I have some confusion on the calculation of unit weight (Wi) for each water quality parameter in the weighted arithmetic water quality index (WQI) method.
Is the figure attached here the correct way to calculate the unit weight of parameters? Can anyone please share some examples or references to the calculation?
You can see this paper for more details in calculations the WQI.
Article EVALUATION OF IRRIGATION WATER QUALITY INDEX (IWQI) FOR AL-D...
Well, a number of WQIs has been proposed by various developers and each of them has different calculation processes in terms of weightage, sub-index and aggregation which might be confusing you.
The image you shared giving a cue that you are trying to calculate WQI by "arithmetic mean method" and that formulation is absolutely correct. For your convenience, the attached file will assure you.
Hello Md. Aminul Islam Khan
See also attached PDF file
WQI was computed in the following four stages. At the first stage, each of the 10 parameters (TDS, pH, Ca2+, Mg2+, Na+, HCO3-, K+, Cl-, SO42-, NO3-) has been assigned a weight (wi) according to its relative importance in the overall quality of water intended for drinking purposes.
The maximum weight of 5 is given to: TDS and NO3-. At the second stage, the relative weight (Wi) for each parameter was calculated using Eq. (1):
📷(1)
Where Wi is the relative weight of each parameter; wi is the weight attributed to each parameter; and n is the number of parameters investigated.
At the third stage, the relative quality (qi) of each parameter was calculated using Eq. (2); accordingly, the value measured for each parameter in the sample was divided by the standard value of that parameter.
📷(2)
Where qi is the relative quality of each parameter, Ci is the concentration of each selected parameter from water sample in mg/L, and Si is the WHO’s standard for each parameter (mg/L). In the final stage of WQI, SI was determined for each water quality parameter by multiplying relative weight (Wi) with quality rating scale (qi). The sum of SI is equivalent to the water quality index.
📷(3)
📷(4)
The computed WQI were classified as follows: Excellent, (WQI < 50); Good, (WQI, 50-10 0); Poor, (100-200); Very Poor, (200-300) and >300 unsuitable for drinking water.
References
[1] Bouderbala, A. & Gharbi, B. Y. (2017). Hydrogeochemical characterization and groundwater quality assessment in the intensive agricultural zone of the Upper Cheliff plain, Algeria. Environmental Earth Sciences 76. doi:10.1007/s12665-017-7067-x.
Dear F. Bouteldjaoui
Thanks a lot for your answer. As you mentioned "At the first stage, each of the 10 parameters (TDS, pH, Ca2+, Mg2+, Na+, HCO3-, K+, Cl-, SO42-, NO3-) has been assigned a weight (wi) according to its relative importance in the overall quality of water intended for drinking purposes.", can you please specify is there any guidelines or standards to identify the relative importance of those parameters and assigning weights? How to chose a specific weightage for a parameter?
The weighting are documented. I suggest you read the papers by F. Bouteldjaoui Bayan Hussien Waqed Al-Mussawi and Avinash Kumar
Dear Joan Nyika,
Thanks for your reply. I have already read the papers by Waqed Al-Mussawi , Bayan Hussien , Avinash Kumar. Thanks a lot to them that their works helped me a lot to remove my confusion. The calculations of the WQI in my paper (attached) also is similar to them.
But now my confusion is that there are two ways of calculating weightage: one is to determine it form the procedure mentioned in my question and another one is to assigning weightage manually according to the relative importance of the parameters (like as F. Bouteldjaoui ). So, which one is more preferable? and how to define the relative importance of the parameters?
Conference Paper EVALUATION OF DRINKING WATER QUALITY IN TERMS OF WATER QUALI...
Like I said in my previous reply there are so many WQIs have separate ways to assign weights. Assigning and calculation depend on which WQI you gonna use. For example in NSFWQI weights for specific parameters (for 9 variables) were assigned by its developer and used as it is by other users.
Still, if someone wants to assign their own weights it requires the expert decision firstly to select effective variables and then weighing process of each variable depends on their relative importance to affect water quality. For this process, I'd like to suggest to go through original literature of that particular WQI.
Dear Md. Aminul Islam Khan , if we assign the relative weight via inverse of standard limit then that is more sensitive way of calculating WQI and would give us much more clear pic and would remove any ambiguity as the standard limits are much more reliable where as if we cal relative wts. based on expert opinion that would vary as we change the panel of experts.
@Md. Aminul Islam Khan
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