Three widely used Lagrangian particle dispersion models (LPDMs)-the Hybrid Single-Particle Lagrangian Integrated Trajectory (HYSPLIT),
Lagrangian particle dispersion models (LPDMs) are a powerful tool for modeling atmospheric transport (Lin et al. 2012). An LPDM tracks a set of tracer particles either forward in time from a source region or backward in time from a measurement location (receptor). Each particle is transported by advective wind fields (obtained from a meteorological model) plus an unresolved tur- bulent (subgrid) velocity component. Lagrangian models have minimal numerical diffusion (e.g., Eluszkiewicz et al. 2000) and can preserve tracer gradients at smaller spatial scales than can Eulerian models because the latter smooth tracer concentrations to the resolution of the meteorological model grid. The inclusion of both the mean (resolved) and stochastic (unresolved) wind components (Uliasz 1994) sets the LPDMs apart from conventional trajectory models that employ only mean winds and thus cannot properly simulate dispersion or surface interactions (Stohl 1998). Through careful uti- lization of outputs from numerical weather prediction models (Uliasz 1993), meteorological realism and mass conservation can be achieved (Nehrkorn et al. 2010; Brioude et al. 2012a).
Forward-in-time LPDM computations are a natural choice for examining the dispersion of tracers from known source regions. An example of forward computations is a release of radioactive materials (e.g., Wotawa et al. 2006) such as that resulting from the accident at
When LPDMs are run in the backward-in-time mode from receptors, they can provide the sensitivity of the modeled concentration to upwind sources (
In recent decades a number of LPDMs have been de- veloped that use a variety of meteorological inputs and employ different methods for calculating atmospheric transport and dispersion. In this study, we compare three widely used LPDMs-the Hybrid Single-Particle Lagrangian Integrated Trajectory (HYSPLIT) model (Draxler and Hess 1997, 1998; Draxler 1999), the
2. Experimental data
CAPTEX consisted of six 3-h perfluoromonometh- ylcyclohexane (PMCH) tracer releases from 18 September to
ANATEX consisted of 66 perfluorocarbon tracer releases, 33 each from two different locations, from 5 January to
3. WRF model configuration
The goal of this study is to establish whether differ- ences in plume transport among the models are due to differences in the LPDM formulation or to the way the meteorological driver fields are generated and applied. When the initial model-evaluation studies using CAPTEX and ANATEX data were conducted (e.g., Stohl et al. 1998), only global meteorological data were available. Mesoscale models have been more recently used to gen- erate the driver fields (e.g., Deng et al. 2004) for dispersion simulations of controlled tracer-release experiments. Mesoscale models have many options in how the me- teorological fields can be calculated, and these selections influence the subsequent dispersion calculations. In this work, the three LPDMs were driven by meteorological fields created by the
The WRF simulations were restarted
Transport models may use WRF standard outputs as is; WRF can also produce additional outputs implemented specifically for the benefit of transport simulations (Nehrkorn et al. 2010). These include 1) time-averaged, mass-coupled horizontal and vertical velocities (using the WRF terrain-following vertical coordinate h) to improve mass conservation and the representation of wind vari- ability and 2) time-averaged mass fluxes from the WRF moist convective parameterization scheme. In our exper- iments, we drove the LPDMs with both the time-averaged fields (denoted as avrg in results) and the instantaneous fields (denoted as inst) in separate sensitivity tests. The instantaneous fields were not mass coupled, used the geometric vertical velocity w, and did not make use of the convective mass fluxes.
