A New Statistical Methodology

Aug. 2, 2013

By: Megan Otto, Paul Hobson, Rita Kampalath, Brandon Steets, Robert Pitt, Jon Jones, Michael Stenstrom, Robert Gearheart, Michael Josselyn, and Debbie Taege.

This article presents a transparent, reproducible, robust, and defensible statistical methodology for siting source controls and structural treatment controls (or best management practices [BMPs]) throughout a watershed based on water-quality monitoring data. The methodology was developed and tested on two watersheds at the Santa Susana Field Laboratory in Ventura County, CA, with stringent National Pollutant Discharge Elimination System (NPDES) numeric effluent limits (NELs) for stormwater runoff that apply at the watershed outlet compliance monitoring locations (or outfalls). Constituents of concern (COCs) include total suspended solids (TSS); 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD); tetrachlorodibenzo-p-dioxin toxic equivalence (TCDD TEQ); and total and dissolved lead (Pb), copper (Cu), cadmium (Cd), and mercury (Hg). For environmental, permitting, and constructability reasons, “end-of-pipe” treatment options at the study area outfalls are not feasible; therefore distributed solutions throughout the watershed are necessary. However, monitoring data must be processed to prioritize such controls. The statistically rigorous approach presented here was applied on an annual basis to evaluate stormwater subarea monitoring data to determine where treatment controls will be most effective. Local background stormwater pollutant concentrations are also computed and considered in the analysis to focus control placement on areas that are above background. The intended outcome of the resulting implementation activities is to reduce COC concentrations and NEL exceedance frequencies using targeted upland source control and distributed BMP placement.

Introduction and Background
The 2,800-acre Santa Susana Field Laboratory, located in the Santa Susana Mountains of eastern Ventura County, CA, was formerly a rocket engine testing site and energy research facility for the federal government (1950–1988). It is currently owned by the Boeing Company (post-1966) and the United States government. Activities at the site are now limited to demolition, remediation, and restoration. The site will ultimately be dedicated as parkland and open space. Stormwater discharges from the site are regulated by the Los Angeles Regional Water Quality Control Board (LARWQCB) through an individual industrial NPDES permit. The permit sets NELs for a wide range of constituents, including dioxins (2.8×10-8 µg/L tetrachlorodibenzo-p-dioxin toxic equivalence [TCDD TEQ]) and metals (such as 14 µg/L total copper and 5.2 µg/L total lead). Because of severe site constraints at the compliance monitoring outfalls (natural drainages located near the property boundary) of the two watersheds in the project (designated as Watershed 008 [62 acres] and Watershed 009 [536 acres]), end-of-pipe stormwater controls are not feasible. Therefore, a watershed-based stormwater management approach is being implemented, including the use of sediment and treatment controls that replicate natural processes and are distributed throughout the watersheds to capture the constituents of concern COCs. Figure 1 depicts an existing treatment control (media filter) at the site area identified as the “B1″ subarea. Another site subarea, identified as the “lower lot” subarea, was recently designed to include a separate sedimentation basin and vegetated media filter (or biofilter), also shown in Figure 1.

With many potential subareas in which BMPs could be implemented within the watersheds, a robust and defensible method was required to determine where sediment and treatment controls would be most effective at reducing COCs at the outfalls. Typical, more arbitrary methods, such as having fixed stormwater background thresholds and a number of samples that are allowed to be exceeded before a BMP decision is made, can be difficult to defend or update when more data become available, and such methods likely do not appropriately consider the number of samples used in the analysis and the percent that exceed. For these reasons, a statistically rigorous method was developed to rank potential BMP subareas based on the overall confidence that a certain site will contain COCs in excess of permit thresholds and background concentrations. To summarize, the methodology presented here has several advantages over more typical methods, including:

  • flexibility to continually adapt recommendations to most current data;
  • consideration of the robustness of the dataset in making management decisions (i.e., both the number of samples and the percent of samples exceeding);
  • acknowledgment of comparison both to background levels, which may vary, as well as to permit limits, in the site ranking process;
  • ranking of sites, rather than identifying some sites to be treated and others to not be treated, thereby allowing management decisions to be based upon both best professional judgment and availability of resources, while allowing flexibility from year to year; and
  • consideration of particulate strength, which allows decision-makers to discern between sites with erosion issues and sites with elevated suspended solids pollutant concentrations, and target appropriate controls accordingly

