The relationship between atmospheric boundary layer (ABL) depth uncertainty and uncertainty in atmospheric transport and dispersion (ATD) simulations is investigated by examining profiles of predicted concentrations of a contaminant. Because ensembles are an important method for quantifying uncertainty in ATD simulations, this work focuses on the utilization and analysis of ensemble members’ ABL structures for ATD simulations. A 12-member physics ensemble of meteorological model simulations drives a 12-member explicit ensemble of ATD simulations. The relationship between ABL depth and plume depth is investigated using ensemble members, which vary both the relevant model physics and the numerical methods used to diagnose ABL depth. New analysis methods are used to analyze ensemble output within an ABL-depth relative framework. Uncertainty due to ABL depth calculation methodology is investigated via a four-member mini-ensemble. When subjected to a continuous tracer release, concentration variability among the ensemble members is largest near the ABL top during the daytime, apparently because of uncertainty in ABL depth. This persists to the second day of the simulation for the 4-member diagnosis mini-ensemble, which varies only the ABL depth, but for the 12-member physics ensemble the concentration variability is large throughout the daytime ABL. This suggests that the increased within-ABL concentration variability on the second day is due to larger differences among the ensemble members’ predicted meteorological conditions rather than being solely due to differences in the ABL depth diagnosis methods. This work demonstrates new analysis methods for the relationship between ABL depth and plume depth within an ensemble framework and provides motivation for directly including ABL depth uncertainty from a meteorological model into an ATD model.
Forecasting atmospheric transport and dispersion (ATD) of substances released into the atmosphere involves multiple sources of uncertainty (e.g., Fox 1984; Irwin et al. 1987; Rao 2005; Hanna 2007). As Rao (2005) notes, this uncertainty includes contributions from errors in the input data to the ATD model, errors in the ATD model itself, and the stochastic component that encompasses both the turbulent nature of the atmosphere and uncertainty in human emissions-related activities. Here, we focus on the uncertainty due to the meteorology ingested by the ATD model. The meteorology contributes to uncertainty in the ATD model due to errors in the numerical weather prediction (NWP) model (e.g., Stauffer 2012) and to the details in the coupling of the NWP and ATD models. These include NWP model initialization, model numerics and physics, and the sampling used when transferring meteorological model output into the ATD model (e.g., temporal and spatial resolutions, choice of meteorological model variables for input into the ATD model, etc.). Most prior studies (e.g., Warner et al. 2002; Lee et al. 2009; Peltier et al. 2010) have focused on the impact of uncertainty in the boundary layer winds on uncertainty of the concentration field. Here, we wish to assess uncertainty in the modeled concentration due to the uncertainty in the boundary layer depth.
Ensembles of both meteorological model integrations and ATD model simulations have been used as a proxy for ATD uncertainty. The variance among ensemble members has been shown to be related to the error variance of the ensemble mean (Eckel and Mass 2005; Kolczynski et al. 2009; Kolczynski et al. 2011); that is, variation among ensemble members represents uncertainty in its results. Methods of utilizing meteorological ensembles in ATD modeling (e.g., Galmarini et al. 2004) include using each member of a meteorological ensemble to drive a single member of an ATD ensemble [explicit ensemble method; e.g., Warner et al. (2002)], using the mean of the meteorological ensemble to drive a single ATD simulation [ensemble mean method; e.g., Warner et al. (2002); Lee et al. (2009)], and choosing the meteorological ensemble member best matching observations [best member or most representative member method; e.g., Warner et al. (2002); Warner and Sheu (2000); Lee et al. (2009)].
The Second-Order Closure, Integrated Puff (SCIPUFF; Sykes et al. 2006) ATD model can utilize variability among meteorological ensemble members to parameterize uncertainty in a single ATD integration. The wind-component variances (σu and συ; SCIPUFF refers to these as UUE and VVE) and covariance (σuυ; SCIPUFF refers to this as UVE) among meteorological ensemble members at each grid point are used by SCIPUFF to increase diffusion (e.g., Lee et al. 2009; Peltier et al. 2010). Although these current parameterizations deal solely with uncertainty in the wind fields, future applications could include additional sources of meteorological uncertainty. Uncertainty in the atmospheric boundary layer (ABL, also known as the planetary boundary layer) depth is expected to exhibit the next most important source of uncertainty for contaminant concentrations in the boundary layer and, thus, at the surface.