4. Lagrangian particle dispersion models
For the evaluations, the three LPDMs were run for- ward in time, driven with identical meteorological fields provided by WRF (in several computational and/or output configurations). In addition, baseline calcula- tions with HYSPLIT and STILT were performed for each experiment using only the NARR meteorological data.1 When an LPDM is run in the forward mode, a number of pollutant particles are released at the source location and passively follow the wind. The particle trajectory is the integration of the particle's position vector in space and time using a velocity field composed of a mean component from the meteorological model and a turbulent component. The turbulent component of the motion defines the dispersion of the pollutant cloud and is computed by adding a random component to the mean advection velocity in each of the three- dimensional wind-component directions. The vertical and horizontal turbulence is computed from the various meteorological inputs by using parameterization schemes that differ in each LPDM, as will be discussed in the sections that follow. Models employ different methods to compute air concentrations, from simply summing the mass of particles as they pass over a concentration grid cell and dividing the result by the cell's volume to ap- plying a technique to distribute the mass of each particle between adjacent cells following a predefined functional distribution kernel. For our study, the calculated con- centrations were averaged over 6 and 24 h for CAPTEX and ANATEX, respectively, to match the tracer-sampling periods. A more detailed description of each LPDM that focuses on their differences is provided in sections 4a--c.
In HYSPLIT, the calculation of particle dispersion is carried out on the native WRF horizontal grid (Lambert conformal in this study). Given that HYSPLIT uses an internal terrain-following vertical coordinate system, however, the WRF meteorological profiles at each hori- zontal grid point are linearly interpolated to this internal vertical grid. The vertical grid is defined with the first level at ;10 m above ground level (AGL) and with de- creasing vertical resolution with height.
Random horizontal and vertical turbulence compo- nents with a Gaussian distribution are added to the mean trajectory. The random components are scaled by the turbulent velocity standard deviation computed from the Lagrangian time scale of turbulence and the diffusion coefficients estimated on the basis of inputs from the driving meteorological model (
The overall integration time step was 1 min (although the integration time step for the dispersion can be as low as 1 s), and the 3-h tracer releases were represented by 50 000 particles in CAPTEX and 25 000 particles in ANATEX. The fewer particles released for ANATEX were compensated for by the longer averaging time. Furthermore, because two ANATEX tracer releases could be on the computational domain at the same time, the same number of total particles was followed as for each CAPTEX release. A limited number of tests in- dicated little sensitivity of the results to the number of particles released beyond 25 000 particles. The resolu- tion of the output concentration grid was set to 0.258 in both latitude and longitude and 100 m in the vertical direction.
STILT is built upon the HYSPLIT software and uses the same mean advection scheme but a different tur- bulence module (Lin et al. 2003). The STILT configu- ration for the tracer simulations is identical to HYSPLIT in terms of the concentration grid, number of particles released in the forward runs, and many of the remaining parameters. STILT contains several distinct features not available in HYSPLIT, however. One of them is a reflection/transmission scheme for Gaussian turbulence (Thomson et al. 1997) that preserves well-mixed distri- butions of particles moving across interfaces between step changes in turbulence parameters. Lin et al. (2003) demonstrated that such a scheme is necessary to prevent accumulation of particles in low-turbulence regions of the strongly inhomogeneous environment of the PBL where a simple drift correction may not work. Another feature is the ability of STILT to directly use the con- vective mass fluxes generated in WRF by the Grell-- Devenyi cumulus scheme in the dispersion of particles, incorporating the vertical profiles of up- and down- drafts and entrainment and detrainment fluxes be- tween the environment and convective cells (Nehrkorn et al. 2010).
We use a version of FLEXPART modified for use with WRF (Fast and Easter 2006; Brioude et al. 2012a). It uses the native horizontal grid of WRF and inter- polates the WRF vertical levels onto an internal terrain- following vertical coordinate for the computation of particle transport and dispersion. The concentrations were output on a 25 km 3 25 km horizontal grid using the same projection as WRF. The WRF-compatible ver- sion of FLEXPART has the option of outputting regular latitude--longitude concentration grids similar to those in HYSPLIT and STILT, but we found that using the WRF projection produced better results, and only those results are used in the statistical evaluation reported below.2 The horizontal grid spacing for the FLEXPART con- centration output was selected to match closely the 0.258 latitude--longitude grid of HYSPLIT and STILT. As with HYSPLIT and STILT, the concentrations were calcu- lated over the lowest 100 m AGL. The scheme of
5. Statistical evaluation
Procedures for evaluatingdispersionmodelshavea long history (Fox 1984;
Both Mosca et al. (1998) and Stohl et al. (1998) recognized the problem presented by uncertainties in ''near background'' measurements that affect statis- tical parameters that are sensitive to small variations in the measurement values, such as ratios between measured and calculated concentrations. For a quick evaluation, it is desirable to have a single parameter that represents the overall model performance. Stohl et al. (1998) found that the ratio-based statistics are indeed very sensitive to measurement errors whereas the correlation coefficient is more robust. Chang and
This section summarizes the statistical evaluation of the LPDM runs for six different CAPTEX experiments and two ANATEX experiments (GGW and STC), each ANATEX ''experiment'' consisting of five releases. The combination of multiple ANATEX releases into a single experiment for this evaluation resulted in a comparable number of measured--calculated data pairs for analysis between the 6-h sample duration during CAPTEX and the 24-h sample duration during ANATEX (354, 365, 346, 299, 306, 183, 562, and 556 for the six CAPTEX ex- periments and two ANATEX experiments, respectively).
