Appendix B – QIP Caclulation Methods

Before Reading this Appendix

We highly recommend reading QIP Visual Explanation to get a better overview of the Quality Impact Percentage – what it is and how it is calculated.

Data Collection

  1. We compiled datasets on water quality from NOAA’s National Oceanographic Data Center (NODC) website (Teruya and HIDOH 2010) and from the HIDOH Clean Water Branch website for the island of Maui for all available years. http://emdweb.doh.hawaii.gov/CleanWaterBranch/WaterQualityData/default.aspx
  2. We sorted the data by collection site and then by sample date. When we began our analysis of the dataset, the dates were November 1, 1999 to October 31, 2015. However, due to the limited number of samples before 2004, those data were not included in the paper before this date, but are presented in this appendix.
  3. We grouped the data into one year periods beginning on November 1 and ending on October 31. For example, November 1, 2011 to October 31, 2013 is the time period forming the basis for the 2014 STATE OF HAWAII WATER QUALITY MONITORING AND ASSESSMENT REPORT (WQMAR), so two years of our data would span that single reporting period.
  4. We further broke down the data into groupings for the wet months, November through April, and the dry months, May through October. These are the groupings referred to in the following steps.
  5. Within these groupings we calculated the geometric mean for the reported water quality (WQ) values. This resulted in one geometric mean for the wet months in each one year period, and one mean for the dry months in each one year period. See Table B1-6, columns labeled GM.
  6. According to the classification of each site (Bay, Coastal, or Estuary) we compared the geometric mean to the applicable standards as given in the Hawaii Administrative Rules. See Table 1 in the main text for the Coastal standards, or it is also available in Appendix C. For example, the Geometric Mean Standard (GMS) for TN (Table 1) is 150 µg N/L in the wet season and 110 µg N/L in the dry season.
  7. We counted the number of samples in each grouping that exceeded the Geometric Mean Standard, the 10% Statistical Threshold Value (STV), and the 2% STV. We also noted the minimum and maximum values within the grouping. See Appendix B Data.xls.
  8. Cross-referencing the sample’s Station Number (Site Number) and Station Name with the various DOH Water Quality Reports to Congress we were also able to determine the reported status for the groupings. The DOH reports “A” for Attained WQS, “N” for Not Attained WQS, and in recent years they sometimes reported “?” if there was no determination. If a site and/or season was not reported then we assigned a “U” for unreported (HIDOH 2002, 2004, 2006, 2008/2010, 2012, 2014).
  9. To facilitate a qualitative estimation of which sites were most and least impacted we generated a Quality Impact Percentage per season (sQIP) for each WQ value for each grouping (Tables B1-B6, columns labeled sQIP) using the following formulas.

Formulas and Calculations

Individual QIPs Formula
GM QIP = 100*GM/(GMS) [1]
n > GMS QIP = 100*(n > GMS)/(0.5 *number of samples) [2]
n > 10% STV QIP = 100*(n > 10% STV)/(0.10 * number of samples) [3]
n > 2% STV QIP = 100*(n > 2% STV)/(0.02 * number of samples) [4]
sQIP = ([1] + [2] + [3] + [4]) / 4 [5]

For both the wet season and dry season the impact percentages for the six WQ values (sQIPs) were averaged together to calculate a Qualitative Impact Percentage for each WQ value for the site for that season. These averages are displayed in Table 2 of the main text, columns labeled TN, TP, NO3+NO2, NH4, Turbidity, and Chlorophyll a. Next, the QIP for each season was calculated as the average of all the WQ values (Table 2, column labeled Mean QIP). Finally, if desired, a QIP for the year can be calculated as the average of the two seasonal QIPs (not shown).

Explanation of Formulas and the STV

To understand the first four formulas used to calculate the QIP it is helpful to think in terms of how the water quality standards were arrived at in the first place. Imagine taking a large number of water samples from a body of water that is as dirty as possible while still being minimally acceptable. If these samples were normally distributed the frequency of values would form a bell shaped curve. (To use QIP techniques on data which fit some other distribution, such as exponential, first use standard statistical techniques to scale and shift the distribution into normal form.) The center of the curve, the high point, would correspond to the Geometric Mean Standard (GMS). Roughly 50% of the sample values would be expected to fall on either side of the GMS. On the far right shoulder of the bell shaped curve, a vertical line could be drawn so that 90% of all sample values would be to the left of the line and 10% would be on the right. The value at the point where this vertical line is drawn is the 10% Statistical Threshold Value (STV). Similarly, a 2% STV can be determined.

