Abstract a mathematical tool for converting the parameters values

Abstract                                

A water quality index based on fuzzy-logic (FWQI) was
developed based on the results of hydrodynamic and water quality
simulation model (MIKE11) in terms of total dissolved solids
(TDS), dissolved oxygen (DO), biochemical oxygen demand (BOD5), and
nitrate (NO3-N). The performance of the FWQI was assessed
by applying the National Sanitation Foundation Water Quality Index (NSFWQI). The
FWQI and NSFWQI values provided a similar trends of the outputs, where the
difference of T-Test value of 7.91 was significant (P < 0.05).  Furthermore, a linear regression coefficient (R2) was used to evaluate the applicability of the FWQI. Statistical analysis results showed that the output data of FWQI was more precise by a value of 10% and represented the real situation of the water quality parameters along El-Salam canal as compared to NSFWQI. Moreover, FWQI output was an accurate and provided reliability to assess the suitability of the agricultural drainage water (ADW) for reuse in irrigation and could therefore be used as a comprehensive tool for water quality assessment.   Keywords: Fuzzy logic; Statistical analysis; Water quality index; El-Salam canal   1.      Introduction   Water scarcity is a serious issue in the world, particularly in Egypt (Elshemy, 2017). Fortunately, 17 BCM of agricultural drainage water (ADW) is annually produced which represented a backbone of the non-conventional water resources in the country (Hafez, 2005). 55% of the ADW are officially reused in irrigation purposes. However, the water quality of the most of drainage canals are polluted due to discharge of domestic and industrial wastewater (Allam et al., 2016). The water quality is crucial particularly for satisfying irrigation purposes (?ener et al., 2017). Several approaches of evaluation of water quality have been set into practice to provide an accurate assessment in a proper way (Zahedi et al., 2017). Among all, water quality index (WQI) is one of the promising methods to develop water quality classification based on a set of parameters for the desired purposes (Allam et al., 2015). Basically, water quality indices (WQIs) are a mathematical tool for converting the parameters values at a certain site and time into a number ranging from 0 to 100 indicating the real water quality status with respect to the desired standards (Feng et al., 2015; Misaghi et al., 2017). The 1st WQI was proposed by Horton (1965). However, several WQIs was further developed i.e. National Sanitation Foundation (NSFWQI) (Brown et al., 1970), Florida Stream (FSWQI) (Safe, 1995), Canadian (CWQI) (Khan et al., 2003), British Columbia (BCWQI) and Oregon (OWQI) (Cude, 2001) Water Quality Indices. Most of these indices were developed based on the NSFWQI (Debels et al., 2005; Kannel et al., 2007; Misaghi et al., 2017). The most disadvantages of application of WQIs are 1. to describe the water quality status at a certain time and location 2. to provide a rough estimation and imprecise results (Bai et al., 2009) and 3.  