Data Collection and Analysis
Within the two watersheds, 68 potential BMP subareas were identified for monitoring. These subareas were selected to have roughly comparable drainage areas and to include runoff from developed or potentially impacted soil areas. For comparison with runoff from these sites, 16 background subareas within the watersheds were selected for monitoring to characterize the quality of stormwater runoff from unimpacted, natural subareas. Runoff samples were collected between 2009 and 2012. COCs included TSS; TCDD, which suggests an anthropogenic contributing source; TCDD TEQ, and total and dissolved lead, copper, cadmium, and mercury. The different number of samples from each subarea reflects the variation in the runoff and sampling durations. In addition, because there were different objectives for each of the two ongoing monitoring programs (BMP subareas and background subareas), not all COCs were sampled at all subareas (for example, dissolved metals were not analyzed at background subareas). Sample sizes and concentration statistics of the COCs for the potential BMP subareas and the background sites are shown in Tables 1 and 2, respectively.

The particulate strength for each sample was calculated with the COC and TSS concentrations in the runoff from each subarea. Particulate strength is a means to normalize stormwater constituent concentrations by TSS and to indicate the treatability of the constituents through sediment controls. Normalizing constituent concentrations by TSS is helpful for evaluating locations that have high COC concentrations in the runoff as a result of high TSS concentrations, especially for the COCs that are highly associated with particulates and are not found in significant quantities in their dissolved form. This normalization with TSS was performed to help identify critical COC source areas that may otherwise have mass discharges diluted by large flows. Particulate strength is computed as total COC concentration minus dissolved COC concentration divided by TSS concentration, resulting in the estimated particulate-associated COC mass per mass of suspended solids. In cases where dissolved metal data were not available or where total COC, dissolved COC, or TSS were below detection limits, standard procedures were followed to estimate particulate strength at each location. It was not possible to calculate particulate strength for sample events in which TSS or the total COC concentration was not available.

Subarea Prioritization Methodology
To identify potential stormwater control locations, subareas were ranked based on the results of comparisons between (a) stormwater concentrations and permit limits and (b) stormwater particulate strengths and stormwater background particulate strengths. A “critical” observation was identified as one in which either (1) the COC concentration exceeded the permit limit or (2) the particulate strength exceeded the 95th percentile particulate strength of the background samples. A statistical methodology was developed to rank the subareas based on these comparison results while accounting for both the number of useable data available at each subarea and the number of “critical” data (i.e., reflecting statistical confidence in how frequently each subarea will exceed the comparison thresholds). For example, a subarea having 20 critical observations out of 20 total observations has a higher degree of confidence that the site more often exceeds thresholds than a subarea with three critical observations out of three total observations. Furthermore, a subarea with one critical observation out of 10 observations has less confidence that the site more often exceeds thresholds than a subarea with eight critical observations out of 10 total observations. Therefore, both the number of critical observations and total observations affect confidence in whether the subarea more often exceeds thresholds.

The methodology relies on weighting factors calculated for each COC for each subarea based on binomial distributions corrected for use with small samples sets. Table 3 contains the calculated weighting factors used in this analysis. When more than 15 observations for a subarea were present (this was true only at the outfalls of the two watersheds), the weight was computed as the unadjusted value of the cumulative distribution function of a binomial distribution with p = 0.5:

p = 0.5
n = nC + nPS, where
nC = Number of concentration sample results
nPS = Number of particulate strength results
m = mC + mPS, where
mC = Number of concentrations sample results that exceed the permit limits
mPS = Number of particulate strength results that exceed the 95th percentile stormwater background particulate strength results threshold

With this approach, a weighting factor was calculated for each COC in each subarea based on all the samples taken from that subarea. The number of samples where concentrations exceeded permit limits was added to the number of samples where the particulate strength exceeded 95% of the background particulate strength to determine the total number of critical observations. A weighting factor for the COC was determined from Table 3. The highest weighting factor among all the metals was used as the metal weighting factor, and the higher weighting factor between TCDD TEQ and TCDD was used as the dioxin weighting factor. A multi-constituent weighting factor was then calculated as the arithmetic mean of the metal weighting factor and the dioxin weighting factor, and the subareas were ranked according to their likelihood of exceeding thresholds based on the multi-constituent weighting factor and the TSS weighting factor.

