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HYSPLIT). Both approaches show CAMx <strong>and</strong> HYSPLIT as <strong>the</strong> highest ranking models for CTEX5<br />

with rankings that are fairly close to each o<strong>the</strong>r, however after that <strong>the</strong> two ranking techniques<br />

come to very different conclusions regarding <strong>the</strong> ability <strong>of</strong> <strong>the</strong> models to simulate <strong>the</strong> observed<br />

tracer concentrations for <strong>the</strong> CTEX5 field experiment.<br />

The most noticeable feature <strong>of</strong> <strong>the</strong> RANK metric for ranking models in CTEX5 is <strong>the</strong> third highest<br />

ranking model using RANK, CALGRID (1.57). CALGRID ranks as <strong>the</strong> worst or second worst<br />

performing model in 9 <strong>of</strong> <strong>the</strong> 11 performance statistics, so is one <strong>of</strong> <strong>the</strong> worst performing<br />

model 82% <strong>of</strong> <strong>the</strong> time <strong>and</strong> has an average ranking <strong>of</strong> 5 th best model out <strong>of</strong> <strong>the</strong> 6 LRT dispersion<br />

models. In examining <strong>the</strong> contribution to <strong>the</strong> RANK metric for CALGRID, <strong>the</strong>re is not a<br />

consistent contribution from all four broad categories to <strong>the</strong> composite scores (Figure ES‐5). As<br />

noted in Table ES‐2, <strong>the</strong> RANK score is defined by <strong>the</strong> contribution <strong>of</strong> <strong>the</strong> four <strong>of</strong> <strong>the</strong> 11<br />

statistics that represent measures <strong>of</strong> correlation/scatter (R 2 ), bias (FB), spatial (FMS) <strong>and</strong><br />

cumulative distribution (KS):<br />

( 1−<br />

FB / 2 ) + FMS / 100+<br />

( 1 KS / 100)<br />

2<br />

RANK = R +<br />

−<br />

The majority <strong>of</strong> CALGRID’s 1.57 RANK score comes from <strong>the</strong> fractional bias (FB) <strong>and</strong><br />

Kolmogorov‐Smirnov (KS) performance statistics with little or no contributions from <strong>the</strong><br />

correlation (R 2 ) or spatial (FMS) statistics. As shown in Table ES‐6, CALGRID performs very<br />

poorly for <strong>the</strong> FOEX <strong>and</strong> FA2/FA5 statistics due to a large underestimation bias. The FB<br />

component to <strong>the</strong> RANK composite score for CALGRID is one <strong>of</strong> <strong>the</strong> highest among <strong>the</strong> six<br />

models in this study, yet <strong>the</strong> underlying statistics indicate both marginal spatial skill <strong>and</strong> a large<br />

degree <strong>of</strong> under‐prediction (likely due to <strong>the</strong> spatial skill <strong>of</strong> <strong>the</strong> model).<br />

The current form <strong>of</strong> <strong>the</strong> RANK score uses <strong>the</strong> absolute value <strong>of</strong> <strong>the</strong> fractional bias. This<br />

approach weights underestimation equally to overestimation. However, in a regulatory<br />

context, EPA is most concerned with models not being biased towards under‐prediction.<br />

Models can produce seemingly good (low) bias metrics through compensating errors by<br />

averaging over‐ <strong>and</strong> under‐predictions. The use <strong>of</strong> an error statistic (e.g., NMSE) instead <strong>of</strong> a<br />

bias statistic (i.e., FB) in <strong>the</strong> RANK composite metrics would alleviate this problem.<br />

Adaptation <strong>of</strong> RANK score for regulatory use will require refinement <strong>of</strong> <strong>the</strong> individual<br />

components to insure that this situation does not develop <strong>and</strong> to insure that <strong>the</strong> regulatory<br />

requirement <strong>of</strong> bias be accounted for when weighting <strong>the</strong> individual statistical measures to<br />

produce a composite score.<br />

22

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