not capable of handling the environmental and experimental uncertainties (Gharibi et al., 2012). Simulation of water quality and quantity using MIKE 11 model was efficiently used in this study to simulate spatial-temporal distribution of physical and chemical changes in El-Salam canal. Moreover, this study presents a novel water quality index based on fuzzy-logic. The performance of the FWQI is assessed by applying the simulation results using the National Sanitation Foundation Water Quality Index (NSFWQI). Alternative water quality assessment approaches based on Artificial Intelligence (AI) computational methods such as knowledge-based systems, neural networks, genetic algorithms, and fuzzy logic, have been evaluated by Vadiati et al., (2016). Fuzzy logic is one of the most common approaches in the AI methods and it was initially proposed by Zadeh (1965).  Fuzzy logic was tested with real environmental problems, to reduce the uncertainty and imprecision in criteria utilized in decision-making tools (Lu et al., 1999; Ocampo-Duque et al., 2006; Sowlat et al., 2011; Li et al., 2016; Rodríguez et al., 2016). Fuzzy inference system (FIS) provided an alternative approach to deal with the objectives and constraints which are not well defined or information is not precise (Chau, 2006; Chang et al., 2001; Liou et al., 2003). The aim of this study is to simulate the water quality and quantity using MIKE 11 model integrated with water quality index based on fuzzy-logic 2.      Methodology 2.1.Study area El-Salam canal is the largest source of agricultural drainage water (ADW) in Egypt where 2.11 BCM/year of the Nile water is mixed with 1.905 BCM/year of water from Bahr hadous drain and 0.435 BCM/year of El-Serw drain (Mohamed, 2013). The Canal is located in the Eastern North region of the Nile Delta, with a total length of approximately 88 km (Fig.1). El-Salam canal extends across Fraskour drain at (1.80 km), El-Serw drain at the (17.85 km) and Bahr Hadous drain at the (54.0 km) from the intake of the canal (Shaban, 2017). The fresh water supplies are mainly from the Nile River at Damietta branch upstream of Fraskour Dam. The ADW from Fraskour, El-Serw and Bahr Hadous drains is mixed with fresh water with ratio of 1:1 (DRI, 2016; Sabry et al., 2015).   Fig.1 Location of El-Salam canal, Egypt   2.2.  Water quality parameters of El-salam drainage canal   The water quality parameters in terms of total dissolved solids (TDS), dissolved oxygen (DO), biochemical oxygen demand (BOD5), and nitrate (NO3-N) of El-Salam canal was used to identify the suitability of drainage water (DW) for reuse in irrigation based on Egyptian standards (Law 48/1982). The water quality results from MIKE11 model previously obtained by Assar et al., (2018) was used to develop the FWQI and NSFWQI. The average annual values of TDS, DO, BOD5 and NO3-N of El-Salam canal are 710.9, 6.58, 21.1 and 11.70 mg/l as shown in Table 1.   Table 1. The average annual water quality parameters of the ADW of El-Salam canal   Parameters Min. Max. Average values Egyptian standards for ADW reuse in irrigation (law 48/1982) TDS – (mg/l) 233.8 1006.1 710.9 < 1200 DO – (mgO2/l) 5.16 9.87 6.58 > 5

