The Introduction to the Water Quality Index
Expressing water quality information in a format that is simple and easily understood by common people
Wednesday, August 31, 2011
By Harbans Lal
Water Quality Definition and Importance
Water quality is the condition of the water body or water resource in relation to its designated uses. It can be defined in qualitative and/or quantitative terms. Parameters in defining water quality can be grouped into three board categories: physical, chemical, and biological. Physical factors include temperature, sediment and bed material, suspended sediments, turbidity, color, and odor. Chemical factors consist of the major and minor elements, and other chemical parameters such as pH, Dissolved Oxygen (DO), Biological Oxygen Demand (BOD), and Chemical Oxygen Demand (COD). The major elements include agro-nutrients such as Nitrogen and Phosphorus; and minor elements include elements such as arsenic (As), lead (Pb), and mercury (Hg), etc. Biological Constituents include Fecal Coli-form and E. coli. Conventionally water quality is expressed in terms of the measured value(s) of one or more of these parameters in relation to their accepted or implied limits. They are expressed in different units, and their magnitudes can vary significantly from one location to another and over time. For example, the temperature is expressed in degrees Celsius or degrees Fahrenheit, and coliforms in numbers, and most chemicals and nutrients in milligrams per liter (mg/L) or in parts per million (ppm).
The conventional approach of expressing different parameters of water quality in varying units is well accepted by water resource experts. However, it is not readily understood by the general public and policymakers who have profound impact on water resource policies. Thus, the need for expressing water quality in a format that is simple and easily understood by common people has been recognized for a long time. Experts have worked internationally—including in the United States—for the past several years and have designed the term Water Quality Index (WQI). The WQI takes the complex scientific information and synthesizes into a single number between zero and 100, by normalizing the observed values to subjective rating curves. It summarizes the relative changes in the underlying group of the water-quality variable.
WQI is easily comprehended and appreciated by common citizens and policy makers. It can also help in meeting regulations and/or making personal lifestyle adaptations for the benefit of the environment. Several organizations in the United States and around the world including United Nations have adopted the WQI concept for expressing the water quality (OR-DEQ 2008, OR-DEQ 2008a, Hallock 2002, CCME 2001, and UNEP 2007) for their water resources.
This paper elaborates on the WQI concepts and reviews different WQI models from the literature. It also presents a case scenario of calculating WQI using different models with an example dataset. All these WQI models have been developed for flowing or standing water resources such as lakes, rivers, streams, and such. There is no reference in the literature for WQI for the runoff water from agricultural fields. The paper also emphasizes the need for developing such a WQI model which could be used for evaluating the effects of agricultural management and conservation practices on private lands supported and cost-shared by the US Department of Agriculture/Natural Resources Conservation Service (USDA/NRCS).
What Is WQI?
WQI is a dimensionless number that combines multiple water-quality factors into a single number by normalizing values to subjective rating curves (Miller et al. 1986). Factors to be included in WQI model could vary depending upon the designated water uses and local preferences. Some of these factors include DO, pH, BOD, COD, total coliform bacteria, temperature, and nutrients (nitrogen and phosphorus), etc. These parameters occur in different ranges and expressed in different units. The WQI takes the complex scientific information of these variables and synthesizes into a single number. Several authors have worked on these concepts and presented examples with case scenarios (Bolton et al. 1978, Bhargava 1983, House 1989, Mitchell and Stapp 1996, Pesce and Wunderlin 2000, Cude 2001, Liou et al. 2004, Said et al. 2004, Nasiri et al. 2007, NSF 2007).
WQI Development Process
The process of developing a WQI involves the following steps:
- Identify water quality parameters of interest and their ranges of acceptability for the intended uses of the water body.
- Compare the measured value with the subjective rating curve and arriving at a dimensionless sub-index value (0–1) for each parameter.
- Define the weighing factor and/or heuristics for each parameter to be considered while building an overall WQI.
- Select an algorithm and computing the WQI with the available data and assumptions.
A number of algorithms (models) for calculating WQI have been developed and reported in the literature. Some of these include:
a) Weighted arithmetic mean (Cude 2001)- In this model, different water quality components are multiplied by a weighting factor and are then aggregated using simple arithmetic mean (Equation 1).