The normalized statistical parameters composing the ranks for each of the experiments are represented graph- ically in Fig. 2. From this figure it is clear that a single statistic such as the correlation coefficient, although generally helpful in ranking models, is not always useful on its own. For example, for CAPTEX-4 the correlation coefficient is near zero for all models because of the simulated trajectory of the plume center being too far south and provides little information on the differences in model skill that are indicated by the other statistical parameters. Therefore, while we recognize that there are limitations in any one parameter, we select the rank as a convenient summary of the modeling results.
The HYSPLIT, STILT, and FLEXPART statistical ranks are presented in Tables 1, 2, and 3, respectively. Except for the column labeled ''NARR only,'' the ranks in each table were generated with identical meteoro- logical inputs provided by WRF in the configurations discussed in section 3. The NARR-only column shows ranks for HYSPLIT and STILT driven directly by the NARR fields, providing a baseline performance metric to evaluate the impact of the higher temporal and spatial resolution afforded by WRF.
The statistical ranks indicate that in all eight experi- ments there is at least one and usually several WRF- based simulations that perform better than their NARR counterparts, and this result is true for both HYSPLIT and STILT. This result confirms that the higher tem- poral (1 vs 3 h) and spatial (10 vs 32 km) resolution available from WRF provides substantial benefit to the LPDM simulations. For the WRF-based runs, it is clear that the best configuration for all three LPDMs included nudging of the PBL winds (pbl 5 1) and time-averaged fields (avrg). For this WRF configuration there is little difference between the LPDMs, as shown by the fact that the average ranks over all experiments (shown in the last row of the tables) differ by less than 0.1. This fact indicates that each of the LPDMs has the about the same skill level if provided with identical meteorological in- puts. There are some notable differences among the LPDMs for other WRF configurations, however, and even for the same LPDM using different WRF config- urations that indicate various model sensitivities to er- rors in meteorological inputs.
With one exception, the nudging of winds within the PBL has either a substantial positive impact or a small negative impact on the ranks (the negative impact is limited to HYSPLIT and STILT and occurs mostly when instantaneous fields are employed, which, as discussed below, result in inferior results when com- pared with the time-averaged fields). The one excep- tion is ANATEX-STC, when the PBL wind nudging lowers the ranks by about 0.3 for all three LPDMs. This case is also unique in that the NARR-based runs for HYSPLIT and STILT are generally better than the WRF-driven runs. The cause of this outlier behavior is likely related to the spacing of the sampling network (this is further discussed in section 7). We conse- quently believe that this experiment should be given less weight in our evaluation and does not invalidate the overall conclusions.
