Site Specific Uncertainty in Regional Haze Rule Haze Indexes

In 1999, the US Environmental Protection Agency (EPA) published the regional haze rule (RHR). The RHR default implementation plan calls for each class I area 20% worst baseline (2000-2004) visibility to improve linearly in time to natural conditions in 2064 and in calendar year 2018, each class I area 20% worst visibility is to comply with the 2018 visibility that falls on the linear improvement glide path from baseline (2000-2004) to natural (2064) conditions. This study shows that accurately assessing compliance depends on assessing the uncertainty in baseline, natural and 2018 visibility estimates. This study identifies ±3 dV and ±4 dV of uncertainty in 20% worst natural and baseline visibility estimates. The percent uncertainty in calculated 2018 glide path visibility values ranges from 10% 45%.


Introduction
The US Environmental Protection Agency (EPA) published the Regional Haze Rule (RHR) [1] in 1999 to protect and improve visibility in national parks and other class I areas.The RHR default implementation plan calls for each class I area 20% worst baseline (2000)(2001)(2002)(2003)(2004) visibility to improve linearly with time reaching natural conditions in 2064.In 2003, the EPA published two guidance documents to provide a default approach regulators can follow to calculate baseline and natural visibility [2,3].A key element of the EPA default method for estimating baseline and natural visibility is to use the Interagency Monitoring of Protected Visual Environments (IMPROVE) model to estimate light extinction.
The IMPROVE model characterizes atmospheric light extinction as caused by light scattering and light absorption by gases and particles.Light scattering and absorption by gases is relatively well-understood.The interaction of light with atmospheric particles is more complex than the interaction of light with gases.Particles are usually a larger contributor to haze than are gases; yet the large variations of particle size and chemical composition in the atmosphere make it difficult to accurately estimate their effects on haze.The IMPROVE light extinction model characterizes particle haze as due to eight aerosol species: ammonium sulfate ((NH 4 ) 2 SO 4 ), ammonium nitrate (NH 4 NO 3 ), organic carbonaceous species (OCM), elemental carbon (EC), species associated with fine soil dust (soil), species contained in course PM (CM, parti-cles with aerodynamic diameters between 2.5 and 10 µm), sea salt, and water (H 2 O).
Using the IMPROVE light extinction model, the EPA method estimates the RHR 2018 linear improving visibility goal as follows.First, using the IMPROVE model each class I area baseline (2000)(2001)(2002)(2003)(2004) 20% worst haze index (HI) is estimated.Second, each class I area 20% worst natural HI to be achieved in 2064 is estimated.For baseline and natural visibility values of 24.8 dV and 6.8 dV, the RHR linear improvement goal of achieving natural haze in 2064 equates to 18 dV (=24.8 dV -6.8 dV) improvement over 60 years (=2064 -2004) and a calendar year 2018 glide path visibility of 20.6 dV that is a 4.2 dV reduction (0.3 dV/yr × 14 yr) from the baseline level.The following sections present the method and findings of uncertainty in regulator baseline, natural and calendar year 2018 glide path visibility estimates.