At the top of the ABL during convective conditions, an inversion typically caps the vertical spread of contaminants; however, there can be a great deal of uncertainty in the ABL depth predicted by a meteorological model at a given time and location (e.g., Han et al. 2008). The product of ABL depth zi and the mean wind speed in the ABL u defines the ventilation factor V (e.g., Panofsky 1969), which relates the volume through which the contaminant spreads to the concentration of the contaminant C within the ABL. Specifically,
Thus, holding u constant, an increase in the ABL depth will result in the contaminant being spread over a larger volume, resulting in a lower concentration throughout the ABL, including at the surface. Therefore, quantifying uncertainty in boundary layer depth will provide information about uncertainty in the surface concentration.
Because ABL depth is important in ATD applications and because there can be substantial uncertainty involved in forecasting ABL depth, the inclusion of ABL depth uncertainty in ATD models should be considered. When using meteorological models to drive ATD simulations, spatial and temporal variations in ABL depth are represented explicitly (although perhaps with insufficient resolution). However, one must still represent uncertainty because of errors in the simulation of the ABL structure or because of the choice of the ABL depth diagnosis algorithm. The use of a meteorological ensemble to create an explicit ATD ensemble is one method, but there is currently no method within SCIPUFF to account directly for variability among meteorological ensemble members’ ABL depths in a single SCIPUFF simulation analogous to the current use of σu, συ, and σuυ by SCIPUFF in order to factor in the ensemble variability in horizontal wind.
We investigate the relationship between ABL depth uncertainty and the associated plume depth uncertainty through interpretation of an explicit ATD ensemble and a mini-ensemble wherein only the ABL depth varies among ensemble members. We illustrate an important aspect of the uncertainty information provided by using a meteorological model ensemble to drive ATD simulations and thus, inform efforts to effectively utilize ensembles for ATD. Our primary goal is to demonstrate that one can associate a large source of uncertainty in modeled concentration with uncertainty in ABL depth and to quantify that uncertainty by employing an ensemble approach. This case study provides information to guide future efforts to incorporate meteorological ensemble-derived ABL depth uncertainty information into ATD models such as SCIPUFF. Section 2 discusses ABL depth uncertainty and the meteorological and ATD models and their configuration for quantifying that uncertainty. The case description is presented in section 3 and experimental design is outlined in section 4. The analysis of the experiment results is described in section 5, and the summary and conclusions appear in section 6.
2. ABL depth uncertainty and modeling approach to quantify that uncertainty
As is evident from considering the ventilation factor, uncertainty in the ABL depth will lead to uncertainty in the concentration field in the boundary layer. Here, we wish to consider the types of processes that lead to such uncertainty, and to quantify that uncertainty by taking an ensemble approach to modeling it. Specifically, we wish to configure an ensemble of NWP runs to examine uncertainty in the physical mechanisms leading to uncertainty in ABL depth. We choose a case study approach and consider two types of ensembles in order to quantify both the uncertainty in the atmospheric physics and the uncertainty due to the method used to diagnose the ABL depth.
a. Uncertainty in the ABL
The ABL depth is influenced by variations in surface forcings such as soil moisture (e.g., Desai et al. 2006; Reen et al. 2006), as well as advection, vertical motion from convergence and divergence, shear-produced turbulence (e.g., Doran and Zhong 1995), subsidence, remnant mixed layers from previous days, and circulation patterns such as sea breezes and mountain–valley breezes (e.g., Warner and Sheu 2000). Errors in the model initial and boundary conditions, as well as simplifications or weaknesses in the atmospheric model physics that represent these processes, both contribute to errors in model-predicted ABL depth and thus contribute to ABL depth uncertainty. This ABL depth uncertainty in the meteorological model impacts the uncertainty in the ATD model that depends on the ABL depth to compute the contaminant concentration. ABL depth can also be highly heterogeneous [e.g., due to soil moisture variability; Reen et al. (2006)] and can change smoothly in time (e.g., growing ABL with increasing surface heat flux), or abruptly collapse (e.g., transition from convective to stable conditions near the surface such as occurs in the transition to the nocturnal regime). The spatial heterogeneity and temporal variability of ABL depth increase the difficulty of accurately predicting the ABL depth and thus increase the uncertainty of ABL depth provided by the atmospheric model to the ATD model. An additional source of ABL depth uncertainty is the variation among the methodologies used to diagnose ABL depth (e.g., Seibert et al. 2000; Seidel et al. 2010).