Equation 1: 
Where WQI = Water Quality Index
SIi = Sub-index i
n= number of sub-indices
Wi = Weight given to sub-index i
b) Weighted geometric mean (McClelland 1974)- Similar to arithmetic weighted mean, each water quality component is weighted by a power factor, and then WQI is calculated using the geometric mean procedure (Equation 2).
Equation 2: 
Where WQI = Water Quality Index
SIi = Sub-index i
n = number of sub-indices
Wi = Weight given to sub-index i
c) Un-weighted harmonic square mean (Dojlido et al. 1994 cited by Cude 2001)- This model is considered an improvement over the weighted arithmetic mean and the weighted geometric mean. This allows the most impaired variable to impart the greatest influence on the water quality index and acknowledges that different water quality variables will pose differing significance to overall water quality at different times and locations (Equation 3).
Equation 3: 
Where WQI = Water Quality Index
SIi = Sub-index i
n = number of sub-indices
Wi = Weight given to sub-index i
d) Using the fuzzy logic model (Lermontov et al. 2009 and Nasiri et al. 2007)- This model employs artificial intelligence (AI) concept and helps capture uncertainties and inaccuracies in knowledge data. It can represent qualitative knowledge and human inference process—quite common in expressing water quality parameters—without a precise quantitative analysis. This approach, as demonstrated by Lermontov et al. 2009 and Nasiri et al. 2007, presents the following advantages over the conventional numerical process:
1. Ability to capture large variety of non-linear relations
2. Easily adoptable to local conditions
3. Could be interpreted verbally
4. Could include information that other methods cannot include such as individual knowledge and experience
5. Possibility of enhancing the results by combining qualitative information with the quantitative data that expresses the ecological status of the water body
6. Better handling of situations with missing data without affecting the results significantly
e)Baseline comparative model (UNEP 2007)- This model compares water quality observations to benchmark values of different parameters instead of normalizing observed values to subjective rating curves. The benchmark values may be derived from national, state, or local water quality standards, or site-specific background values. The Canadian Council of Ministers of the Environment (CCME) used this approach for their model known as Canadian Water Quality Index (CWQI). The Global Environmental Monitoring System (GEMS)/Water Program of the United Nations Environment Program (UNEP) adopted and used the CWQI model for evaluating the quality of drinking water around the globe (UNEP 2007).
The CWQI (Equation 4) incorporates three elements:
1. Scope—number of variables not meeting water quality objectives (Equation 4a),
2. Frequency—the number of times these objectives are not met (Equation 4b), and
3. Amplitude—amount by which the objectives are not met (Equation 4c).
Equation 4: 
Where WQI = Water Quality Index
F1 represents Scope: the percentage of parameters that exceeds the guideline (Equation 4a).
F2 represents Frequency: the percentage of individual tests within each parameters that exceeds the guideline (Equation 4b).
F3 represents Amplitude: the extent (excursion) to which the failed test exceed the guideline which includes a three-step process for calculation (Equation 4c).
Equation 4a: 
Equation 4b: 
Equation 4c: 
Where nse (Normalized sum of excursion) is expressed as:
and
-1
Where failed test value is greater than the objective value, for cases where test value must not fall below objective value, then
-1
Similar to other WQIs, this model also produces a number between zero (worst water quality) and 100 (best water quality). In this case, the index is flexible in terms of the benchmarks that are used for calculations, and depends on the information required from the index. For example, guidelines for the protection of aquatic life may be used (when available) if the index is being calculated to quantify ecological health of the water, or drinking water quality guidelines may be used if the interest in the index is in drinking water safety.
The CCME WQI has been widely used in Canada. It has also been adopted by the UNEP for evaluating the quality of water in different countries around the globe. This model expresses well when a history of monitored data for different water quality parameters is available. It is recommend that at a minimum four variables sampled at least four times be used in calculation of the index for this approach (CCME 2001).
Examples of WQI Calculation
The CCME Water Quality Index User’s Manual (CCME 2001) presents a dataset for demonstrating their procedure. We used their dataset (Table 1) for demonstrating WQI calculation procedures of different models. The CCME dataset contains observations on 10 parameters for the North Saskatchewan River at Devon, Alberta, in Canada, for the period of one year (1997). Most variables were sampled on monthly basis with one missing observation for mercury, and quarterly observations for pesticide (2,4-D and Lindane). The parameters included are: dissolved oxygen (DO), pH, total phosphorus (TP), total nitrogen (TN), fecal coliform (FC) bacteria, arsenic (As), lead (Pb), mercury (Hg), 2-4-D, and lindane.