Method
The updated IMPROVE formula [4] for light extinction (b ext ) calculates haze in units of inverse megameters (Mm -1 ) as the sum of light extinction (b ext ) from the light scattering by particles (b sp ), light absorption by particles (b ap ), and light scattering by gases (b sg ).Light scattering is from PM 2.5 (NH 4 ) 2 SO 4 , PM 2.5 NH 4 NO 3 , PM 2.5 OCM, PM 2.5 soil dust, PM 2.5-10 mass (CM) and sea-salt.Light absorption is by PM 2.5 elemental carbon and Rayleigh scattering is by gases.The IMPROVE light extinction formula is:  The RHR states that baseline, natural and 2018 visibility must be estimated in units of deciviews (dV).The conversion of daily light extinction and light scattering estimates in Mm -1 to a daily haze index, HI was calculated using Equation (2a) below.This was followed by statistically averaging the daily HI values in each tail of the distribution using Equation (2b) to arrive at yearly 20% best and 20% worst HI values.The multi-year average baseline (2000)(2001)(2002)(2003)(2004) and natural haze 20% worst HI values were calculated using Formula (2c) below.
The National Institute of Standards and Technology [5] states it is scientifically impossible to judge the fitness of a calculated value (e.g., 20% worst HI, or a 2018 progress goal) without assigning a corresponding uncertainty estimate to the value.In this study, the uncertainty associated with the baseline, natural and 2018 visibility estimates was developed by calculating the average difference between IMPROVE model light scattering HI predictions and nephelometer light scattering HI observations: The calculated 2018 Progress Goal uncertainty (ΔPG) depends on baseline and natural haze uncertainty: To estimate the uncertainty in the IMPROVE model light extinction estimates, this study compares IMPR-OVE daily records of nephelometer (light scattering) measurements with IMPROVE model predictions.IM-PROVE model predictions were formed from daily aerosol concentration data and daily RH multipliers by class I site [6].Actual hourly RH data were used to calculate actual daily RH multipliers and for comparison regulators assign monthly RH multipliers for use by class I site in the RHR application.These monthly RH multipliers were downloaded from the VIEWS web site.

IMPROVE Model Aggregate Performance Using Same Day RH Multipliers
The IMPROVE light extinction model aggregate performance averaged across multiple sites is as follows.A total of 6109 previously compiled and published [7] 1 shows the aggregate performance of the IMPROVE model across multiple sites is of significant over prediction (1.5 and 2.0 dV) of the light scattering measurements from 0 -5 and 5 -10 dV, a modest 0.3 dV -0.4 dV of light scattering over prediction from 10 -30 dV, and a significant 2.1 dV of over prediction of light scattering data above 30 dV (where there are few data points).The purpose of this exercise is to show the IMPROVE model is exceptionally good in the range of 10 -30 dV consistent with the authors [4] data fit development of the IMPROVE light extinction model.

IMPROVE Model Site-Specific Performance Using Same Day RH Multipliers
The 6109 daily light scattering visibility values and IM-PROVE model light extinction visibility (HI) predictions represent data collected across twenty class I sites [7].The 6109 light scattering and IMPROVE model light scattering prediction data points were collected over 11-years.This 11-year data set ranges from 2-time to slightly more than 3-times as many years of data as regulators used to develop baseline (2000)(2001)(2002)(2003)(2004) and natural HI estimates.Regulators used at little as 3-years (49 class I sites), 4-years (53 class I sites) and at most 5-years (43 class I sites) of data for making baseline (2000)(2001)(2002)(2003)(2004) and natural HI estimates.Less than 5-years of data were used at some sites because of incomplete IM-PROVE aerosol concentration daily data for some years.
To establish uncertainty in regulators baseline and natural visibility estimates from using 3-years to 5-years of data, this study compiled site-specific 5-year average 20% worst and 20% best light scattering HI visibility values and compared them to worst-case IMPROVE light extinction model visibility predictions using 3-years, 4-years and 5-years of data.Seven sites were found to have enough days (35 days minimum) of data by year and at least 5 consecutive years of data to perform this analysis.Table 3 shows the 3-years, 4-years and 5-years IMPROVE model highest visibility over predictions are 3.8, 3.3 and 3.0 dV of 5-years of site-specific 20% best nephelometer HI data.The 3-years, 4-years and 5-years IMPROVE model highest visibility over predictions are 3.1, 2.6 and 2.2 dV of 5-years of 20% worst nephelometer HI data.To extrapolate these findings from the 7-sites with enough data to make this comparison to all 20-sites with data, the 4-years IMPROVE model worst-case 20% worst and 20% best baseline HI performance biases (Table 3) of 2.0 and 1.5 times the uncertainty calculated using all site years of data (Table 2) were multiplied by the 20-sites of IMPROVE model multi-year uncertainty estimates.This was done to develop this study's 2nd tier estimate of uncertainty in regulators 3-years to 5-years visibility estimates.This 2nd tier uncertainty estimate ranges from 2.8 dV of under prediction to 3.0 dV of over prediction (~±3 dV uncertainty) (see Table 2).

