NowCast (air quality index)

Let ${\displaystyle c_{1},c_{2},...c_{12}}$ represent the hourly PM concentrations for the most recent 12-hour period, with ${\displaystyle c_{1}}$ the most recent hourly value, and let ${\displaystyle c_{min}}$ and ${\displaystyle c_{max}}$ represent the minimum and maximum hourly concentration for the 12-hour period.

Define:

${\displaystyle w^{*}=1-{\frac {c_{max}-c_{min}}{c_{max}}}={\frac {c_{min}}{c_{max}}}}$

and let

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

With these definitions the PM NowCast[2] is given by:

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

For the special case where there is no variability in the hourly values, ${\displaystyle c_{min}=c_{max},w=1}$, and the NowCast reduces to the twelve-hour average:

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

For the special case where w=1/2:

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

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

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

Because the most recent hours of data are weighted so heavily in the NowCast when PM levels are changing, EPA does not report the NowCast when data is missing for c₁ or c₂.

Consider a day when the hourly average PM_2.5 concentration is zero for all hours of the day, except for a single hour from noon to 1 pm, where a monitor records a concentration pulse of 71 micrograms per cubic meter (µg/m³). According to the equation above, the Nowcast is 71/2 µg/m³=35.5 µg/m³ the hour after the pulse, two hours later it is 71/4 µg/m³=17.8 µg/m³ and three hours later it is 71/8 µg/m³= 8.9 µg/m³. To calculate the corresponding AQI values, each NowCast concentration is substituted into the AQI equation in place of the 24-hour average PM_2.5 concentration:

${\displaystyle I={\frac {C-C_{low}}{C_{high}-C_{low}}}(I_{high}-I_{low})+I_{low}}$

where:

${\displaystyle I}$ = the AQI,

${\displaystyle C}$ = the 24-hour average PM_2.5 pollutant concentration,

${\displaystyle C_{low}}$= the concentration breakpoint that is ≤ ${\displaystyle C}$,

${\displaystyle C_{high}}$= the concentration breakpoint that is ≥ ${\displaystyle C}$,

${\displaystyle I_{low}}$= the index breakpoint corresponding to ${\displaystyle C_{low}}$,

${\displaystyle I_{high}}$= the index breakpoint corresponding to ${\displaystyle C_{high}}$.

and:

${\displaystyle C_{low}}$	${\displaystyle C_{high}}$	${\displaystyle I_{low}}$	${\displaystyle I_{high}}$	Category
0	12.0	0	50	Good
12.1	35.4	51	100	Moderate
35.5	55.4	101	150	Unhealthy for Sensitive Groups
55.5	150.4	151	200	Unhealthy
150.5	250.4	201	300	Very Unhealthy
250.5	350.4	301	400	Hazardous
350.5	500.4	401	500	Hazardous

Thus, the three NowCast concentrations correspond to air quality indices[3] of 101, (AQI Color Code Orange, Air Quality: Unhealthy for Sensitive Groups), 63 (AQI Color Code Yellow, Air Quality: Moderate ), and 37 (AQI Color Code Green, Air Quality: Good) respectively. After the day is over and all of the hourly data is available, the AQI for the day is calculated from the 24-hr average; 71/24 µg/m³= 3.0 µg/m³, an AQI of 12 (Color Code Green, Air Quality: Good). EPA has developed a calculator to compute the PM NowCast, AQI, and AQI category and color from the most recent 12 hours of monitoring data.[4]