Results were also evaluated graphically, as shown in Figures 2 through 5, which further illustrate the fundamental question the methodology is intended to address: Which subareas contribute to downstream permit limit exceedances as a result of elevated COC concentrations that are most likely due to particulate strengths above subarea-specific background levels? In the probability plots, these subareas are identified by potential BMP subarea stormwater sampling results that fall to the right of the permit limit in the concentration chart and fall to the right of the stormwater background best-fit line on the particulate strength chart.

Runoff from subareas with the highest multi-constituent and TSS weighting factors was assumed to have the highest likelihood of exceeding thresholds. Therefore, the sites with the highest ranking were evaluated for new erosion control and/or treatment controls in conjunction with consideration for constructability and site-specific concerns.

Multi-constituent weighting factors among the sites ranged from 0.00 to 0.94 with approximately 20% of the subareas having a weighting factor higher than 0.50. This range allowed for a prioritization of sites where treatment controls would have the largest impact on downstream COC concentrations. Other factors were considered in addition to the multi-constituent weighting factors and TSS weighting factors, such as the individual metals and dioxin weighting factors, the COC concentrations (note that weighting factors do not explicitly account for concentration magnitudes, but rather for frequency of exceedances), and detections of TCDD (which was detected from only four subareas).

The subareas with the four highest maximum metals and dioxins weighting factors were also in the top nine subareas based on the multi-constituent score, suggesting that rankings are robust and not highly sensitive to the individual constituents used to calculate the rankings. These same four subareas were also the only subareas in which TCDD was detected. The rankings were similar to results from previously tested statistical approaches, further supporting the robustness of the methodology and suggesting that the results are not highly sensitive to the particular statistical methodology employed.

The 2012 analysis concluded with the recommendation of stormwater control BMPs at four main subareas, including the “ELV/CM1″ subarea, culvert modification 9 “CM9″ subarea, “24-inch culvert” subarea, and “B1″ subarea, including treatment controls for dioxin at the most highly ranked location and enhanced sediment controls at all four locations (Figure 6). It is anticipated that the likelihood of downstream exceedances will be reduced because the highest-priority subareas with the most significant COC contributions will be addressed.

The rankings were also used to evaluate performance of individual BMPs by a comparison of pre-BMP water quality to post-BMP water quality, and influent to effluent, at specific sites. Results for BMPs at the “CM” subareas, the “Helipad” subarea, and the “B1″ subarea are illustrated in Figure 7.

Runoff samples will continue to be collected during the wet season, and the ranking process will continue to be repeated annually, thereby increasing statistical significance in the complete dataset while allowing for the evaluation of effects of implemented treatment controls and changing site conditions (BMP construction, impacted soil removal, etc.). This methodology can be applied to other large sites requiring a distributed treatment approach to meet NELs and provides the added advantage of identifying the most highly contributing subareas. This approach is anticipated to save the site money by providing the most “bang for the buck,” rather than BMPs being implemented evenly or less methodically across the upper watershed. This methodology also has the advantage of taking into consideration the number of observations and can continually be updated as more data become available. In addition, this method helps determine when sufficient data have been collected to satisfy statistically based confidence and power objectives, which would then enable reduced future sampling efforts. Lastly, it should be acknowledged that 100% compliance may not be possible due to background concentrations and/or natural variability.

Author Bios:
The following authors contributed to this article: Megan Otto, Paul Hobson, Rita Kampalath, and Brandon Steets of Geosyntec Consultants; Robert Pitt, University of Alabama; Jon Jones, Wright Water Engineers Inc.; Michael Stenstrom, University of California, Los Angeles; Robert Gearheart, Humboldt State University; Michael Josselyn, WRA Environmental Consultants; and Debbie Taege, The Boeing Company.

Photo 39297166 © Mike2focus | Dreamstime.com
Photo 140820417 © Susanne Fritzsche | Dreamstime.com
Microplastics that were fragmented from larger plastics are called secondary microplastics; they are known as primary microplastics if they originate from small size produced industrial beads, care products or textile fibers.
Photo 43114609 © Joshua Gagnon | Dreamstime.com
Dreamstime Xxl 43114609