1. Background and objectives

Nearly all atmospheric transport and dispersion (ATD) models make use of inputs of the mixing depth, also known as the mixing height or the planetary boundary layer height (Arya 1999). The mixing depth defines the top of the layer near the surface where turbulent mixing is occurring. During the daytime, the mixed layer typically has an adiabatic or superadiabatic temperature lapse rate and the mixing depth is often marked by a capping inversion. During sunny convective conditions, the turbulence in the mixed layer is mostly generated by the sensible heat flux. When the wind is strong, the mixed layer near the surface is nearly adiabatic at all times of the day and the turbulence is mostly mechanically generated. There may be a capping inversion at the top of the windy boundary layer during clear conditions. During the night, the mixed layer may be stable near the ground if conditions are mostly clear. There is usually a shallow mixed layer very near the surface in stable conditions due to generation of turbulence by wind shear, although the mixed layer may be only a few meters deep.

The mixing depth can be observed by a variety of methods. The most widely used method employs radiosonde soundings, which provide vertical profiles of temperature and relative humidity (RH). The mixing depth can often be identified on these vertical profiles by the capping inversion and also by a sharp drop in RH. However, these criteria do not always work because the temperature and RH profiles sometimes can be ambiguous. Also, there can be elevated “residual” mixing depths that are holdovers from the previous day or may have formed some distance upwind and were advected over the region of interest. Other methods of observing the mixing depth include remote sensing devices such as radars (Angevine et al. 1994; Bianco and Wilczak 2002) and lidars (Cohn and Angevine 2000). In this case the mixing height is indicated by a discontinuity in a remotely observed variable.

Most of the methods for estimating mixing depth will have difficulties during stable nights when the mixing depth may be less than 10 or 20 m and the radiosonde or remote sounder cannot measure that close to the ground. In this case, an instrumented tower is useful, with temperature sensors at multiple heights through 30–40 m.

An alternate source of mixing depth estimates is a regional or mesoscale meteorological model. Mesoscale meteorological models such as the fifth-generation Pennsylvania State University–National Center for Atmospheric Research Mesoscale Model (MM5) (Liu et al. 2006) produce outputs of mixing depth that can be based on the height where the model-simulated turbulent kinetic energy (TKE) first drops below some fraction of its value at the surface or below some arbitrary lower limit based on experience. Alternatively, the mixing depth can be based on the height where the bulk Richardson number for the model outputs surpasses a critical value (as discussed in Angevine and Mitchell 2001).

Many modern dispersion models contain methods to parameterize the mixing depth in the absence of nearby direct observations of the mixing height or without the aid of mesoscale meteorological models. For example, the American Meteorological Society (AMS)/Environmental Protection Agency (EPA) Regulatory Model (AERMOD) Meteorological Processor (AERMET) model (EPA 2004) is a meteorological preprocessor that parameterizes mixing depth. For convective conditions, these methods rely on the morning (1200 UTC) radiosonde profile and an estimate of the sensible heat flux. For neutral and stable conditions, the methods rely on an empirical function that includes the friction velocity u* and the Monin–Obukhov length L (e.g., Sykes et al. 2007).

The current study focuses on a specific model—the Hazard Prediction and Assessment Capability (HPAC) (DTRA 2004), which is a comprehensive modeling system that includes the Second-Order Closure Integrated Puff (SCIPUFF) ATD model (Sykes et al. 2007). The HPAC application in this paper uses observations from the Joint Urban 2003 field experiment (JU2003) (Allwine et al. 2004; Clawson et al. 2005), which was conducted in the Oklahoma City (OKC) area in July 2003. JU2003 provides an extensive dataset for transport and dispersion model evaluation. JU2003 included 10 intensive observation periods (IOPs) during which the tracer sulfur hexafluoride (SF₆) was released for 30-min periods. An IOP was conducted on a day that was deemed favorable by the field managers of the study. This paper addresses IOPs 3, 4, 5, and 6, which took place during the daytime on 7, 9, 13, and 16 July 2003, respectively (these are sometimes referred to in the JU2003 reports as Julian days 188, 190, 194, and 197). Each of these IOPs included three 30-min continuous tracer releases, separated by 2 h. The SF₆ from these releases was sampled by bag samplers at outer arc distances of 1, 2, and 4 km from the release location. Numerous other samplers operated at distances less than 1 km. In addition to the numerous tracer samplers used in JU2003, extensive meteorological measurements were taken from diverse observational platforms that were set up across a broad area, ranging from the downtown area to rural areas located 10 to 20 km upwind and downwind of the city.

