Performance, compliance and reliability of Waste stabilization pond: Effluent discharge quality and environmental protection agency standards in Ghana

: Measuring performance has been arguerably, one of the metric with many facets with different school of thoughts, as there exist different approaches of measuring it. Several of the existing approaches measure such metric by comparison with standards esherined in policy documents and as a result, takes less look to its compliance and reliability of values being matched to an established standards. This study seeks to integrate reliability and compliance into measuring of performance of Waste Stabilization Pond (WSP) and Treatment Plant (TP) as well as to generate the appropriate standard chart tables using the Ghana Environmental Protection Agency (EPA) approved discharge values for physico-chemical and some biological parameters to account for these shortfalls on over reliance of EPA discharge standards. Probability distribution density function was applied on the lognormal distribution function to establish the relationship between the statistical coefficient of variation and the coefficient of reliability based on r th moment about the origin in the moment of generation function to generate the functions of the mean and standard deviation, properties of the standard Z normal distribution were used to establish the coefficient of reliability relationship depending on the coefficient of variation influenced by the standard of deviation. Discharge values of Physico-chemical Parameters measured from the WSP were found be performing acceptably based on the EPA standards, whereas only four of the TP were acceptable. Discharge Values of physico-chemical and biological parameters which are found to be accepted under comparison with EPA standards were found to have compliance levels below what is generally accepted for Waste Stabilization Ponds (WSP) designed compliance. Based on these shortcomings, reference charts were develop to serve as reference points in assessing the various characteristics of compliance and performance of WSPs in Ghana on (28) physico-chemical and biological parameters. These charts are intended to make it easier to assess the performance of WSPs and its corresponding reliability and compliance level to compensate for overreliance on EPA standards alone.


INTRODUCTION
The use of Waste Stabilization Ponds (WSPs) as an economical and efficient way of re-cycling water has taken centre stage for the use in agricultural production over the past two decades, it's been noted that, WSPs are usually the most cost effective procedure in dealing with domestic and municipal wastewater treatment for agricultural purposes in Africa due to the condition of favorable climate and low cost of maintenance (Mara, 2004), which are very important factors for tropical countries such as the sub-Saharan Africa.
Owing to the natural process of treatment of water in WSP, the treatment processes are highly dependent on the physical design of the WSPs; conversely these physical designs do not consider the ecological process, which takes place in the system. Purposefully, WSP consist of anaerobic ponds, facultative and maturation ponds in series, or several of these maturation series ponds in parallel (Gawasiri, 2003;Mara, 1996Mara, , 2004 with each having a specific purpose, though they sometimes overlap. Specifically, facultative ponds are needed for the removal of Biochemical Oxygen Demand (BOD 5 ) when the effluent is meant for restricted irrigation and fish pond fertilization as well as for the discharge of treated water into surface water. For unrestricted irrigation, maturation ponds are needed for the removal of pathogen in order to meet the WHO standard of '<1000 fecal coliform bacteria per 100 mL' (Mara, 2004;WHO, 2006).
Several studies (Haydeh et al., 2013;Shah, 2008;Oliveira and Sperling, 2008;Mbwele et al., 2003) have evaluated the performance of the WSPs by comparing the percentage of removal of Biochemical Oxygen Demand (BOD 5 ), Total Nitrogen (TN), Total Suspended Solids (TSS), Total Phosphorus (TP), Total Coliform (TC), Faecal Coliform (FC) and Salmonella with design standards, with few focusing on the extend of compliance of the ponds to its design standards. However, few works (Redda, 2013;Oliveira and Sperling, 2008) have compared the percentage of removal of the parameters of evaluation performance of WSPs to the compliance and reliability of the WSPs according to the standards set up by the local policy. However, Oliveira and Sperling (2008) mainly conducted the reliability concentrated on different treatment plants by comparing their reliability level of which a real WSP was excluded. Based on the shortcomings of over relying on EPA standards without due inclusion of compliance level of WSP and treatment plants, performance short fall of accounting for compliance and hence underestimate the effluent discharge values deemed to be acceptable. This study seeks to integrate reliability and compliance into measuring of performance of WSP and treatment plant as well as to generate the appropriate standard chart tables using the Ghana EPA approved discharge values for physico-chemical and some biological parameters to account for these shortfalls on over reliance of EPA discharge standards.

