The Nemerow pollution index (NPI) for a quality parameter (say, air quality or water quality) is the substance ratio relative to an acceptable value, so NPI ≤1 is acceptable.  This is ambiguous, however, for parameters such as pH that do not vary linearly.  Water pH, for example, may change as a result of acid rainfall, but the response of pH is logarithmic relative to the stressor (acid).  In addition, the acceptable pH value is close to neutrality (pH = 7.0), so the NPI value (ratio of actual pH to acceptable pH) is unsuitable because it would form a curve rather than a straight line as one approaches neutrality from (say) below, and proceeds to values in excess of 7.0.

When one addresses multiple pollutants, a ratio is calculated for each pollutant.  An acceptable quality index, then, is achieved when the sum of all NPI values also is less than unity (NPI ≤1).  This would seem to represent a neutral weighting, or non-weighting, of individual pollutants.  One might infer that an exceedance of unity for zinc is just as 'bad' as an equal exceedance of unity for lead (Pb), but this depends entirely on the particular health effects that each pollutant might case.  The NPI is not entirely unweighted, however, because the acceptability values are (or should be!) higher for less toxic substances than for more toxic substances.

To improve the NPI, I have two suggestions.  The first is simply to improve the acceptability values.  Many highly toxic substances (example, perfluorooctanoic acid, PFOA) may lack acceptability values, or have inappropriately permissive values, or unenforceable guidance values.  A water quality index based upon an inappropriate acceptability value will be unreliable:  garbage in, garbage out.

My second suggestion is related to the first.  Specifically, one might apply acceptability values that relate to specific health effects, so that (say) drinking water quality might be judged relative to a particular health effect of interest.  That is, drinking water with too much lead (Pb) might pose neurological risks, but not cancer risks.  This strategy is standard in toxicological health risk assessment, in which a hazard quotient (HQ) value is calculated via an exposure level divided by an acceptability level.

When multiple stressors are being considered, each has an HQ value, and the sum of the values is the Hazard Index (HI), which is likewise acceptable if less than unity (HI ≤1).  Separate HI values may be calculated for separate health effects.  Standard setting for individual substances, of course, focuses (or should focus!) on the 'critical effect', that is, the health effect (among many) that can occur at the lowest exposure level.  Standards then are set based upon that critical health effect, with safety and uncertainty factors added as appropriate to the available database.

Thank you so much, Sir Robert! :) It definitely opened my thoughts on the "standards"/acceptability values of different elements. However, you focused more on health effects (which is great given that I may be able to use this someday in another environmental research), but can there be any acceptability values for uhh let's say a value that would be very detrimental to plant metabolism and growth? :) Thank you so much again, Sir Robert! :)

Thank you so much, Sir Kot! :) Although, may I ask why NPI is a baseless intention when it is actually used for research on pollution indices? In fact, it's usually utilized by (and even improved e.g. Nemerow's Synthetical Pollution Index, etc.) many Chinese researchers. :) But, that's quite interesting. What could make NPI baseless? 

Hi Enrico,

Your observation that I focused on human health is correct, as my main area is assessing risks potentially posed to public health by environmental and other stressors, such as Pb and PFOA that I mentioned.  Acceptability standards, however, also are promulgated for environmental effects.  In the U. S. (for example), the Environmental Protection Agency (EPA) is tasked by the Safe Drinking Water Act to issue acceptability standards ('criteria') for contaminants in drinking water, but the Clean Water Act does the same for ecological effects.  Indeed, the intent of Congress in passing this law was to make all navigable waters in the U. S. "fishable and swimmable."

When EPA proposes an acceptability standard under the Clean Water Act, the Agency also issues a detailed support document ('criteria document') that explicates effects potentially posed by the substance on a wide range of organisms and also ecosystems, as substances may exert effects at the population and/or at the community level even when effects on individual organisms are not evident.  Such effects may become evident only when the organisms already are stressed by competition with conspecifics and with other species in a resource-limited environment, as is typical in nature.

In my view, as I highlighted in my earlier response, two problems exist:  too few substances are addressed by acceptability standards, and existing standards may be too lax; indeed, most probably are outdated!  This is NOT a criticism of the NPI approach, only of its (all too common) implementation in the face of inadequate data.

Very concise and abundantly helpful for my thesis proposal. :) Thank you so much, Sir Robert! :) Will be able to use what you've taught me when I get to Medicine. :)