The FLEXPART model shows the greatest positive impact of PBL wind nudging, with average ranks im- proving by 0.21 and seven (avrg) and six (inst) of eight experiments improving when it is enabled (Table 3). For HYSPLIT and STILT, the impact is smaller but still consistent, with average ranks improving by 0.08 and 0.13, respectively, and five and six of eight experiments improving, respectively, when time-averaged fields are used. The impact of PBL wind nudging for HYSPLIT and STILT is not as consistently positive when instan- taneous fields are used, as average ranks only improve by 0.05 for HYSPLIT and actually decrease by 0.01 for STILT, with four HYSPLIT and six STILT experiments showing improvement. Despite this overall lesser im- pact, several experiments still show a substantial posi- tive impact of PBL nudging even when instantaneous fields are used. For example, for CAPTEX-2, the ex- periment simulated best by all LPDMs, PBL wind nudging improves the avrg (inst) ranks by 0.55 (0.29) for HYSPLIT and by 0.50 (0.15) for STILT; while these im- provements are smaller than the corresponding values of 0.70 (0.63) for FLEXPART, they are still substantial. Both HYSPLIT and STILT have higher average ranks than FLEXPART, however, suggesting there may be a limit to the improvement that can be achieved by PBL wind nudging and time averaging.
The inclusion of nudging of the PBL winds in WRF seems to have had the most noticeable impact on the LPDM simulations. In our initial design phase of the experiments, we tested several other configurations, including continuous runs versus daily restarts, one-way versus two-way nesting, observational nudging, and grid nudging above the PBL in the outer domain versus in both domains for HYSPLIT and STILT simulations of the CAPTEX cases. The results of all of these runs were similar, however, and it was only with the in- clusion of PBL wind nudging that substantial, generally positive, impacts were achieved. Although grid nudg- ing of winds at all vertical levels was recommended for previous generations of mesoscale models at coarser resolution (Stauffer and Seaman 1990; Stauffer et al. 1991), our initial hypothesis was that, given the rela- tively high spatial resolution of our inner domain, grid nudging should only be applied above the PBL to allow the presumably more advanced WRF PBL schemes to develop mesoscale features in response to the influences of the resolved finescale terrain and land-use features without the artificial damping effects of nudging to a comparatively coarse analysis. From our results it appears that the advantages of nudging to control error growth in WRF outweigh the possible damping effects, however. As discussed in section 7, nudging helps to reduce larger-scale plume transport errors that may result from a speed bias in the WRF PBL winds.
Time-averaged fields are clearly beneficial for HYSPLIT and STILT, producing an average rank improvement over the instantaneous velocities of 0.13 for both mod- els and improvements in four and six of eight experi- ments, respectively in the pbl 5 1 configuration. For FLEXPART, time-averaged fields are of lesser benefit, producing an average improvement in rank of only 0.01 and the same or improved ranks in five of eight experi- ments with or without PBL wind nudging. This result is consistent with Brioude et al. (2012a), who found that using time-averaged velocities reduced the bias and uncertainty by less than 5% for FLEXPART sim- ulations over complex terrain. For some cases, however, the impact of time-averaged fields is substantial for all three LPDMs-for example, improving the ranks for the CAPTEX-5 pbl 5 1 simulations by 0.10, 0.19, and 0.13 for HYSPLIT, STILT, and FLEXPART, respectively. As discussed in more detail in section 7, the use of time- averaged fields produces a more uniform simulation of the plume dispersion.
7. Case studies
In section 6, we presented several statistical conclu- sions regarding the overall LPDM performance. In this section, the results will be examined in more detail by analyzing model combinations that showed the largest differences in rank between the simulations for both re- gional and continental scales. We use concentration plots together with the statistics presented earlier to examine the impact of PBL wind nudging on regional-scale transport with CAPTEX-2 (Fig. 3) and on continental- scale transport using ANATEX-GGW (Fig. 4) and the contrasting case of ANATEX-STC (Fig. 5). For the im- pact of time-average flux fields, we examine CAPTEX-5 (Fig. 6). All of the concentration plots that are presented were generated using the same HYSPLIT plotting soft- ware to facilitate comparisons among the LPDMs. Since FLEXPART produces concentrations on the WRF projection grid, these outputs required interpolation to the regular latitude--longitude grids of HYSPLIT and STILT. A visual comparison of the FLEXPART interpolated concentration plots and noninterpolated concentration plots (generated by the FLEXPART plot- ting software) indicated that the interpolation did not substantially alter the dominant features of the tracer plumes.
