for providing a uniform basis for the comparison of measurement results. The equation that illustrates the eff ect of temperature is as follows (Rindels et al.,1990) (2) where: A E -the transfer effi ciency at actual water temperature; A E20 -the transfer effi ciency for 20 °C, T -the temperature; f is the exponent described as:

Experimental work
The experiments were conducted using a prismatic open rectangular channel 0.40 m wide, 0.60 m deep, and 5.00 m long. The open channels and storage tanks were made of steel plates with glass side tilting. A schematic representation of the experimental setup is shown in Figure 2. Deoxygenated water was pumped from the storage tank to stilling tank. The fl ow was gradually fed to the target fl ow rate. The discharge was measured by means of an electromagnetic fl ow meter installed in the supply line. At the beginning of each experiment run, the storage tank was fed with Na 2 SO 3 and CoCl 2 for chemical de-oxygenation. During the experiments, Dissolved Oxygen (DO) measurements upstream and downstream were taken with a measuring accuracy of ±1%.
Twenty-four Parshall fl ume models were prefabricated from steel and consequently were fi rmly fi xed in the main experiment open rectangular channel. The dimensional details of the fl ume's models are presented in Table 1.

Data sets framework
Six dominant independent variables are selected to investigate the eff ect of Parshall fl ume characteristics and confi gurations on its aeration effi ciency (A E20 ) as dependent variables: Parshall discharge (Q), throat widths (B), throat lengths (G), sill heights (K), oxygen defi cit ratio (O g ), and exponent

Aeration effi ciency modeling techniques
In this study, three main forecasting techniques were selected to develop aeration efficiency prediction. These techniques are principal component regression (PCR), partial least squares (PLS), and ridge regression (RR).

Principal component regression (PCR)
PCR is one of the famous statistical techniques that are mainly used to reduce the dimension in a linear framework. However, PCR is concerned with using multiple linear regression and mathematically utilization is mainly based on the following equation, (Watson et al., 2002).
where: y t -the dependent variable (aeration effi ciency), z it β i , and ∈ t -the original variable, the component weight, and estimated error respectively.

Partial Least Squares (PLS)
PLS is a method for relating two data matrices, X and Y, by a linear multivariate model. PLS prediction model is mainly determined based on the following equations, (Helland et al., 1990) The fi rst PLS component z 1t is defi ned as: Next, calculate the second PLS component z 2t is defi ned as: The PLS linear regression is represented as: Ridge Regression (RR) The formation of ridge regression prediction model is mainly based on the following equations: where: β -the coefficient vector; ℷ -the ridge parameter that has k x k identity matrix and ℷ > 0.

MODEL VALIDATION STATISTICS
In this study, model validation statistics were implemented to evaluate its prediction accuracy. Four statistical measures are chosen to evaluate the errors in the optimum alum dose simulated results.

Mean absolute percentage error (MAPE)
The optimum value of MAPE for best fit simulated with regarding to the observed is zero, (Shamsi et al., 2016)]. It can be calculated according to Equation (11).

Relative bias (RE)
To evaluate the bias of simulated results from observed data, the relative t can be suitable statistical measure to evaluate the size of the bias due to under coverage with respect to the true unknown data to estimate. The relative bias can be calculated according to Equation (14).

RESULTS AND DISCUSSION
In this experimental program, 360 runs were implemented to evaluate the influence of the Parshall flume characteristics on the aeration efficiency. After these runs, the optimum values of the experiment dominant parameters were achieved. Table 2 summaries the mean values of experimental results that were used as the main input data for the development of the predictive models.
According to the experimental aeration results, the predictive models that interrelate aeration performance as a main independent variable other Parshall flume characteristics and configurations were developed by using PCR, PLS, and RR techniques.

I-Principal component regressions models
In the presence of current study's multi collinearity data, PCR are utilized to process multiple linear regressions data. The results of a PCR are denoted in terms of principal component scores and loadings to satisfy satisfi es the linear eigenvalue equation as expressed in Equation (15).
A E20 = 10 -4 Q + 4*10 -4 K + + 0.6978 O g − 0.7968 (15) II-Partial least squares models Additionally, PLS was selected as important technique to develop the Parshall fl ume predictive model because of its reasonable accessibility to treat the missing values of data. On the basis of PLS techniques, the Aeration effi ciency is driven as shown in Equation (16).

III-Ridge regression model
In this study, to permit an amount of acceptable bias tolerance in aeration effi ciency prediction, ridge regression has advantage in reducing the variability of the estimated coeffi cients and gives a more stable and interpretable model. The ridge regression predictive model is illustrated in Equation (17).
A E20 = 10 -4 Q + 10 -5 G + 3.89*10 -4 K + + 0.7657 O g − 0.7886 (17) To evaluate the interrelationship between the observed and predicted values of A E20 at Parshall fl umes, the verifi cation plots of PCR, RR, and PLS Models is shown in Figure 3.
It can be noted a reasonable agreement between experimental aeration data and the corresponding PCR predictive model results with a correlation coeffi cient of 0.892. On the other hand, from the comparison of PLS and PCR models, it is obvious that a relatively improvement in correlation coeffi cient between observed and modelled aeration effi ciency value with an approximate increasing percent of 3%. While, a relatively decreasing in the correlation coeffi cient value is noted by more than 4% due to applying RR techniques in comparing to PLS model.

Models comparative evaluation and validation
To facilitate the comparative evaluation and validation of Parshall fl ume developed model performance, the heat-map plot is selected to clarify the relative comparison among the three denoted aeration effi ciency predictive models, Figure 4. This comparison was mainly based on standardized models' parameters values.
It can be noted that the values predicted by RR model are lying signifi cantly closer to the optimum recommended values of the four denoted evaluating statistical indicators. However, RR predictive model is the most suitable developed models for predicting A E20 at Parshall fl umes. On the other hand, a distinctive graphical model performance evaluation was implemented based on integrated statistical measurement with the correlation coeffi cient as shown in Taylor diagram Figure 5. From the Taylor diagram, it is obvious confi rmed that the RR model has the superior performance in aeration effi ciency prediction followed by PLS model. In turn, the PCR model had the lowest accuracy in Parshall fl ume aeration efficiency prediction.

CONCLUSIONS
In the experimental program of this study, 360 runs on twenty-four fabricated Parshall fl ume with various characteristics and confi gurations were implemented to investigate their infl uence on the Parshall fl ume aeration effi ciency. In this study, three main forecasting techniques were selected to develop aeration effi ciency prediction. These techniques are principal component regression (PCR), partial least squares (PLS), and ridge regression (RR). The predictive models developed in the study were statistically compared to the experimental data. The comparison confi rms a good reliability and high accuracy. According to the comparison of PLS and PCR models, a relative improvement in correlation coeffi cient between the observed and modeled  aeration efficiency value was observed with an approximate increasing percent of 3%. In turn, a relatively decreasing in the correlation coefficient value is noted by more than 4% due to applying RR techniques in comparing to PLS model. The study revealed that the RR model has the superior performance in aeration efficiency prediction, followed by PLS model. Conversely, the PCR model had the lowest accuracy in Parshall flume aeration efficiency prediction. The results indicate that the proposed predictive Parshall flume aeration efficiency models can be used for accurate water body aeration estimation, especially in the case of channels having low slopes.