The IMPROVE algorithm for estimating light extinction was adopted by the U.S. Environmental Protection Agency (EPA) as the basis for the regional haze metric used to track progress in reducing haze levels for visibility protected areas under the 1999 Regional Haze Rule (RHR). The RHR uses the IMPROVE algorithm to estimate light extinction, which is then converted to the deciview haze index.

*The First IMPROVE Equation*

The IMPROVE algorithm was originally developed by* Malm et al, *1994. This algorithm, often referred to as the IMPROVE Equation, is based on the assumptions that absorption by gases (b_{a,g}) is zero, that Rayleigh scattering (b_{s,g}) is 10 Mm^{-1} for each monitoring site, and that particle scattering and absorption (b_{s,p} and b_{a,p}) can be estimated by multiplying the concentrations of each of six major components by typical component-specific mass extinction efficiencies. The sulfate and nitrate mass extinction efficiency terms include a water growth factor that is a function of RH (displayed as f(RH)) multiplied by a constant dry extinction efficiency.

*b*_{ext} ≈ 3 × *f*(*RH*) × [*Ammonium Sulfate*] + 3 × *f*(*RH*) × [*Ammonium Nitrate*] +

4 × [*Organic Mass*] + 10 × [*Elemental Carbon*] + 1 × [*Fine Soil*] + 0.6 × [*Coarse Mass*]

+ *Rayleigh scattering*

where light extinction and Rayleigh scattering (10 Mm^{-1}) are given in inverse megameters (Mm^{‑1}); concentrations shown in brackets are in microgram per meter cubed (μg m^{-3}); dry mass extinction efficiency terms are in units of meters squared per gram (m^{2} g^{-1}); and the water growth terms, f(RH), are unitless.

** fRHOriginalIMPROVE.csv** f(RH) values for calculating light extinction from IMPROVE data using the Original IMPROVE Equation.

** IMPROVE_site_frh_2015.xls** Because many monitoring sites do not include on-site RH monitoring, monthly averaged water growth terms for each site were developed for RHR calculations. Monthly values for the first IMPROVE equation are given as ‘frh’ (columns AN-AY).

*The Second IMPROVE Equation*

The first IMPROVE algorithm performed reasonably well; however, it tended to underestimate the highest extinction values and to overestimate the lowest extinction values. As such, a revised algorithm was developed by *Pitchford et al.*, 2007. Like the first IMPROVE equation, the revised algorithm is relatively simple, it produces consistent estimates of light extinction for all remote-area IMPROVE aerosol monitoring sites, and it permits the individual particle component contributions to light extinction to be separately estimated. Five major revisions were made to the original IMPROVE algorithm for estimating light extinction from IMPROVE particle speciation data. They include:

- Addition of a sea salt term, which is a particular concern for coastal monitoring locations;
- Change of the assumed organic compound mass to OC mass ratio from 1.4 to 1.8;
- Use of site-specific Rayleigh scattering based on the elevation and annual average temperature of the monitoring sites;
- Development and use of a split component extinction efficiency model for sulfate, nitrate, and OC components, including new water growth terms for sulfate and nitrate to better estimate light extinction at the high and low extremes of the range; and
- Addition of a NO
_{2}light absorption term that would only be used at sites with available NO_{2}concentration data.

*b*ext ≈ 2.2 × *f*_{S}(*RH*) × [*Small Ammonium Sulfate*] + 4.8 × *f*_{L}(*RH*) × [*Large Ammonium Sulfate*] +

2.4 × *f*_{S} (*RH*) × [*Small Ammonium Nitrate*] + 5.1 × *f*_{L}(*RH*) × [*Large Ammonium Nitrate*]

+ 2.8 × [*Small Organic Mass*] + 6.1 × [*Large Organic Mass*] +

10 × [*Elemental Carbon*] + 1 × [*Fine Soil*] + 1.7 × *f*_{SS}(*RH*) × [*Sea Salt*] +

0.6 × [*Coarse Mass*] + *Rayleigh Scattering *(*Site Specific*) + 0.33 × [*NO _{2} (ppb*)]

where light extinction and Rayleigh scattering are given in inverse megameters (Mm^{-1}); concentrations shown in brackets are in microgram per meter cubed (μg m^{-3}); dry mass extinction efficiency terms are in units of meters squared per gram (m^{2} g^{-1}); and the water growth terms, f(RH), are unitless. Sulfate, nitrate and organics are split into small and large modes based on their mass. For masses less than 20 μg m^{-3}, the fraction in the large mode is estimated by dividing the total concentration of the component by 20 μg m^{-3}. For example, if the total fine particulate OC concentration is 4 μg m^{-3}, the fraction in the large mode is calculated as 4/20 = 1/5 of 4 μg m^{-3} = 0.8 μg m^{-3}; the remaining 3.2 μg m^{-3} is in the small mode. If the total concentration of a component exceeds 20 μg m^{-3}, all of it is assumed to be in the large mode. The small and large modes of sulfate and nitrate have associated hygroscopicities, f_{S}(RH) and f_{L}(RH), respectively, while f_{SS}(RH) is for sea salt.

** fRHRevisedIMPROVE.csv** f(RH) values for calculating light extinction from IMPROVE data using the revised IMPROVE algorithm.

** IMPROVE_site_frh_2015.xls ** Because many monitoring sites do not include on-site RH monitoring, monthly averaged water growth terms for each site were developed for RHR calculations. Monthly values for the second IMPROVE equation are given as ‘FRHS’, ‘FRHL’, and ‘FRHSS’ (columns D-AM).

** IMPROVE_Lat_Lon_Elev_Temp_Rayleigh_7_2015.xls** Site specific Rayleigh Scattering values.