It was originally thought that meteorological conditions were “similar” during the four daytime IOPs. However, independent evaluations of the HPAC/SCIPUFF ATD model by Warner et al. (2008) and Hanna et al. (2007a) report large underpredictions in concentration by HPAC/SCIPUFF during IOP 5 (13 July 2003), when tracer releases took place at 0800, 1000, and 1200 LST (1400, 1600, and 1800 UTC). These large underpredictions did not occur during the other daytime IOPs (3, 4, and 6). The observed concentrations during IOP 5, which were a factor of 10 or more larger than the concentrations observed during the other daytime IOPs, were more typical of concentrations observed during the nighttime IOPs (7, 8, 9, and 10). The current paper describes the results of an investigation of the reasons for the large underpredictions during IOP 5. It appears that the large observed concentrations were caused by a relatively low mixing depth, as observed by on-site remote sounders and as explained by looking at synoptic and radar maps. The HPAC/SCIPUFF model, on the other hand, was using parameterized mixing depths that were much larger and more typical of climatological values. Even when using the MM5 outputs of mixing depth, there were still large underpredictions by HPAC/SCIPUFF, although not as large as when the parameterized values were used.

2. Observations and ATD model predictions of concentrations during daytime IOPs

Figure 1 shows the observed arc maximum tracer concentrations C, normalized by source emission rate Q, at downwind distances of 1, 2, and 4 km for the tracer releases during daytime IOPs 3, 4, 5, and 6 (indicated on the histogram by different shaded bars). The concentration averaging time is 30 min. For each release time in the figure, there are three groupings of vertical bars, indicating the normalized concentrations at the three arc distances. The start times for the 30-min SF₆ releases during IOPs 3 and 4 were 1600, 1800, and 2000 UTC (1000, 1200, and 1400 LST), while the start times for the SF₆ releases during IOPs 5 and 6 were 1400, 1600, and 1800 UTC (0800, 1000, and 1200 LST). Note that, because of the different IOP start times, Fig. 1 shows arc maximum concentrations for only two IOPs for the 1400 and 2000 UTC release times.

It is seen in Fig. 1 that the maximum concentrations measured during the first two SF₆ releases of IOP 5 (1400 and 1600 UTC, or 0800 and 1000 LST) were almost an order of magnitude higher than those measured at the same times of day during the first two releases of IOP 6 and the first release of IOPs 3 and 4. The maximum concentration measured during the third release of IOP 5 (1800 UTC or 1200 LST) was comparable to the levels measured during the other IOPs for the same time period. Later it will be shown that the observed mixing depth during IOP 5 was much less than the other IOPs for the releases at 0800 and 1000 LST, but had increased to close to the values for the other IOPs by 1200 LST.

The HPAC/SCIPUFF ATD model (version 4.04), with standard options, was used to calculate the 30-min average arc maximum normalized concentrations, C/Q, for comparison with the observed concentrations during the daytime IOPs. The same HPAC urban dispersion model option and meteorological inputs, including point wind measurements from a special field experiment site about 1 km upwind of the tracer release, were used in the HPAC predictions for all daytime IOPs. It should be noted that the model’s parameterized mixing depths were used in the ATD model runs reported here.