Table 2 presents the CCME-WQI calculation for two scenarios. The first scenario deals with the complete dataset of 103 observations presented in the CCME-WQI manual (CCME 2001). It is the exact reproduction of the example in the CCME manual. The second scenario is with the reduced dataset of 60 observations for five parameters (DO, pH, TP, TN, and FC). They were selected to demonstrate WQI calculation with other models such as OR-DEQ model. We used the subjective rating curves and sub-index algorithms from Cude 2001 to analyze annual averages of the five parameters for calculating WQI using other models.
Table 3 presents annual averages, ranges, SI-logic (algorithms), and calculated sub-index for each of the five parameters of the reduced dataset. This table also presents the calculated values of SI*Wi, SI^Wi, and 1/SI2 for the three WQI models: 1) weighted arithmetic mean (Equation 1), (2) weighted geometric mean (Equation 2), and (3) un-weighted harmonic square mean (Equation 3). Table 4 shows the WQIs and their qualitative ratings (Excellent, Good, Poor, etc.) based on different models. All these values were calculated using the reduced dataset expect for the CCME-WQI, which was calculated both for the complete and reduced dataset.
The WQI using CCME approach remains almost same (88) both for the complete and reduced datasets—classifying the water as “Good.” On the other hand, the WQIs based on the Oregon DEQ models for the three equations are around 95, thus classifying the water as “Excellent.” It implies that the OR-DEQ model is more liberal than the CCME model. However, it is not the intent of this exercise to evaluate different models, but rather to demonstrate the procedure for calculating WQI using different models.
Interpreting WQI and Its Advantages and Limitations
The WQI synthesizes complex reality of multiple water quality parameters into a single value that can be appreciated and understood by common man. The single WQI number ranges between zero and 100. It expresses water quality where a higher number indicates better water quality. For example, Oregon DEQ models (Cude 2001) score water as:
- very poor for WQI less than 60
- poor for WQI between 60–70
- fair for WQI between 80–84
- good for WQI between 85–89
- excellent for WQI between 90–100
These indices are considered trustful. However, the possibility of some parameters having disproportionate influence on the final results producing a biased index always exists. Thus, a thorough review and considerations to the weighing factor for each parameter should be discussed and well documented with experts and stakeholders of the water resource. The WQI aids in assessing water quality for general purpose. To determine the suitability of the water body for a specific usage, it should be combined with other appropriate information.
WQI for the Agricultural Field Use
Within the US Farm Bill provision, the USDA/NRCS provides technical assistance and financial assistance (cost share) that enable agricultural producers to be good stewards of the Nation’s soil, water, and related natural resources on non-federal lands. One of the key goals of implementing conservation practices is to maintain and improve water quality within the watershed.
The NRCS is always looking for approaches and techniques to evaluate the effects of its programs on the environment including water quality. The Conservation Effects Assessment Project (CEAP) is an example of such as program (USDA/NRCS 2011). The WQI could serve as a simple first-step tool for such an evaluation process for improving and/or sustaining the quality of water in the watershed. However, the structure and components of the WQI models discussed in this paper would need to be modified for it to be appropriate for the runoff from agricultural fields. Efforts are underway by the National Water Quality and Quantity Team of the NRCS/USDA to develop such a WQI model—referred to as WQIag.
Concluding Remarks
Similar to other indices such as Dow Jones Industrial Index, the WQI takes information from a number of sources and combines them into a single number that represents an overall snapshot of the quality of the water at a particular time and location. There is some debate as to which parameters (measures) should be included in the derivation of such an index; however there is general agreement that WQI is a useful tool for comparing water quality across water systems and over time. It can also answer to questions such as: “Can I eat the fish, drink the water, or swim in it without fear?”, in common man terms. The simplicity of WQI in expressing the water quality would be much more appreciated by farmers, the common public, and the policy makers. The WQIag, when developed, could serve as a benchmark for evaluating success and failures of management strategies, and help answer questions such as how effective a conservation practice has been in improving the water quality in the watershed. It could even inspire farmers to serve as better stewards of the conservation practices because they can easily understand its impacts.
Author's Bio: Harbans Lal is an Environmental Engineer for the National Water Quality and Quantity Team at the West National Technology Support Center, NRCS/USDA in Portland, OR. |
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