Regulators Used Monthly RH Multipliers as Input to the IMPROVE Model
Regulators baseline and natural visibility estimates use the IMPROVE model with monthly RH multipliers whereas same day RH multipliers were used to develop and validate the IMPROVE model [4] (see Sections 3.1 and 3.2).To assess whether the regulators use of monthly RH multipliers impacts uncertainty in visibility estimates, the following analyses were undertaken.
Table 1 identifies that this study finds the IMPROVE model using regulators assigned monthly RH multipliers consistently over predicts the 6109 daily light scattering measurements.The average over prediction of the IM-PROVE model when using monthly RH multipliers is 3 dV across the visibility range of 10 to 31 dV. Figure 1 pictorially shows this finding that the regulators use of monthly RH multipliers (Figure 1, right) causes the IMPROVE model to over predict, by 3 dV on average, 6109 same day light scattering HI readings.Figure 1 also shows the data fitted IMPROVE model using actual same day RH multipliers (Figure 1, left) has no such over prediction issue.The following analysis was conducted to further document this issue.IMPROVE model daily light extinction HI values using both agency designated monthly RH multipliers and "actual" RH multipliers as input to the IMPROVE model were compared.Columbia River Gorge, WA calendar years 2003 and 2004 and Great Smoky Mountains NP, TN 2000-2004 data were used in this comparison.Each yearly set of daily visibility HI values were sorted, the tails of the distributions averaged, and the yearly 20% worst and 20% best visibility values averaged.For Columbia River Gorge, WA, the IMPROVE formula using monthly RH multipliers 20% worst baseline HI (24.4 dV) and 20% best baseline HI (9.2 dV) are 1.0 dV and 1.2 dV higher than the validated IMPROVE formula using actual RH multipliers 20% worst baseline HI (23.4 dV) and 20% best baseline HI (8.0 dV).For Great Smoky Mountains NP, TN, the IMPROVE formula using monthly RH multipliers 20% worst baseline HI (30.2 dV) and 20% best baseline HI (13.6 dV) are both 1.0 dV higher than the validated IMPROVE formula using actual RH multipliers 20% worst baseline HI (29.2 dV) and 20% best baseline HI (12.6 dv).Since other sites may show IMPROVE model under prediction and not over prediction, this study assigns a minimum of ±1 dV of uncertainty to the RHR IMPROVE model use of monthly RH multipliers rather than actual RH multipliers to develop 20% worst baseline HI values.This ±1 dV uncertainty estimate in the IMPROVE model [4] when using monthly RH multipliers instead of daily RH multipliers has limitations.Specifically, the IMPROVE model data fit was constructed using a data set with RH multipliers predominately in the range of values from 1 to 4. For comparison, the regulators estimate baseline and natural visibility for 1/3 of the class I sites using higher maximum monthly RH multiplier ranging from 4 to 6.8.The regulators extrapolation of the IMPROVE model to predict visibility well beyond the RH multipliers used in the data fit adds uncertainty.The amount of uncertainty cannot be quantified, but that does not mean the added uncertainty may not be significant.For example, this study's data set contains only seventeen out of the 6109 days where the daily RH multiplier (f s (RH)) was above 4 and ranged in value from 4 to 4.7, and the IMPROVE formula on these days using actual RH multipliers averaged 17.8 dV of visibility that over predicts by 1.2 dV (on average) the nephelometer readings HI average for these days of 16.6 dV.