Figure 2 compares the predicted and observed arc maximum normalized concentrations for each of the three tracer releases for IOPs 3, 4, 5, and 6. For the arc maximum concentrations, the predicted and observed values at each sampling arc do not necessarily occur at the same sampling location on the arc. In Fig. 2, the solid diagonal line represents perfect agreement and the dashed lines represent factor of 2 differences between predicted and observed normalized concentrations. The general tendency in the figure is for HPAC to underpredict the observed normalized concentrations, with most of the values for IOPs 3, 4, and 6 near the line indicating a factor of 2 underprediction. However, the HPAC predictions for the first two releases of IOP 5 are about an order of magnitude lower than the observations. The correspondence between predicted and observed concentrations for the third release of IOP 5 is comparable to that obtained for the other IOPs.

An investigation was mounted to determine the reasons for the high observed concentrations and severe model underpredictions for IOP 5. Possible reasons could be low wind speeds, low turbulence intensities, or low mixing depths. Low wind speeds were unlikely to be the cause, since a previous study by Hanna et al. (2007b) found that the IOP average wind speed difference between daytime IOPs was relatively small. Our primary hypothesis was that the higher observed normalized concentrations were related to relatively low mixing depths, which were less than mixing depths parameterized by HPAC/SCIPUFF when run in the default mode.

3. Observations of mixing depth

Vertical profiles of temperature and humidity from the Argonne National Laboratory (ANL) and Pacific Northwest National Laboratory (PNNL) radiosonde soundings during JU2003 were studied to determine the observed mixing depths during IOPs 3, 4, 5, and 6. Additionally, the observed mixing depths estimated from the boundary layer turbulence measurements by Dugway Proving Ground’s Frequency Modulated/Continuous Wave (FM/CW) radar (Gallagher et al. 2004) were studied. The ANL radiosonde site was approximately 4.3 km north of the tracer release site, the PNNL radiosonde site was approximately 2.2 km south-west of the release site, and the FM/CW radar was approximately 1.5 km north of the release site. The tracer release sites were within the Central Business District (CBD) or on its upwind edge. The radiosonde releases and the radar were generally located in the suburbs, as opposed to the CBD. The radiosonde launch times occurred at or near the start of each of the tracer releases.

The FM/CW radar provides continuous readings of the boundary layer turbulence structure. Mixing depths are estimated using the knowledge that the radar return in a convective boundary layer is large in the superadiabatic layer near the surface, small in the well-mixed portion of the boundary layer above the surface layer, and large again in the elevated inversion layer at the top of the mixed layer (Gallagher et al. 2004). The radar can also provide details on the complexity of the near-instantaneous structure of the daytime boundary layer.

As an illustration of the use of the radiosonde profiles to estimate mixing depth, Fig. 3 contains the vertical profiles of temperature and RH observed by the PNNL radiosonde during IOP 5. The height of the capping temperature inversion and the height where RH sharply decreases clearly indicate the mixing height for the 1400 and 1600 UTC profiles (about 100 and 210 m, respectively). The profiles are less sharp at 1800 UTC, but still suggest a mixing depth at about 400–450 m.

Tables 1 and 2 list the mixing depths observed by the two on-site radiosondes and the FM/CW radar during IOPs 5 and 6, respectively. The FM/CW mixing depths were estimated at the start times of the tracer releases using the procedures described by Gallagher et al. (2004). As shown by the fourth column in each table, the average observed mixing depth ranged from approximately 100 to 490 m for IOP 5 and from approximately 430 to 1200 m for IOP 6. Thus, the observed mean mixing depths for IOP 5 were 3–4 times smaller than the mean mixing depths for IOP 6.

Figure 4 contains continuous time series of the estimated FM/CW radar mixing depths for the four daytime IOPs. The estimation method, based on the paper by Gallagher et al. (2004), is described three paragraphs above. The black, green, red, and blue lines represent IOPs 3, 4, 5, and 6, respectively. The red horizontal lines at the top of the figure identify the tracer gas release periods. It is obvious in the figure that the mixing depths for IOP 5 are considerably lower than the depths for the other daytime IOPs.

