Abstract

In semi-arid or arid regions, where available freshwater is limited, surface water requires repeated quality testing to avoid pollution. Sampling trips of different frequencies are onerous and require expensive laboratory analysis. Simulation appears to be a reliable alternative method to overcome such challenges. The simulation presented here was conducted by solving the mass balance equation while considering the inputs controlling each simulated parameter. The mass balance equation (a differential equation) was solved by finite difference numerical approximation to provide parameters for pollutant concentrations at each station or moment (based on selected steps). This solution was integrated to simulate pollution indicators (biochemical oxygen demand and dissolved oxygen), nitrogen forms, and orthophosphates. The National Sanitation Foundation water quality index (NSF-WQI) was calculated using these parameters. Using 12 months of measurement data, results were compared for NSF-WQI calculated through measured and simulated data, showing a significant correlation with R² = 0.8, meaning the model demonstrated good calibration and validation. The elaborated model is a useful tool for decision makers to test and propose quality improvement solutions for watercourses suffering from quality deterioration.

1 Introduction

As water demand continually increases with population growth and economic development, the gap between water supply and demand in Morocco is becoming larger (Agoussine and Bouchaou 2004; Bzioui 2004). Water pollution has been increasing in recent years, which makes this problem much more serious. A major challenge for government decision makers is to plan for considerable future uncertainty, not only in water demands but also in water quality (Loucks and Van Beek 2017). The method discussed in this article is to incorporate both water quantity and water quality into water resource allocation. It has the potential to provide significant support for decision makers to face challenges associated with water demands (de Azevedo et al. 2000; Ward and Pulido-Velazquez 2008).

Some researchers address this issue by including water quality in the allocation process, using programming models (simulations) to achieve optimal use for available water (Ambroise 1998; de Azevedo et al. 2000; Brabec et al. 2002; Keupers and Willems 2017; Martin and McCutcheon 2018; Zao 2004). Simulation may replace experimental approaches that are expensive and require considerable time and effort (Shampine et al. 2003).

The simulation process requires that many tasks be completed before starting programming. These tasks define the required model complexity, the data needed, the development time, the complex problems to be solved, and the expected execution time of the model. These tasks are basic for constructing a simulation model (Rauch et al. 1998). Selecting a model that is too simple can lead to a lack of precision and uncertainty in decision making, while selecting a complex model can result in misdirection of available resources, study delays, and increased costs of demand parameters (Chapra 2008).

Many water quality models are widely used around the world, such as QUAL2E, QUAL2K, IberWQ, SWAT, and Vensim PLE (Ghosh and McBean 1998; Park and Lee 2002; Zhang et al. 2012). Each one has its specific characteristics and particular uses. For example, QUAL2K, which is a modern version of QUAL2E that was developed by the U.S. Environmental Protection Agency (USEPA), is used to evaluate the self cleaning capacity of rivers in the United States that receive treated wastewater from urban sources (Brown and Barnwell 1987). Unfortunately, QUAL2E, like other models, has limitations to its application (de S.I. Gonçalves and Giorgetti 2013). QUAL2E was created specifically to analyze the effects of permanent pollution sources according to U.S. standards (Birgand 2004). Modeling a flow subjected to highly variable pollutant sources that vary from one section of a watercourse to another is complicated when using the QUAL2E model (Gao and Li 2014).

The majority of available water quality models include structures that cannot be changed by users. As a result, users cannot to introduce equations or factors that better describe a particular situation (de S.I. Gonçalves and Giorgetti 2013).

For certain models (except QUAL2K) the assignment of kinetic coefficients for different sections along a river is not allowed (Tao 2008). This becomes a serious constraint when effluents with distinct biodegradation levels are released at different points in the river. Assuming a single biodegradation coefficient for water quality modeling in a river can underestimate or overestimate the actual impact, reduce or amplify its power and increase the margin of error that exists in the modeling process (Yu and Salvador 2005).

Faced with these constraints and limitations, developing a simulation model that allows manipulation of its basic equations and coefficients is necessary. The model we developed was tested on the El Abid River, located in the High Atlas Mountains of Morocco. This watercourse is a suitable case study since its water quality recently became degraded and it needs to be frequently tested, while our ability to take samples along the river is limited by site access and funds.