Uncertainty in Regulators RHR HI Estimates
Regulators have formed RHR 20% worst baseline and the 20% worst natural visibility HI estimates by class I site [6].The 20% worst baseline HI values range from 9.6 -31 dV.The 20% worst natural HI values range from 5.6 -16 dV.This study assigns ±4 dV uncertainty to regulators RHR 20% worst baseline HI estimates and ±3 dV uncertainty to 20% worst natural HI estimates.The ±3 dV of uncertainty is assigned because regulators 3years to 5-years 20% worst baseline and natural HI uncertainties when using actual RH multipliers are this uncertain compared to 5-years of site-specific 20% worst nephew-lometer visibility values (see Table 2).This study adds an additional ±1 dV of uncertainty to the 20% worst baseline visibility estimates because of added uncertainty from regulators use of monthly rather than actual RH multipliers (see Section 3.3).
Table 4 lists for thirty-seven class I sites, this study's 20% worst baseline, natural and 2018 glide slope HI estimates (which are basically the same as reported by the regulatory agencies [6]).

Conclusions
Regulators comply with the EPA RHR requirements by calculating 20% worst baseline and natural visibility values by class I site.The baseline and natural visibility estimates are then used to calculate the calendar year 2018 glide slope visibility.Cornerstones of the regulators baseline, natural and 2018 visibility calculations that were evaluated for uncertainty were 1) the IMPROVE light extinction model, 2) assigned monthly RH multipliers, and 3) use of between 3-years to 5-years of calendar year 2000-2004 data.This study finds the regulators use of the IMPROVE model with monthly RH multipliers and 3-years to 5years of data creates uncertainty in baseline and natural visibility values equal to ±4 dV and ±3 dV, respectively.The percent uncertainty this causes in regulators 20% worst baseline and natural HI values ranges from 10% -40% and 20% -50%, respectively.The corresponding uncertainty in regulators 2018 glide slope visibility values ranges from 10% -45%.
Other uncertainties in regulators visibility values were identified and are: 1) the IMPROVE model uses monthly RH multipliers that produce visibility values that average ~3 dV higher than the nephelometer data, and 2) the IMPROVE model is extrapolated for use at ~1/3 of the regulated class I sites using monthly RH multiplier values above the effective upper limit of RH multiplier values used in the IMPROVE model data fit.Still other sources of visibility uncertainty exist not discussed in this paper.These other uncertainties include the fact that regulators natural visibility estimates assume two sets of uniform background concentrations of PM 2.5 (NH 4 ) 2 SO 4 , PM 2.5 NH 4 NO 3 , PM 2.5 OCM, PM 2.5 soil dust, PM 2.5-10 mass (CM) that apply across the entire western and separately across the entire eastern United States.The assumed uniform west and east background concentrations ignore large predicted spatial concentration variability [8] and omit the large transboundary contribution of other country emissions to haze in the United States [8,9].
aerosol concentrations are substituted for C i and represent the daily average ambient concentration of species i.All concentrations are input in μg/m

Figure 1 .
Figure 1.Daily light scattering (dV) compared with IMPROVE model predictions.
3. The daily RH multipliers (f s , f L and f ss ) account for water absorption by (NH 4 ) 2 SO 4 and NH 4 NO 3 and sea-salt.The IMPROVE formula uses dry light scattering efficiencies for (NH 4 ) 2 SO 4 of 2.2 and 4.8 m 2 /g, for NH 4 NO 3 2.4 and 5.1 m 2 /g, for OCM 2.8 and 6.1 m 2 /g, for soil dust, CM and sea salt used are 1, 0.6 and 1.7 m 2 /g, respectively, and the light absorption coefficient used for EC is 10 m 2 /g.b Ray is the Rayleigh scattering (1/Mm), and C OCM is estimated as 1.8 C OC .

Table 2 . Site specific nephelometer and IMPROVE model light scattering HI values.
HI values.The 1.4 dV of under prediction to 2.0 dV of over prediction (~±1.7 dV uncertainty) is this study's 1st tier site-specific uncertainty estimate of regulators RHR visibility estimates. data