4. Turbulence observations during the daytime IOPs

Data from a meteorological tower on the northern edge of Oklahoma City were inspected to determine whether anomalous mixing conditions occurred during IOP 5. Mean and fluctuating velocity and virtual temperature measurements were available from the Lawrence Livermore National Laboratory (LLNL) crane pseudotower, which was located approximately 750 m NNW of the downtown area (Lundquist et al. 2004). This pseudotower consisted of a cable ladder under tension, anchored by a construction crane. Eight R. M. Young Model 81000 ultrasonic anemometers were mounted along this pseudotower, from approximately 8 to 84 m above the surface. The LLNL crane pseudotower microscale dataset provides high-resolution wind speed observations necessary for the calculation of variances, TKE, and the local dissipation of TKE. The crane data have been tilt corrected, using the correction algorithm suggested by Wilczak et al. (2001), lending credibility to the calculation of vertical fluxes in particular. More details on the construction of this pseudotower are presented in Gouveia et al. (2007).

The measurements of sensible heat flux from the LLNL crane pseudotower shown in Fig. 5 reveal a clear distinction between the delayed development of the convective boundary layer during IOP 5 and the more typical growth observed during IOPs 3, 4, and 6. Note that days 188, 190, 194, and 197 in the x-axis labels in Fig. 5 correspond to IOPs 3, 4, 5, and 6, respectively. The heat flux time series in IOPs 3, 4, and 6 show typical daytime behavior, following an approximate sine wave, starting to increase at 0700 or 0800 LST and reaching a maximum at about 1300 or 1400 LST. The time series for IOP 5 (lower left) remain negative or near zero, with plus and minus variations, until after 1100 LST. Note that tracer releases occurred at 0800, 1000, and 1200 LST. The negative heat fluxes observed during IOP 5 are associated with the influences of a distant thunderstorm complex, and suppress mixing activity and boundary layer growth in the JU2003 domain.

5. Synoptic maps and radar maps during IOP 5

The synoptic situation was studied for IOP 5 (13 July 2003) to find an explanation for the anomalously low mixing depths. NWS observations at the nearby Wiley Post Airfield indicated mostly cloudy to cloudy conditions over the area from 0700 to 1400 UTC (0100–0800 LST) 13 July 2003, but no precipitation. However, some of the surface observations from the Norman, Oklahoma, weather station, located to the south of OKC, reported lightning to the distant NW direction during this time period. The surface weather map analysis for 0000 UTC 13 July 2003 (or 1800 LST on the previous day) showed a propagating wave moving along a stationary front, with the frontal boundary over OKC and areas of rain showers in central Oklahoma. The surface map for 1200 UTC (0600 LST) 13 July, which is given in Fig. 6, shows that the wave moved into northwest Arkansas and the area of rain over central Oklahoma increased.

The radar map analysis at 1045 UTC (0445 LST) 13 July 2003 showed a general area of rain generated by convective activity from southwest to north of OKC. This is consistent with the observation of lightning reported by the Norman weather station. Figure 7 [the radar map at 1345 UTC (0745 LST)] shows that there is a moderate area of convection NW of Oklahoma City, and a larger line of cells centered along the Oklahoma–Arkansas border. This mesoscale convective complex is active at the time (0800 LST) of the first tracer release during IOP 5. The timing of this development corresponds to the location of the propagating wave along the frontal boundary at 1200 UTC 13 July (Fig. 6).

We suggest that the combination of the outflow from the nearby convective activity and the propagating wave along the frontal boundary caused the surface heat flux to be nearly zero and sometimes negative on the morning of IOP 5. These factors inhibited the growth of the mixing depth. The low mixing depths (100–200 m) during the first two tracer releases are more representative of nighttime situations.