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BOD5
– (mg/l)

8.10

27.1

21.10

< 40 NO3- N – (mg/l) 10.70 12.50 11.70 < 50   2.3. Fuzzy inference system Membership functions, fuzzy set operations and inference rules are the principals of FIS to develop water quality index based on the fuzzy logic as described earlier by Ross (2004).  A membership function can be expressed in various forms such as trapezoidal, triangular, etc., which identifies each point in the input space mapped to a membership value between 0 and 1. The input set has a domain namely the universe of discourse and the output-axis represents the membership value µ. A fuzzy set A is derived from Eq. 1 where X is the universe of discourse and its elements are denoted by x.   Where, ?A(x) value represents the degree of membership of element x in fuzzy set A.   The relationships among the fuzzy subsets are union (OR), intersection (AND) and additive complement (Negation) (NOT). These basic operators determine the core of fuzzy logic. If two fuzzy sets A and B are defined on the universe X, for a given element x belonging to X. Eqs. 2, 3 and 4 express the operations of fuzzy set.   OR:      AND:    NOT:      The relationships among the subsets of the inputs and outputs are defined as the inference rule. The if-then rule is carried out to generate a new output subset. Each rule consists of two parts. The if-part is named the antecedent, while the then-part is called the consequent. The if-then rule has the form: IF A is a THEN C is c. IF B is b THEN C is c. where a, b, and c are the linguistic values for the subsets defined for fuzzy sets in the universes of discourse A, B, and C, respectively.   2.4. Development of the water quality index 2.4.1.      Water quality index based-on fuzzy logic A fuzzy model for assessment of water quality for reuse in irrigation has been developed. The prediction of the fuzzy model depends on the number of fuzzy sets used in the mapping process, since it facilitates to give more continuity to the universe of discourse (Bai et al., 2009). Triangular membership function was used for TDS, DO, BOD5 and NO3-N. Fig.2 shows the fuzzy sets of parameters which were applied through the FIS. The fuzzy sets, in this index, were defined by the linguistic variables "very low" (VL), "low" (L), "medium" (M), "high" (H), and "very high" (VH). Each parameter was assessed to be one of the five fuzzy sets in terms of the membership functions. Based on the developed fuzzy sets and linguistic terms for the fuzzy-based index, the fuzzy sets were developed according to the following Eq. 5, The FIS normalized the specified water quality parameters to a value between 0 and 100, in which values near 100 represent better quality of water. Five classes were proposed to assess the water quality as shown in Table 2.   Table 2. the FWQI and NSFWQI index range and associated water quality categories Index value Water quality category 0-25 Very bad 26-50 Bad 51-70 Average 71-90 Good 91-100 Very good        Fig. 2. the fuzzy set membership functions of the input variables, TDS (a) DO (b), BOD5 (c) and NO3-N (d)   The Mamdani systems were used for the fuzzy model (Ross, 2004). The rules in the FIS were set to achieve the maximum possible number of water quality conditions creating the inference rules (75 rule). The inference rules generated are given as follows, If (DO is VL) and (BOD is H) then (FWQI is VB), If (TDS is VH) and (DO is VL) then (FWQI is VB) and If (DO is H) and (NO3 is M) then (FWQI is VG). Defuzzification of the outputs was carried out using the center of gravity (Centroid) method, which is the most prevalent and physically applicable approach. Its derivation is based on the following algebraic expression (Ross, 2004), Fig. 3 shows the relationship between two of the parameters i.e. included in the FWQI with their effects on the final index value. All computations were implemented using the "fuzzy logic toolbox" in MATLAB2015.       Fig. 3.  surface graph representing the interactions between two of the parameters and the FWQI value   2.4.2. The national sanitation foundation water quality index   The performance of the FWQI was assessed by applying the same simulation results using the NSFWQI. The latter was calculated as the weighted sum of sub-indices which was developed earlier by Horton (1965). Water quality parameters (TDS, DO, BOD5 and NO3-N) had a specific weighting factor based on detailed description of the calculation procedures (Abbasi, 2002). Table 2 shows the associated water quality categories, where the index values ranged from 0 to 100, to provide a qualitative description of the index outcome. The NSFWQI could be estimated using Eq. 7. n is the number of parameters, Wi is the weight factor, Qi is sub-index of the parameter, Mi is the observed value, li is the ideal value and Si is the standard values based on law 48/1982 and Table 1. The ideal value (li) for pH is 7, and for other parameters, it is equal to zero (Zahedi, 2017).   