The impact of PBL wind nudging is most striking for CAPTEX-2, with rank improvements of greater than 0.5 for all three LPDMs when time-averaged fields are used (Tables 1--3). The concentration plots for these runs for the 6-h sampling period that began 28 h after the start of the tracer release indicate that the plumes simulated with PBL wind nudging (Fig. 3) tend to move more slowly, intersecting samplers in northwestern
The nudging of PBL winds has a similar impact on the continental-scale simulations, as illustrated by the con- centration plots for the 24-h period beginning
Figure 4 also illustrates some substantial differences among the LPDM simulations. The eastern plume is more cohesive in the HYSPLIT and STILT simulations, whereas in the FLEXPART pbl 5 1 simulation it splits into northern and southern branches. The split plume is hinted at in the observations, with lower values of 2-- 50 pg m23 in
As noted in the statistical evaluation presented in section 6, the ANATEX-STC simulations are degraded when PBL wind nudging is employed, in a clear contrast to other cases. A visual inspection of the concentration plots for ANATEX-STC indicates that the plumes in the pbl 5 1 simulations agree with observations about as well as those with pbl 5 0, however. A possible explanation for this inconsistency and for why the ANATEX-STC ranks are so low may be the sparseness of the obser- vations downwind of the release. As illustrated in Fig. 5 for the HYSPLIT ANATEX-STC simulation of the 24-h period beginning
Another key result regarding the use of meteorolog- ical data is that the calculations using time-averaged fields are generally better than those using instantaneous fields. This finding is not as universally applicable as the impact of PBL wind nudging, however, being limited to HYSPLIT and STILT. The only case for which it has a substantial positive effect for all three LPDMs is CAPTEX-5, illustrated in Fig. 6 for the 6-h sampling period that began 17 h after the release. In this experi- ment, the winds were strong, the plume was very narrow, and all simulated plumes essentially covered the same sampling stations. Calculations using time-averaged fields (Figs. 6a--c) generally provided smoother concentra- tion patterns, more consistent with measurements than those simulated using instantaneous fields (Figs. 6d--f).
Although we have only shown selected cases, the graphical differences in these examples represent a consistent pattern across all experiments and the three LPDMs, as evidenced in Tables 1--3. In particular, the tendency for the plumes to be transported too quickly downwind in all simulations without PBL wind nudging suggests a bias in the near-surface wind speeds gener- ated by WRF. Such a bias in WRF is noted by Jim^enez and Dudhia (2012), who attribute it to an inadequate representation of the frictional drag imposed by subgrid- scale topographic features.3 It is interesting that nudging to NARR acts to correct this problem, suggesting that the NARR analysis does not have this bias.
8. STILT reversibility
LPDMs are often used in the backward mode (e.g., to support top-down estimates of GHG fluxes), and this fact raises the question of how well the forward results presented so far reflect their accuracy in this common mode of application. Since resources did not permit a comparison of all three models in forward and back- ward mode and because STILT is primarily used in backward mode, we selected this model for these com- parisons. A similar forward--backward comparison for FLEXPART was recently performed by Brioude et al. (2012a), however, and the similarities between HYSPLIT and STILT reflected in the forward runs suggest that the forward--backward comparison for STILT should be representative of HYSPLIT.
For the backward-mode tests, we simulated CAPTEX and ANATEX measurements by convolving STILT- generated footprints with the known tracer fluxes and then averaging over the same time periods as the mea- surements (either 6 or 24 h). Fluxes were approximated on a 18 grid centered on the tracer release location, at hourly temporal resolution, over the 3-h tracer release time periods. The fluxes convolved with the STILT particle footprints yield a ''delta'' mixing ratio for each point in time along the particle trajectory, and these are summed over the entire particle trajectory to yield the total delta mixing ratio for that particle. The total delta mixing ratio for a single receptor is the average of the total delta mixing ratios of all particles emanating from that receptor. The simulated 6- or 24-h averaged measurement at each location was calculated as the av- erage total delta mixing ratio of 6 or 24 receptors, defined at hourly increments throughout the measurement pe- riod. Note that the delta mixing ratios represent the ac- tual mixing ratios because the background concentrations of the artificial tracers are assumed to be zero. They were converted to concentrations at the measurement sites, and the validation statistics were calculated in the same manner as in the forward calculations.