6. Mixing depths estimated by MM5

As part of JU2003, high-resolution (4-km horizontal grid spacing) runs were made with MM5 (Liu et al. 2006). The HPAC/SCIPUFF ATD model is able to directly use mixing depth (and other) outputs from MM5. The Hanna et al. (2007a) HPAC/SCIPUFF (version 4.04) model evaluation exercise using the JU2003 field data considered the MM5 mixing depth input option as well as the observed and the HPAC/SCIPUFF parameterized mixing depth inputs. The MM5 mixing depths, which partially account for the stationary front and the rain showers, are about halfway in between the parameterized and the observed mixing depths and thus partly correct for the large HPAC/SCIPUFF underpredictions. However, since it is difficult for MM5 to simulate the timing and the spatial patterns of the outflow from the mesoscale convective complexes, the extremely low mixing depths during IOP 5 were not captured by MM5.

7. HPAC/SCIPUFF model-parameterized mixing depths compared with observations, and revised HPAC/SCIPUFF runs with observed mixing depths

The mixing depths parameterized by the HPAC/SCIPUFF (version 4.04) model, when run in its default mode, have been compared with the observations by the PNNL radiosonde. The comparisons are shown in Fig. 8 for each release time of IOPs 3, 4, 5, and 6. The HPAC/SCIPUFF parameterized mixing depths for IOP 5 are seen to be much larger than the observed mixing depths. For example, for the first IOP 5 tracer release (at 0800 LST), the HPAC/SCIPUFF parameterized mixing depth is about 650 m while the observed mixing depth is about 100 m. In contrast to the mixing depth discrepancies found for IOP 5, all of the mixing depths parameterized by HPAC/SCIPUFF for the other daytime IOPs are within a factor of 2 of the observed values in Fig. 8.

The HPAC/SCIPUFF model calculations were repeated for IOPs 3 through 6 using the same meteorological data and urban modeling options as in the previous runs, but with the mixing depths based on the radiosonde observations. The use of the observed mixing depths increases the simulated IOP 5 concentrations so that they are within the range of the simulated concentrations for IOPs 3, 4, and 6.

8. Conclusions

This study shows that the high normalized tracer concentrations observed during the morning releases of JU2003 IOP 5 can be attributed to unusually low mixing depths, which are evident in the radiosonde and FM/CW radar soundings and, by inference, from the measurements of sensible heat flux at a meteorological tower. The low observed mixing depths were likely caused by the presence of a stationary front combined with the effects of outflows from nearby thunderstorm complexes. The standard mixing depth parameterization in the HPAC/SCIPUFF ATD model, which is similar to the parameterizations in other state-of-the-art ATD models, led to large underpredictions of the observed concentrations during IOP 5. Thus, standard operational use of an ATD model may not account for atypical weather situations and may lead to large errors. Underpredictions are especially undesirable because the public may not be adequately protected from serious air quality impacts. Clearly, it is better to make use of local meteorological soundings or analyses that capture those conditions in the place of the model default parameters.

This detailed investigation of mixing depths has been possible only because of the intensive research-grade observations taken during JU2003. The soundings were made often and produced excellent vertical resolution. Routine soundings are seldom available at this time and space resolution. Thus, our recommendation that local soundings be available to better observe mixing depths would require large expenditures. Nevertheless, our study has shown that without realistic mixing depths, the ATD model may have large errors, including the potentially harmful underpredictions described here. Perhaps a compromise would be to install enhanced vertical sounders in critical locations such as near large cities or where pollution problems are severe.

Finally, atmospheric dispersion field studies almost always are conducted under fair-weather conditions, because of safety concerns and because of the desire for well-behaved dispersion patterns. But, as illustrated by the tracer concentration measurements made during JU2003 IOP 5, critical meteorological regimes resulting in the highest concentrations can be missed when field studies are restricted to fair weather. We recommend that more field experiments be planned and carried out during non–fair-weather conditions.