1.1 Study area

The El Abid watershed is located in the north–central part of Morocco. It covers 8041 km² and its main watercourse length is 638 km (Figure 1). This watershed is characterized by multiple ranges of elevations from High Atlas Mountains, the piedmont, and Tadla plain.

Figure 1 Study area location.

The study area population is estimated to 13 990 inhabitants (Haut Commissariat au Plan du Maroc 2014). Based on the national average flow (80 L/d/person), such a population can be expected to generate 46.6 m³/h in liquid pollutant load. This volume is partly treated by three purification plants (Azilal, Ouaouizeght, and Aghbala) and the rest is poured into degraded septic tanks in each agglomeration center (Karaoui et al. 2017).

The regional climate is semi-arid, marked by seasonal variability (Knippertz et al. 2003). The average rainfall is 260 mm/y in the downstream area and 456 mm/y in the mountainous regions. The average annual temperature is 16.9 °C, with a small difference between the upper reach and the river mouth (Ait Ouhamchich et al. 2018a).

2 Materials and methods

The physical, chemical, and biological phenomena derived from natural environments are generally described by complex systems of partial differential equations (Chapra 2008). Finding the mathematical solutions of these equation systems is not an easy task and sometimes it is impossible (Shampine et al. 2003).

In this study, we focused on mass balance equation numerical approximation using the finite difference method (Equation 1). With this approximation, we aimed to simulate the processes of the nitrogen, orthophosphate, and oxygen cycles. These approximations transform a continuous problem governed by differential equations into a discrete problem. Then, using an initial concentration C₀ (which should be known), we can deduce other concentrations at different times and locations.

(1)

  where:

C	=	parameter concentration,
t	=	time,
K	=	velocity reaction coefficient,
Dx	=	longitudinal dispersion coefficient,
SInterne	=	source/sink terms, and
Vx	=	flow velocity in x spatial direction.

Different reaction coefficient intervals were already well defined thus allowing us to create many iterations for calibration to adapt our model to the study area characteristics (Chapra 2008). The source terms (gain or loss) are generally associated with punctual phenomena that influence each parameter concentration. These sources are important when liquid loads (domestic, agricultural, and industrial fluids) are discharged into the watercourse (Mirbagheri et al. 2009).

The calibrated model was tested only for the downstream region (starting from the Bin El Ouidan dam to the river mouth) which has recently experienced severe degradation (Karaoui et al. 2017). Different solutions were tested, allowing feasible ameliorations to reduce the water quality degradation. The geometric configurations were composed of seven sections (Figure 2), with different dimensions (width, length and water level). Each section was named according to the closest village or settlement.

Figure 2 Location of simulated sections.

2.1 Simulated section geometry

The geometric parameters were identified by combining Google Earth images, digital elevation models (STRM 30 m) and results of previous gauging of the river to estimate its flow. Table 1 shows the geometric characteristics of each simulated section.

Table 1 Geometric characteristics of simulated sections.

	Station name	Length (km)	Width (m)	Water level (m)	Slope %
P01	Ait Attab	41.5	19	0.5	0.41
P02	Tabia	27.44	24	0.3	0.26
P03	Bzou	25.10	14.7	0.65	0.44
P04	Oued El Abid centre	19.19	16	0.3	0.24
P05	Downstream Oued El Abid	6.29	23	0.5	0.22
P06	Upstream Oum Er-Rbia	21.7	30	0.3	0.08
P07	Downstream Oum Er-Rbia	2.31	28	0.32	0.12

2.2 Liquid discharge estimation

Liquid waste concentrations at each section were predicted based on measurements taken closest to the center of the study area (Table 2) (Idrissi et al. 2015). As wastewater flow measurements were unavailable, the quantified liquid discharges were based on average inhabitant output estimated as 80 L/d/person (Table 3). These estimated discharge quantities flow directly or indirectly into the El Abid River, causing degradation of the water quality (Karaoui et al. 2017).

Table 2 Mean concentrations of simulated wastewater parameters.