Only time-averaged fields were used in these back- ward runs, with particles released from heights of 50 and 10 m AGL. The 50-m height is the midpoint of the av- eraging layer for which the concentrations were calcu- lated in the forward runs, allowing a direct comparison, and the 10-m height is closer to ground level at which the measurements were taken. As in most STILT-based footprint calculations (e.g., McKain et al. 2012), we employed 500 particles in the backward runs. For se- lected experiments, sensitivity runs using 5000 particles produced minimal changes in the results. Because of the computational expense of the ANATEX runs, we only simulated the
The ranks for the backward STILT runs shown in Table 4 indicate that the backward runs were as accurate as their forward counterparts. For the 50-m-AGL pbl 5 1 case, the average backward rank for the CAPTEX runs (2.65) is actually slightly greater (by 0.11) than its forward counterpart (2.54), whereas for ANATEX- GGW it is slightly lower (by 0.11). For the best overall case, CAPTEX-2, the backward and forward ranks are within 0.01 of each other. Furthermore, PBL wind nudging exerts similar positive influence on the simula- tions, increasing the average ranks by 0.21 and 0.20 for the backward and forward CAPTEX runs, respectively. The ranks for the 10-m-AGL runs are only slightly lower than for 50 m (by an average of 0.04 when PBL wind nudging is employed), reflecting the ability of the LPDM to work well near the surface. Overall, these backward STILT runs demonstrate the reversibility and good performance of this LPDM in the receptor-oriented mode.
We evaluated three widely used LPDMs (HYSPLIT, STILT, and FLEXPART) with controlled tracer release data from the CAPTEX and ANATEX experiments. The LPDMs were driven by identical meteorological fields, enabling the differences attributable to the LPDM formulation and to their sensitivities to the various con- figurations of input data to be separated. With the ex- ception of one case in which sampling artifacts may have degraded the reliability of our statistical analysis, several robust conclusions have emerged from this study. In particular, all three LPDMs had comparable skill in simulating the tracer plumes when driven with modern meteorological inputs (including NARR and several configurations of WRF), indicating that differences in their formulations play a secondary role. Our simulations demonstrate the benefit of employing 10-km customized WRF runs over NARR at 32-km resolution. The LPDMs exhibited significant sensitivity to the WRF configura- tions. Perhaps most striking is that all three LPDMs performed substantially better when the WRF wind fields within the PBL were nudged to NARR, with FLEXPART benefitting most from this nudging. The PBL wind nudg- ing appears to correct an overestimate of the plume transport speed, possibly caused by a positive wind speed bias near the surface. On the basis of only this study we cannot generalize that nudging of PBL winds is necessary for all LPDMs, but it should be a consideration for fu- ture LPDM studies using WRF. Another consistent finding from our study is that all three LPDMs benefitted from the use of time-averaged velocity and convective mass flux fields generated by WRF, but in this case the impact on HYSPLIT and STILT was greater than on FLEXPART. The STILT backward runs performed as well as their forward counterparts, demonstrating this model's reversibility and good performance in its most common application to inverse flux estimates.
Transport simulations offer an opportunity to evalu- ate meteorological models that extends beyond con- ventional verification that involves comparisons of the model-predicted meteorological variables with obser- vational data. These typical comparisons are fixed in space and time, whereas the comparison with tracer data represents a time and space integration of the meteorological field in which small differences accu- mulate to provide a more integrated comparison. Our study provides a detailed evaluation of the current state of LPDMs using historical tracer-release data and thus provides a limited benchmark of their performance as they are used in a growing range of applications, in- cluding inverse GHG flux estimates, air quality, and the dispersion of toxic airborne contaminants.
Acknowledgments. We gratefully acknowledge support for this study from the
1 The FLEXPART version used here could not be driven with NARR.
2 As discussed in the text, for plotting purposes the FLEXPART results are interpolated to a regular latitude-longitude grid.
3 In the most recent WRF version (version 3.5), the surface-layer parameterization has been upgraded to correct this bias by adding a momentum sink.
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Corresponding author address:
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