APS have provided an online tool to calculate representative percentiles based on the short-term operation within a year.

Hypergeometric distribution probability function!

Please select which form you wish to use. Once you press Submit, it will take a short period to calculate.

The short-term air quality impacts are complex to assess, given that several AQOs are based on an acceptable number of exceedences of the threshold per annum. For example for 1-hour NO2, the AQO permits 18 occurrences of 1-hour mean NO2 concentrations above a threshold concentration of 200 μg/m3 per year.

The 1-hour mean NO2 AQO is therefore often assessed by considering the 99.79th percentile of 1-hour concentrations, which represents the 19th highest hourly concentration from a full year of hourly values (a full year is 8,760 hours).

In most cases, especially where specific operating hours are not defined, it is important to run the model for a full year of continuous operation, in order to capture the varied meteorological conditions that can occur throughout the year. However, when the operation of the plant is not continuous and annual operation is significantly lower than a full year this approach is too conservative. Instead, an approach using hypergeometric distribution can be adopted that considers the number of hours of operation.

A hypergeometric distribution is a discrete probability distribution which can be used to determine the probability that the operation of a pollutant source for a limited number of hours in a year will cause an exceedence of a given threshold condition. In the case of the 1-hour mean NO2 AQO, the hypergeometric distribution is used to determine the probability that, from a set of mutually exclusive randomly selected hourly values from a full year’s dataset (8,760 hours), there will be 19 hourly NO2 concentrations which will exceed the threshold concentration of 200 μg/m3. The probability is dependent on the number of proposed hours of operation, such that the lower the number of operating hours, the lower the probability that 19 or more of the randomly selected hours will exceed the threshold.

This approach can be used in reverse so that, when selecting a limited number of hourly values that corresponds to the number of hours of operation, there is a less than 1% chance that more than 18 of the selected hourly values exceed the 1-hour mean threshold. This is done by calculating the number of hourly values from a full dataset (8,760 hourly values) that can exceed the 1-hour threshold in order for there to be a less than 1% chance.

The number of hours that exceed the threshold in the full dataset can be used to calculate representative percentiles for the operational scenario. This impacts can then be assessed against this representative percentile.

For example, for the 1-hour mean NO2 objective for plant operating for a maximum of 2,500 operating hours, if fewer than 40 hours of a full year (8,760 hours) exceed 200 μg/m3 then there is a <1% chance that of the 2,500 selected hourly values, more than 18 hours will exceed the limit. The representative percentile is thus the 40th highest hourly value (99.54th percentile). Providing this percentile is not exceeded there is a less than 1% risk of the AQO being exceeded.

The form above can be used to calculate your representative percentiles.