Parameters measured at liquid discharges	Average concentration used (mg/L)
Dissolved oxygen (DO)	1.115
Biochemical oxygen demand for 5 d (BOD)	433
Organic nitrogen (Norg)	17
Ammonium (NH4+).	0.21
Nitrite (NO2−)	0.42
Nitrate (NO3−)	0.15
Orthophosphate (PO43−)	22

Table 3 Populations and their generated quantities of liquid discharge.

Centre	Population (inhabitants)	Liquid discharge (L/s)
Ait Attab	15 000	13.88
Tabia	7936	7.34
Bzou	14 072	13.03
Oued El Abid centre	6158	5.70
Downstream Oued El Abid	41 731	38.64
Upstream Oum Er-Rbia	55 170	51.08
Downstream Oum Er-Rbia	4156	3.85

2.3 Overall water quality status

To assess general water quality in the downstream part of the river, the National Sanitation Foundation water quality index (NSF-WQI) was calculated using simulated data and laboratory measurements. This index classifies water quality on a 0–100 scale, where the interval 76–100 represents very poor quality, and 0–25 represents excellent water quality. NSF-WQI was calculated using the weighted arithmetic index method (Smith 1990), Equation 2:

(2)

where:

qn	=	quality rating that reflects parameter relative value with standard permissible value (Rao et al. 2010),
Wn	=	unit weight of water quality parameter n (Sapkal and Valunjkar 2013), calculated using Equation 4,
N	=	number of parameters, and
n	=	index of a parameter.

The quality rating q_n was calculated using the ideal value V_i that is equal to zero (V_i = 0) except for pH (V_i = 7), temperature T (V_i = 25) and DO (V_i = 14.6 mg/L), observed value (V_n), and measured parameter standard permissible value (S_n).

(3)

where:

Vn

=

measured concentration of each parameter in the laboratory.

(4)

where:

K

=

proportionality constant, calculated using Equation 5.

(5)

Since temperature (T), pH, electrical conductivity (EC), and water hardness (hydrotimetric titer TH) are not governed by the mass balance equation, we used stepwise regression to reveal any existing correlation with simulated parameters.

3 Results and discussion

3.1 Biochemical reaction coefficients

The iterations made for kinetic coefficients of various biochemical reactions attempt to render our model results similar to those obtained by laboratory analysis. The coefficient values were verified based on 12 months of measurement data collected during 2016 and 2017 (Table 4).

Table 4 Chosen reaction coefficients.

Parameter coefficient	Final modeled values
K1: Bio-oxidation coefficient for biochemical oxygen demand (1/d)	0.64
K2: Aeration coefficient (1/d)	4.10
K3: Sedimentation effect coefficient (1/d)	0.6
Os: Oxygen saturation point	0.8
KA: Dissolved oxygen from chlorophyll A (1/d)	0.02
A1: Chlorophyll A phytoplankton (mg/L)	0.001
A2: Sessile chlorophyll A algae (mg/L)	0.001
Kkg: Organic nitrogen decomposition rate (1/d)	0.4
KNH4: Ammonium decomposition rate (1/d)	0.4
KNO2: Nitrate or nitrite decomposition rate (1/d)	0.1
KPO4_1: Orthophosphate decomposition rate (1/d)	0.2
KPO4_2: Orthophosphate consumed by algae (1/d)	0.1
KB: Nitrate consumed by algae (1/d)	0.1

3.2 Comparison of simulated and measured concentrations

Our model results are presented for the wet season (March 2017) and the dry season (July 2017). As shown in Figure 3 (wet season), there was a high correlation between the simulated and measured data, except for P07 (downstream Oum Er-Rbia) where the model underestimated the laboratory measurements. This difference could be explained by dilution regenerated when Oum Er-Rbia River and El Abid River combine, or it could be because the water from both rivers had not mixed at the location where the samples were taken. Combining both those factors, our model suggested that both rivers were well mixed at P07, when they were in fact not.

The biochemical oxygen demand (BOD) and orthophosphate results were not well fitted to the field measurements at most stations, while the rest of the simulated parameters matched well with the laboratory measurements.

The dry season validation results (July 2017) are shown in Figure 4. According to these results, there was still a significant difference between measured and simulated results at the last sampling station. This may confirm that this station was poorly chosen and both rivers were not well mixed at this location.

