Here is the 3rd installment of Alan Bland’s Analysis of the Risk of Consent Failure in UK WWTPs. If you’d like to review the first 2, please follow the corresponding links: Part I, Part II. Please comment and provide feedback so we can better reach your interests as readers of the water quality and security blog.
In Part 2, I described the workings of the Look Up Table (LUT) for conventional UK wastewater consents issued by the Environment Agency. These WRA (Water Resources Act) consents require 95% compliance with numeric standards for BOD, SS, NH4 and occasionally other determinands. In the early 1990s water companies were concerned to meet the consents as far as possible. Rather than wait for failure based on formal compliance samples, they conducted informal internal sampling, usually at a higher frequency than required for the formal sampling. This was an expensive activity, but the idea was to identify risky treatment works and try to “nurse” them into compliance until capital investment could be carried out to provide a longer term solution. In the water company I worked for, samples were taken and analysed, often on a weekly basis, and labelled “pass” or “fail”. When a treatment works accumulated around half of the failed samples needed to indicate non-compliance, the works was added to the “at risk” list, which meant it received a higher level of specialist attention.
Of course, the mere fact that a discharge is at risk of consent failure reveals nothing about the reasons for the poor performance. Also, the “at risk” list strategy was rendered ineffective when the EA introduced upper tier consents. These consents are breached if a single sample fails the upper tier consent limit. Since there was no clear statistical relationship between WRA LUT consents and upper tiers, the “at risk” list was no guide to performance against upper tiers.
To make life even more difficult, the Urban Waste Water Treatment Directive required the introduction of new consents based on percentage removal of BOD, SS and COD. These new consents were being phased in as additional requirements, rather than replacements for the WRA consents. Now both formal and internal sampling had to include paired samples taken on the same day from the works inlet and effluent discharge. The only way to predict failure now was to analyse the statistics of the treatment works performance. It was time to reveal the wealth of information that could be extracted from all of the collected data!
Shown in the chart below are the BOD results from samples taken over some 8 years during the 1990s at one medium-sized treatment plant. The main point to note is that performance appears quite variable but is possibly somewhat better towards the end of the period than at the start. The black line shows the average of all the sample results, and the BOD lies generally above it at the start but mostly below it at the end of the period.
However, we can look more closely at the performance by performing a cusum analysis. This simply calculates a cumulative sum of the differences between the sample values and the average. Over the full record, the cusum will move from zero to zero, with positive and / or negative values in between. In this case, because the sample results are generally above the average in the early years, the cusum can be expected to gradually increase to begin with and then reduce in later years. This is in fact what we find, as shown below. The blue straight line is just to indicate the selection of the main hinge point in the cusum from increasing to decreasing.
If we now calculate the BOD averages before the hinge point and after it, we can plot these on the original chart and see that the average performance has changed dramatically at a specific date (which happens to be 10 May 1992).
The average BOD has reduced from about 11mg/l to about 6 mg/l, almost 50% reduction, and this is due to work carried out to increase final settlement tank capacity, which was commissioned in the same week in May.
We can go further and drill deeper into the data by calculating the residual values remaining after the cusum means are subtracted from the sample results. The chart below shows some residuals are positive and some negative, as one would expect, but otherwise there does not appear to be any particular pattern.
If, however, we repeat the cusum calculation on the residuals, the following picture emerges.
Again we see several hinge points, but the main one is in 1995 (18 July in fact). After that date, the performance is clearly improved compared to the prior period. If we add that change to the BOD plot, it looks like this:
So now we know the earlier improvement wasn’t quite as dramatic as we thought, because there was a subsequent improvement hidden in the data (a long time ago now, but I think it was the result of improvements in the de-sludging arrangements). Not only has the average reduced again but the variance has also reduced. This is important because it tells us what period we should analyse to assess the current risk of failure. In 1997 we could include sample data from July 1995 but no earlier, because both mean and variance were greater before that date.
Next time I will focus on how this affects the risk calculation.