LITERATURE REVIEW
Statistical effluent data distribution: Exploratory Data Analysis (EDA) gives overview of how data analysis is done, by first fitting the appropriate distribution to describe the data through making distributional assumptions about the data (Thode, 2002); this could be done by plotting the dataset and finding the classical or traditional distribution, which fits the dataset. Most statistical tests assume data to be normally distributed (Ott, 1995), but this is not necessary true. Failing to understand the appropriate statistical distribution of data may lead to invalid assumptions and consequently incorrect conclusions (Thode, 2002). Several studies Niku et al., 1979Niku et al., , 1982Oleiveira andSperling, 2006, 2008;Redda, 2013) have all reported that, lognormal distribution gives a good overall fit to effluent values, but there are some cases where neither normal nor lognormal seems to approximately fit the distribution of the observed data, in such cases the distribution of effluent values should be treated independently to fit its own distribution as such (Niku et al., 1979). Niku et al. (1979) and Hovey et al. (1977) developed a linear model through the use of simple regression analysis to determine the percentile values for the distributions of effluent parameters concentrations exceeding various percentages of the time related to the mean values. Their approach could be used if the effluent concentration is not known or does not follow a classical distribution function.
Recent work by Redda (2013) attempts to use the logistic regression model to find the level of compliance as a function of other independent parameters of the treatment plants which influences the parameters of measuring performance and give rise to the reliability level without using the distribution function of effluent concentration. Oliviera and Sperling (2010) explained that due to variation in performance, treatment plants should be designed to produce effluent quality below the discharged standards. This suggests a mean value should be used to guarantee an effluent concentration consistency and which should be less than standard with a certain reliability and compliance level. To meet such high standards especially with WSPs which do not have any adjustable controls once in operation, the onus is placed on the design stage and regular maintenance; hence design engineers must be able to estimate the expected effluent quality and its variations for a given time as well as know the efficiency of each WSP portions. Besides, Mbwele et al. (2003) and Redda (2013) concluded that, care should be taken in the interpretation of performance data, as some performance variations likely result from biotic and abiotic factors other than design standard values alone.

Process of reliability:
Several studies have defined reliability as the ability to perform the specified requirements free from failure (Niku et al., 1979); e.g., the percentage of times a wastewater treatment plant complies to discharge standards (McBride and Ellis, 2001;Smith et al., 2001). The WSPs will be completely reliable if the process performance does not violate the target standards of the regulatory bodies specifications (Oliveira and Sperling, 2008), Hence mathematically: Due to the numerous uncertainties underlying the design and operation of a wastewater treatment plant, a risk of failure is always unavoidable and the wastewater treatment plant should be designed based on an acceptable risk or degree of violation. Hence the mean operational effluent quality and the coefficient or reliability developed by Niku et al. (1979) is based on the assumption of the lognormal distribution to assess the reliability of the treatment plants. The minimum reliability requirements must be determined to establish the failure-probability magnitude that can be accepted'. Niku et al. (1979) model as follows: By Eq. (1) and (2) becomes: The lognormal distribution owning to deviation in symmetry measured by the skewness coefficient, has positive skewness since there is usually a lower bound for effluent concentration, but there are no upper bounds: The probability density function of the lognormal distribution of effluent quality is given as: where, X = Effluent variable concentration σ = Standard deviation of the natural logarithm of X m = Median of X For the J moment of about the origin in the moment generation function: Hence: where, ˭ and $ represent the mean and variance of the original data, respectively from the moment function. Re-arranging Eq. (6) and (7) accounting for the relationship of parameters of probability density function of lognormal distribution in terms of moment of variable I are: where, ˭ is the average natural logarithm of X. For some probability of failure at , the lognormal distribution