Surrogates are a useful technique for aiding the spatial estimation of air pollutant concentration fields. A method has been previously developed and implemented that applies a single surrogate for estimating concentration fields. Applying multiple surrogates may provide more reliable estimates than a single surrogate. The previously developed technique was restricted to a single surrogate. One possibility for implementing multiple surrogates was to apply the single surrogate approach sequentially so that one surrogate would be used first and then a second surrogate applied to the results from the first surrogate aided estimation. This would force "favoritism" of surrogates and would require choosing a surrogate to dominate the estimation procedure over others. This report describes a modification of the existing method that extends it to the use of multiple surrogates.

An example of using a surrogate is the extinction coefficient as a surrogate for fine mass concentrations. An extinction coefficient value is obtained from a spatially interpolated B_ext grid for each fine mass monitoring station. The ratio of surrogate/fine mass is calculated and then spatially interpolated. The resulting surrogate/fine mass ratio grid is multiplied by the surrogate grid to obtain a higher resolution fine mass grid. In mathematical terms, the concentration at a location j is estimated by,

(1)

where c_i is the fine mass concentration at the estimation location

c_j are the fine mass concentrations at the monitoring sites

s_i is the surrogate concentration at the estimation location

s_j is the surrogate concentration at the fine mass monitoring sites

w_ij is the distance dependent weight that relates location i to j

N is the number of fine mass monitoring sites

The multiple surrogate approach does not have the surrogate/fine mass ratio as its focus. Instead the focus is on the ratio of the surrogate value at the fine mass monitoring site location to the surrogate value at the estimation location. Assuming a linear relationship between the surrogate and fine mass, the surrogate ratio provides a factor that relates the fine mass at the monitoring location to the fine mass at the estimation location. The figure below is an illustration of the surrogate ratio. Fine mass is being estimated at the location in eastern Kentucky. The B_ext value at the estimation location is about 0.2 km^-1 while at the fine mass monitoring site in Missouri it's about 0.08 km^-1. The surrogate ratio is therefore about 2.5. If the fine mass monitored in Missouri is 10 ug/m³ and it is the only site to influence the estimation location, the estimated fine mass concentration will be 25 ug/m³.

The approach starts out the same as the single surrogate method with a surrogate value extracted for the location of the fine mass monitoring site but instead of being done once and then interpolating the finemass/Bext ratio, the output grid (estimated finemass) is traversed. For each grill cell to be estimated, the neighboring fine mass sites are found. The Bext is then obtained for the grill cell location as well as at all of the neighboring fine mass stations. At each fine mass station, the ratio of the surrogate value at the grill cell to the surrogate value at fine mass station is calculated. This ratio relates the fine mass at the monitoring site to the estimation point. The measured fine mass is multiplied by the surrogate ratio and then used in the spatial interpolation of fine mass concentration at the estimation point. Applying the surrogate only at one point during the interpolation allows multiple surrogates to be applied simultaneously.

When looking at equation 1, from a surrogate centric perspective, it becomes,

(2)

where c_j is the fine mass concentration at the estimation location

c_i are the fine mass concentrations at the monitoring sites

s_kj is the surrogate k concentration at the estimation location

s_ki is the surrogate k concentration at the fine mass monitoring sites

w_ij is the distance dependent weight that relates location i to j

N_C is the number of fine mass monitoring sites

N_S is the number of surrogates

The two methods (equations 1 and 3) were compared using a single surrogate of B_ext to generate fine mass grids. When compared, the two estimated fine mass girds were the same within round off error.

One way of looking at the multiple surrogate approach is that it weights the spatial pattern of each surrogate . For example, if the B_ext pattern is a better surrogate in the northeast, then B_ext can receive the dominant weight and the resulting fine mass map in the northeast will reflect the B_ext pattern.  Likewise, PM10 may receive a higher weight in the midwest and the resulting fine mass map will inherit the PM10 pattern.

The following images shows carious weightings of B_ext and PM10 surrogates for the estimation of fine mass. The top row of images shows the fine mass monitoring locations with a simple 1/r² interpolation, the B_ext surrogate grid and the PM10 surrogate grid. The images thereafter illustrate the progression from giving all of the weight to the B_ext surrogate to giving all of the weight to the PM10 surrogate.

When B_ext receives the entire eight and PM10 none, the resulting fine mass has peak concentrations in Virginia and North Carolina. High (>17.5 ug/m3) concentrations are found in the Ohio River Valley and extends down through Alabama. The Northern Plains have low concentrations. Weighting B_ext with 90% and PM10 with 10% produces a similar spatial pattern but the peak concentration area in VA and NC decreases because the PM10 concentrations are lower there than in other parts of the PM10 grid. When the weight is changed to B_ext 70%, PM10 30% the area of higher concentrations expands to cover more of Indiana, Kentucky, and Tennessee . When the two surrogates are 50-50, the higher concentrations extend even further westward, the highest concentrations are in NC, VA, and W.Virginia, and the concentrations in the northern Plains is slightly increased. As the weight is shifted to the PM10 surrogate, the peak concentrations are no longer found in NC, the higher concentrations stretch further west and south, and the concentrations in the Northern Plains increase. These changes are a reflection of the PM10 concentration grid.

Cross validation was applied to compare the estimation of fine mass concentration fields using simple 1/r2 interpolation, B_ext surrogate, PM10 surrogate and 50-50 B_ext-PM10 surrogate. It is difficult to draw any solid conclusions from the results but it seems that with an adequate weighting system, multiple surrogates can improve the estimation of fine mass concentrations. At some locations B_ext was the better surrogate while at others PM10 proved better. The cross validation showed that using both surrogates gave the highest R² value (0.72) while the best slope and offset were achieved by using only the B_ext surrogate. The PM10 surrogate gave a higher R² value than did the B_ext.