2.6. Statistical analysis   T-Test was used to compare between the FWQI and NSFWQI. A linear regression coefficient (R2) was considered as a good indicator of the predictive performance of the indices. A high level of R2 value signifies conformity between the output of the model and the real measured data.   3. Results and discussion 3.1 Water quality indices performance The results in Fig. 4 show the FWQI and NSFWQI values from the intake up to 17 km of the canal for TDS, DO, BOD5 and NO3-N. The FWQI and NSFWQI values were quite good and varied from 71.4 to 75.6 and from 79.6 to 88.79 respectively which indicates that the water quality was in the category "Good". for both indices. The water quality was complying for safely reuse in agricultural purposes. The FWQI and NSFWQI values was surprisingly remained almost constant at a level of 75.0 and 83 respectively after connecting with Faraskor drain at 1.8 Km. Apparently  the annual discharge of drainage water from Faraskor ( 8 m3/sec.) did not adversely affected the water quality of Elsalam canal. However, at 15 km distance from the upstream the FWQI and NSFWQI values was dropped to 71.4 and 79.6 due to the depletion of DO for degradation of organics. The FWQI value was exceeded 75.5 at 17 km due to water self-purification (Negulescu, 2011). The NSFWQI value was quite high at 17 km resulting a value of 83.63. However, the values for FWQI and NSFWQI at 17.85 km was significantly dropped to 55.3 and 71.38 due to the discharge of 31.1 m3/sec. from El-Serw drain as shown in Fig. 5. The water quality index is slightly decreased at 20.2 km from the upstream to 55.2 for FWQI and 69.86 for NSFWQI due the mixing with drainage water from El-Serw drain. The FWQI (55.7) and NSFWQI (70.25) was improved at a quite short distance of (1.55 km) from 20.2 to 21.75 km due to the diffusion of oxygen into the water. Before mixing with Bahr Hadous drain the FWQI and NSFWQI was increased up to 65.5 and 82.1 at 53Km respectively. Fig. 4 the FWQI versus NSFWQI from the upstream to 17 Km of the canal The results in Fig. 6 show the FWQI versus NSFWQI values after mixing with Bahr Hadous drain at 54 Km where the water quality is slightly deteriorated resulting an "Average" class. 53.9 and 68.05 was registered for FWQI versus NSFWQI at 54Km respectively. At short distance of 0.3 km (from 54 to 54.3 km) the FWQI was negatively affected resulting a value of 52.1 due to the mixing with the discharge from the drain (39.3 m3/sec). However, the NSFWQI was slightly increased up to value of 68.31 at distance of Fig. 5 the FWQI versus NSFWQI from El-serw drain at 17.85 to 53 Km of the canal 54.3 km due to an increase of BOD value from 27.09 to 26.45. Moreover, the DO values were decreased from 5.3 to 5.1 where a slight change of the water quality parameters was not accounted for calculation of NSFWQI. However, the results for FWQI and NSFWQI was increased at 79.63 Km as shown in Fig. 6. The values were increased from 52.2 to 53.9 for FWQI and from 68.8 to 71.65 for NSFWQI. The FWQI values were reduced to 53.7 while NSFWQI was increased up to 71. 9 at the downstream of the canal (88 Km).  Fig. 6 the FWQI versus NSFWQI from Bahr Hadous drain at 54 to the end of the canal at 88 km. 3.2. Statistical analysis of water quality indices   The FWQI and NSFWQI values provided a similar trends of the outputs as shown in Figs. 4, 5 and 6. The difference of T-Test value of 7.91 between FWQI and NSFWQI was significant (P < 0.05). The R2 value between FWQI and water quality parameters of the ADW along El-Salam canal was quite high 89.18 % (Fig. 7a). This indicates that the values of the observed data was quite fitted to the predictive one in the case of FWQI. Nevertheless, the R2 for NSFWQI and water quality parameters were lower (79.74 %) as shown in Fig. 7b. The output data of FWQI was more precise by a value of 10 % and represented the real situation of the water quality parameters along the canal as compared to NSFWQI. This could be attributed to how each parameter was compared with the standard value in the calculations. Moreover, the inference rules was used for FWQI calculation and not only deal with numerical data, but also apply the expert's knowledge and experience. Based on these results, the FWQI was an accuracy and provided reliability to assess the suitability of the ADW for reuse in irrigation and can therefore be used as a comprehensive tool for water quality assessment. Gharibi et al., 2012; Lermontov et al., 2009; Liou et al., 2003 and Ocampo-Duque et al., 2006, which described the development of water quality indices based on fuzzy logic have reported similar results.     Fig. 7. Linear regression model for FWQI (a) and NSFWQI (b)   4.      Conclusions   Water quality index based on fuzzy-logic (FWQI) was very efficient to assess the suitability of agricultural drainage water (ADW) for reuse in irrigation. The integration of FWQI and the results of a hydrodynamic and water quality simulation model (MIKE11) provided an accurate result along the canal. The index values was deteriorated along the canal. However the water quality was in a range of good to average and complying with the standards for reuse.  The T-Test of 7.91 was significant (P < 0.05) between the NSFWQI and FWQI and the linear regression coefficient (R2) were 89.18% for FWQI and 79.74% for NSFWQI. The FWQI introduced a more accurate output by a value of 10% and represented the real situation of the water quality parameters along the canal as compared to NSFWQI.