Figure 3 Comparison between simulated and measured results during the wet season.

Figure 4 Comparison of simulated and measured results during the dry season.

The orthophosphate results were less well calibrated with the measured data; however, the BOD in the dry season gives good results compared to those of the wet season. In general, simulated BOD and orthophosphate results were acceptable.

3.3 Stability analysis

Stability analysis ensures that monthly variation effects on our proposed model are minimized. This analysis is performed by comparing linear correlations between simulated and measured parameter concentrations. The coefficient of determination (R²) and root mean square error (RMSE) were used to assess model efficiency and derive the error margin between simulated and observed data.

The stability test for the simulated and measured parameters indicates a high correlation (R² >0.9) for nitrogen and forms of phosphate (Figure 5). The dissolved oxygen (DO) and BOD results were acceptable (R² >0.7). This instability could be explained by the pollution source load originating from nearby regions. This load was not well estimated due to the absence of a sanitation network in these sites.

Figure 5 Correlation between simulated and measured parameters.

As shown in Table 5, the electrical conductivity can be deduced from the simulated NH₄⁺, NO₃⁻ and OD parameters, while pH can be determined using a combination of three parameters (BOD, NO₃⁻ and water hardness) with high accuracy (R² = 0.75). Using the correlation results, we created an equation for estimating these parameters using the simulated parameters.

Table 5 Correlation between simulated parameters and pH, EC, and TH.

	Correlated parameters	R2	RMSE
Electrical conductivity	NH4+, NO3− and OD	0.62	29.3
Water hardness (TH)	NO2− and PO43−	0.64	7.02
pH	BOD, NO3− and TH (estimated by NO2− and PO43−)	0.75	0.16

A comparison of the NSF-WQIs derived from simulated and measured parameters throughout the period the data was collected revealed a high correlation (R² = 0.82) (Figure 6). This correlation showed that the reliability of the simulated data for NSF-WQI calculation was high.

As mentioned above, wastewater is discharged into El Abid River, imposing major risks in terms of water quality. For this reason, wastewater treatment plants, among other solutions, were tested to assess their feasibility. Four scenarios were checked using various values of wastewater treatment efficiency (25%, 50%, 75%, and 100%, which represents full treatment of liquid discharge). Suitable solutions were evaluated in terms of success in improving water quality and minimizing costs.

Figure 6 Comparison between NSF-WQI calculated using simulated and measured data.

As shown in Figure 7, it is not possible to deliver complete wastewater treatment with 100% efficiency for the last two stations, P06 and P07, located at Oued Oum Er-Rbia, which could be explained by other (natural) factors involved in poor water quality (such as geological structures that are formed by evaporite rocks increasing the anion content of the water).

Figure 7 Observed efficiency of NSF-WQI evolution.

In terms of efficiency, the scenarios tested demonstrated that treatment of liquid discharges at the 25% level was insufficient to improve water quality in all sections of the watercourse. However, when the treatment levels exceeded 50%, the effects of liquid discharge noticeably decreased. As shown in Figure 7, the reduction in water quality deterioration by wastewater treatment plants with 50% efficiency was significant at P02, P04 (Tabia and Oued El Abid centre), while at P01, P05, P06, and P07 a 75% efficiency was required. Depending on climate conditions and the nature of the terrain, natural lagoons, associated low cost implementation and maintenance have proved effective in towns near the study area (Ait Ouhamchich et al. 2018b).

5 Conclusions

Simulation of chemical and biological processes by solving mass balance equations is an efficient tool that can help to predict water quality and in choosing suitable and relevant solutions to the challenge of improving water quality. This simulation process can reduce the analytical cost associated with each sample taken, and help decision-makers in choosing, planning, or optimizing such solutions.

Testing our simulation model on areas suffering from water quality degradation showed that the most sustainable protection method is to create at least three natural lagoon wastewater treatment plants with at least 50% efficiency for P02–P04 (Tabia and Oued El Abid centre), while 75% is the minimum treatment level required at the P06 site (upstream Oued Oum Er-Rbia).

Funding sources

No financial support was received for this research.

Conflict of interest statement

The authors declare that they have no conflict of interest.

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