will have a property of I, thus: where, I is the effluent concentration standard fixed for policy assessment. Hence choosing the parameters of the lognormal distribution, Eq. (10) becomes: The standard I normal distribution can also be defined from Eq. (10) as: Hence at a reliability level of 1 − of a failure level of , a known standard of effluent concentration level could be calculated given a coefficient variation, the I # values were obtained using the NORMDIST function in Microsoft excel (Table 1) for the cumulative probability at 1 − and its percentiles. It should be noted that, the higher the normal variate value the higher the corresponding compliance level (cumulative probability) hence by Eq. (8) and (9) into (11) results in: Making the mean value the subject of Eq. (13) results in the following: By simplification, Eq. (13) results: The statistical parameters used in the reliability to relate the mean constituent value ˭ to standard I defines the Coefficient of Variation (CV) as ˢ : From Eq. (14), hence Coefficient of Reliability (COR) is given as:    (17) Putting Eq. (16) into (17): The ˕˛˞ values are obtained as a function of coefficient of variation and reliability level (Table 2), the different values of the coefficient of variation suggests the different mean and standard deviation parameters of measuring reliability might produce of which are mainly less than 1.0 in practices (Niku et al., 1979;Oliveira and Sperling, 2008). Hence by Eq. (18) into (14) simplifications becomes: where, I = The effluent quality standard ˕˛˞ = The coefficient of reliability ˭ = The mean effluent concentration needed to achieved a certain compliance level of effluent quality standard Study site and data: Data was obtained through two separate studies on each of the two different sites, all the sites are located within the Kumasi metropolis which is located latitude (6°35' to 6°40'N) 1'30 W and on longitude (1°30' to 1°35') 60 W, 40 N. It has a climate which falls within the wet sub-equatorial type with an average minimum temperature of 22.5°C and a maximum average of 30.7°C. The two study sites were the KNUST treatment plant and Ahinsan WSP. The KNUST treatment plant was constructed to receive wastewater from residential facilities within the university campus and its design was based on the conventional designs of WSPs. The Ahinsan Estate WSP was designed to receive wastewater from the residential areas which includes Ahinsan and Chirapatre estates.

EPA's discharge standards used in the study:
The Ghana Environmental Protection Agency discharge standards were adopted for the Coefficient of Reliability (COR) study, the parameters included (Table 3) correspond to other developing countries standards which are considered as more realistic as well as areas which falls within the tropical regions such as Brazil and elsewhere (Oakley et al., 2000;Ragas et al., 2005;Oliveira and Sperling, 2006). These standards are set as local guideline for discharge of effluents into either stream for irrigation or for replenishing aquifers.

RESULTS AND DISCUSSION
Reliability and compliance: Two statistical parameters characterize the Coefficient of Reliability (COR) the mean and the standard deviation. These two values determines the nature of the coefficient of variation and hence influences the COR express. As presented in several studies (Niku et al., 1979;MetCalf and Eddy, 2003;McBride and Ellis, 2001;McBride, 2003;Olieveira and Sperling, 2008;Oakley et al., 2000;Redda, 2013) the COR tells the values of the mean design concentrations to the standard that should be achieved, on a probability basis according to the desired level of the operators of the treatment plant, while the standard normal variate calculates the expected percentage of compliance with the discharge standards.
The expected percentage of compliance can be used to access the performance of the different segment of the plant as well as for the overall performance, which helps to identify critical points of malfunction i.e., points out discharge standards having unexpected values according to design parameters.
Various standard values of the EPA Ghana were used to find the different compliance level given different levels of coefficient of variation. Twenty eight parameters were selected to develop a reference chart (See baxzes for charts) and used to ascertain the level of compliance at different CVs. Result of effluent discharge performance are much to be desired when the effluent discharge is compared to the fixed standard value only and where it is assume that if the discharge concentration is less than the standard value, the performance is good and indicates a better compliance level of the WSPs. However as shown in the reference chart (See baxzes for charts), such assumption is not always true.
