Nowcast (Air Quality Index)

The NowCast is a weighted average of hourly air monitoring data used by the United States Environmental Protection Agency to report the Air Quality Index (AQI) for fine particulates (PM_2.5).

PM_2.5 AQI of US monitors, Calculated Utilizing NowCast, Courtesy US EPA

PM2.5 AQI map, Calculated Utilizing NowCast, Courtesy US EPA

The NowCast is computed from the most recent 12 hours of air monitoring data, but the NowCast weights the most recent hours of data more heavily than an ordinary 12-hour average. The NowCast is used in lieu of a 24-hour average PM_2.5 concentration in the calculation of the AQI until an entire calendar day of hourly concentrations has been monitored.

Let c₁,c₂,...c₁₂ represent the hourly PM_2.5 concentrations for the most recent 12-hour period, with c₁ the most recent hourly value, and let c_min and c_max represent the minimum and maximum hourly concentration for the 12-hour period.

Define:

$w^{*}={\frac {c_{min}}{c_{max}}}$

and let

$w={\begin{cases}w^{*}&{\mbox{if }}w^{*}>{\frac {1}{2}},\\{\frac {1}{2}}&{\mbox{if }}w^{*}\leq {\frac {1}{2}}.\\\end{cases}}$

With these definitions the NowCast is given by:

$NowCast={\frac {\sum _{i=1}^{12}w^{i-1}c_{i}}{\sum _{i=1}^{12}w^{i-1}}}.$

For the special case where there is no variability in the hourly values, c_min = c_max, w = 1, and the NowCast reduces to the twelve-hour average:

$NowCast={\frac {\sum _{i=1}^{12}c_{i}}{12}}.$

For the special case where w=1/2:

$NowCast={\frac {c_{1}+({\frac {1}{2}})c_{2}+...+{({\frac {1}{2}}})^{11}{c_{12}}}{1+{\frac {1}{2}}+({\frac {1}{2}})^{2}+...+{({\frac {1}{2}}})^{11}}}$

But 1/(1-x)=1 + x + x²+ ... , x < 1, so to a good approximation, when w = 1/2:

$NowCast={\frac {1}{2}}c_{1}+({\frac {1}{2}})^{2}c_{2}+...+{({\frac {1}{2}}})^{12}{c_{12}}$

References

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