A large number of samples from a clean body of water would yield a bell shaped curve shifted to the left of the curve used for determining the standard. The GM for the clean water would be lower than the GMS. Fewer than 50% of the samples would be greater than the GMS. Fewer than 10% of the samples from the clean water would exceed the 10% STV. Likewise for the 2% STV. Using Formulas [1] through [4] on this set of samples would yield numbers less than 100 for each formula, and the resulting QIP would be less than 100.

Conversely, a large number of samples from a dirty body of water would yield a bell shaped curve shifted to the right of the curve used for determining the standard. The GM would be greater than the GMS and Formula [1] gives us a quick way to quantify the size of the geometric means relative to one another. For the dirty water it would be likely that more than 50% of the samples would be greater than the GMS. Formula [2] is a quick simple way of looking at the number of samples to the right of the GMS compared to how many we would expect if the body of water was barely clean enough to attain the standard.

Likewise, if 25% of the samples from an unknown body of water fall to the right of the 10% STV then that body of water is likely to be dirty and Formula [3] is a quick simple way of getting a sense of how impacted it might be. In a large number of samples taken from a body of water barely clean enough to meet the standards we would expect 10% of the samples to exceed the 10% STV. Hence, if 25% of the samples are greater than the 10% STV we could estimate the unknown body of water as being possibly 2.5 times as impacted as the standard allows, and formula [3] would yield a QIP value of 250. Formula [4] for the 2% STV is based on the same concept as Formula [3].

Taken together, these four formulas yield a QIP value which gives us a qualitative idea of how impacted a body of water is. Since they are unitless, QIPs for different nutrients or pollutants can be compared to one another. Since they are merely a crude measure of how well a sparse set of samples conforms to an expected statistical distribution, QIPs can give a relative impression of which nutrient or pollutant is farthest from meeting its standard, and hence is likely to be the most impactful. QIPs can help decision-makers know where to apply scarce resources for the greatest potential benefit.

Dataset

Click to view Appendix B Data spreadsheet with tabs for all seven datasets.

Example view below of first tab: Total Nitrogen

Literature Cited

HIDOH. 2002. List of impaired waters in Hawai’i prepared under Clean Water Act §303(d). Prepared by Hawai’i State Department of Health Environmental Planning Office. http://health.hawaii.gov/cwb/.

HIDOH. 2004. Final 2004 List of Impaired Waters in Hawai`i, Prepared Under Clean Water Act 303(d). http://www.state.hi.us/health/environmental/envplanning/wqm/303dpcfinal.pdf.

HIDOH. 2006. State of Hawai’i Water Quality Monitoring and Assessment Report: Integrated Report to the U.S. Environmental Protection Agency and the U.S. Congress Pursuant to Sections 303(d) and 305(b) Clean Water Act (P.L. 97–117). http://health.hawaii.gov/cwb/files/2013/05/Integrated_2006_StateOfHawaii.pdf.

HIDOH. 2008/2010. State of Hawai’i Water Quality Monitoring and Assessment Report: Integrated Report to the U.S. Environmental Protection Agency and the U.S. Congress Pursuant to Sections 303(d) and 305(b) Clean Water Act (P.L. 97–117). http://health.hawaii.gov/cwb/files/2013/05/Integrated_2006_StateOfHawaii.pdf.

HIDOH. 2012. State of Hawai’i Water Quality Monitoring and Assessment Report: Integrated Report to the U.S. Environmental Protection Agency and the U.S. Congress Pursuant to Sections 303(d) and 305(b) Clean Water Act (P.L. 97–117). http://health.hawaii.gov/cwb/files/2013/04/IntegragedReport.pdf.

HIDOH. 2014. State of Hawai‘i Water Quality Monitoring and Assessment Report: Integrated Report to Congress Pursuant to Sections 303(d) and 305(b) Clean Water Act (P.L. 97–117). http://health.hawaii.gov/cwb/files/2014/11/Final-2014-State-of-Hawaii-Water-Quality-Monitoring-and-Assessment-Report.pdf.

Teruya, T. and HIDOH. 2010. Water sample data set from the State of Hawaii, Department of Health, 1973-1998 in Hawaiian waters (NODC Accession 0013724). National Oceanographic Data Center, NOAA. Dataset. Access date, 2015.