For example, the required standard of effluent discharges concentration of BOD 5 or TSS is 50 mg/L (EPA, Ghana Standard). If a sample taken from a specified WSP gives a mean effluent quality of 48.00 and with standard deviation of 14.4 will have a CV value of 0.3, by referencing to Chart 1 (See baxzes for charts) corresponds to a compliance level (COR) of 60% i.e., less than the required less stringent compliance level of 80% for WSPs (Oliveira and Sperling, 2008;Redda, 2013), This is despite the fact that the mean effluent concentration from the WSP as compared to the EPA standard falls below the standard value of 50 mg/L and can be classified as a good discharged value. Nevertheless, the WSP is underperforming, its effluent discharge value is just less than that of a compliance level of 60%, hence its compliance level is below what's generally accepted (even in a less stringent level of 80%), such information, if available can trigger a further check to be done to identify the segment of the pond (Anaerobic, facultative and maturation) that is underperforming, which could support the routine maintenance of the ponds.
The same procedure could be used by comparing the expected mean effluent concentration of the segments of the pond to its samples using its design compliance and hence finding the compliance level of effluent to check for malfunctioning of pond segments, this is necessary due to the different expected work to be done by each segment to enhance the maintenance of the ponds regularly, Nonetheless, a critical look should be taken because CV values directly relate to reliability and inversely to COR values, hence CV value with high standard deviation and lower mean of an effluent can have the same value as a CV of high mean and low standard deviation value of an effluent, the later shows a more consistent discharge. This shows that, a lower value of CV does not necessarily indicate better results.
Moreover, with the use of the charts (See baxzes for charts) for various parameters of WSPs in Ghana, once an effluent concentration average is known and its compliance level at design is also known, a quick reference point can be made to find what was expected to be discharging and compare to its current discharge to be assure of its compliance without necessary   comparing it to fixed standard values, due to the unaccounted for information on compliance the EPA fixed standard gives, These reference charts were develop to serve as reference points in assessing the various characteristics of compliance and performance of WSPs in Ghana. These tables are intended to make it easier to assess the performance of WSPs and its corresponding reliability and compliance level without going through the task of using the log-normal procedure as shown above.

Performance analysis:
The influent and effluent conditions of the different pond cells or portions of water quality in terms of physical parameters (Table 4), chemical parameters (Table 5) and biological parameters (Table 6) of the Ahinsan WSP are given below. The physical condition performance (Table 4) in terms of removal percentage were as follows; conductivity (52.15%), total dissolved solids (53.43%) and total suspended solids (71.83%) in the anaerobic pond, the facultative pond continued the removal efficiency of the physical parameters except for temperature which recorded negative percentage (-0.38) indicating a temperature rise from the anaerobic pond into the facultative pond and a continued rise in the maturation pond as well. However, the rise in temperature was insignificant and fell within the level essential for algae growth. Moreover, TSS also increased in the maturation pond as well. Notably, the cumulative efficiency removal was high for both anaerobic and facultative ponds which are specially designed to remove most of the physical properties WSPs (Mara, 2004). Nevertheless, the maturation pond also helps in the reduction of all of the physical parameters of the Ahinsan pond with the exception of the temperature, pH and TSS. The chemical parameters saw an efficient removal in the anaerobic and facultative ponds and most of the removal was done before the effluent entered the maturation pond. TP increased in the facultative pond, but declined in the maturation ponds I and II, On the other hand, dissolved oxygen removal was predominant only in the anaerobic pond, whereas the DO content increased in the maturation pond, leading to the recording of negative percentage. This is due to the high removal activity in the anaerobic pond (78.57%) whereas microbiological activities in the other ponds use oxygen due to the algae growth. The nitrate family continued to decline, indicating that there was no limitation to nitrification in the Ahinsan Estate Pond. On the biological parameters (Table 6) BOD 5 and COD efficiency of removal was very high in the anaerobic pond as well (82.85 and 79.96%, respectively). This removal efficiency was also evident in the facultative pond and maturation pond I. In maturation pond II, a reverse efficiency was recorded, confirming that the anaerobic and facultative ponds are essential for the removal of (TN, TP, BOD 5 , COD, Conductivity, pH), whereas the anaerobic pond is essentially for DO. The E. coli and TC were having a high efficiency of removal in the anaerobic pond and the TC increased further in the facultative, but increased considerably in the maturation ponds resulting in negative percentages. Still, the overall removal efficiency was high.
In respect of the KNUST plant, the physicochemical parameters (Table 7) showed a continuous removal of BOD 5 , TN, TP, TSS, TURB, pH and Temperature, indicating that the BOD 5 content declines as the wastewater passes through the primary chamber up to the secondary chamber from which wastewater can be used for restricted irrigation. The percentage efficiency of the removal trend was not different from the Ahinsan WSP, though the latter has higher percentage removal.
The average values of removal efficiency percentages of the physical, chemical and biological parameters of the Ahinsan plant as well as the physico-chemical parameters of the KNUST plant are all presented in the respective Effluent discharge and EPA standards: From the comparison of the various discharge qualities to the standards of EPA, it is very evident that, some of the parameters for the KNUST plant do not conform to EPA standards (Table 8). Though some exceptions like the temperature (24.66), TN (10.83), TC (79.69), pH (6.78) and turbidity (59.69) level, which recorded a lower discharge values than the EPA standard, all other parameters such as TSS (51.53), TP (12.2), BOD 5 (81.75) and E. coli (26.50) were higher than the standard. In contrast, the Ahinsan WSP was performing better in terms of discharge values than the KNUST plant. This WSP had most of its effluent discharge values lower than the EPA which included; temperature (26.6), pH (7.3), TN (0.01), Ammonia (0.36), BOD 5 (38), COD (99), Conductivity (484), TDS (242). The performing discharge values of the Ahinsan WSP is attributed to some form of maintenance during the trial work of aqua-culture in the ponds, whereas, the KNUST plant did not receive any form of maintenance over quite a number of years, which can explain its under-performance.
Compliance and reliability analysis: EPA's discharge standards to be achieve in operation concentration: The current reliability of the KNUST treatment plant and Ahinsan WSP (Table 9)        COD,95.2% and TDS,98.%) conforming to the standard compliance of 95% compliance and achieving its observed effluent discharge being less than the mean design concentration with the required compliance level (Table 10), whereas the rest were not complying with the design compliance level. These included; Temperature (69.5%), pH (48.0 to 74.2%), TSS (64.1%), TP (8.4%), BOD 5 (77.3%), DO (74.9%), TC (0.00%) and E. coli (0.00%). Again, temperature, pH, BOD 5 , conductivity and DO effluent discharge meet the EPA standard but its compliance level does not meet the design specification.

CONCLUSION
From this study, it was observed that, measuring performance of WSP and treatment plants using effluent discharge values in a comparison to standards alone is sufficient only for knowing effluent quality but cannot be used to evaluate compliance of the WSP or treatment plant. It is evident that compliance because it considers both effluent quality discharge as well as design capability in its performance measure is more appropriately than the use of removal efficiency and fixed standard values alone. In this study, we developed reference charts (Table 1 to 3: Supplementary Results) which can be used for assessing effluent discharge qualities. These were done for different compliance levels from the Ghana EPA standard discharge values. Nevertheless, the importance of a stable operation and thus low CV should be remembered at all time, so that the WSP or treatment plant should not need to be designed to achieve very low mean effluent concentration. The effluent discharge values of the sites used for the study were not complying fully with the design specification (for the less stringent specifications of WSP and treatment plant). However, the Ahisan WSP had some of its water quality parameters (TN, Ammonia, TDS and COD) meeting both the compliance level of 95% and the EPA discharge standards. However, irrespective of the presence of two maturation ponds in series for the Ahinsan WSP, it could not meet the pathogen reduction standard values expected.