Previous studies have concluded that model-predicted ABL depth can differ from observations substantially: errors in the mean absolute error (MAE) tend to be in the range of 20%–40% or more. Studies investigating NWP performance in predicting ABL depth often must rely on twice-daily rawinsondes, but in some cases other observational data allow for a more detailed evaluation. For a single case day over the southern Great Plains, Reen et al. (2006) compared daytime ABL depths diagnosed from airborne lidar data with ABL depths forecast by the nonhydrostatic fifth-generation Pennsylvania State University–National Center for Atmospheric Research Mesoscale Model (MM5; Dudhia 1993; Grell et al. 1995) and found that the MAE in the ABL depth varied among the experiments between 23% and 30% of the (≈1100 m) mean observed ABL depth. Similarly, a comparison of MM5 forecasts with ABL depths diagnosed from airborne lidar data from aircraft transects over three case days found that the model-predicted daytime ABL depth had an MAE that ranged from 13% to 25% of the (≈1300–1600 m) mean observed ABL depth depending on the case day and model configuration (Reen et al. 2013). For the same three case days, Hanna et al. (2010) compared ABL depths from MM5 and the Nonhydrostatic Mesoscale Model version of the Weather Research and Forecasting Model (WRF-NMM; Janjić 2003) with 3-h rawinsondes. Hanna et al. found that MM5 ABL depth was within ±20%–40% with small mean bias whereas WRF-NMM ABL depth predictions had similar scatter, but had an average positive bias of approximately 30%. For a total of 100 rawinsondes within the eastern two-thirds of the contiguous United States over 49 case days at approximately 2300 UTC, Coniglio et al. (2013) found that the Advanced Research version of WRF (WRF-ARW;Skamarock et al. 2008) ABL depth MAE was approximately equal to 300–400 m (depending on the model configuration) with a mean ABL depth of approximately 1400 m, leading to MAE averaging 21%–29% of the ABL depth. Hu et al. (2010) compared the WRF-predicted ABL depths with estimations from eight radar wind profiles in the south-central United States over 3 months. Although they do not report mean absolute error, the case-day-averaged diurnal cycle of the mean model versus the observed ABL depth indicates that the magnitude of the mean error varies widely by location, time of day, and model configuration.
The magnitudes of errors in model predictions of ABL winds also differ widely depending on the case and the model configuration. Verification against aircraft observations of the operational 13-km-horizontal-grid-spacing Rapid Refresh model, which is based on WRF-ARW, was obtained via the Earth Systems Laboratory Real-Time Verification System (Earth Systems Research Laboratory 2013). These data indicate an MAE of vector wind in the 1000–850-hPa layer (roughly representative of a daytime convective ABL) of 0.9 m s−1 averaged over the United States for its first year in operation (1 May 2012–30 April 2013) with an averaged observed wind speed of 7.7 m s−1. Gilliam et al. (2012) found a wind speed RMSE of approximately 1.8 m s−1 for 300–1000 m AGL for 3 months of 12-km-horizontal-grid-spacing WRF-ARW dynamic-analysis simulations over the continental United States. For the previously discussed study of Reen et al. (2013), there was a vector wind difference MAE of approximately 2.5 m s−1 in the lowest 1000 m (Reen 2007).
While there are many meteorological factors that can influence plume concentrations at a given location, the ventilation factor highlights the importance of wind speed and ABL depth. To illustrate the relative sensitivity of plume concentration to ABL depth and wind speed, based on the literature described above, we find the ventilation factor by using an ABL at 1400 m with 25% error and a wind speed of 7.7 m s−1 with varying assumed error from 0.9 to 2.5 m s−1 to account for the wide variation in reported wind errors. This very rough calculation results in the ventilation coefficient varying by 53% due to ABL depth error, and by 24%–73% due to wind speed error depending on the value chosen for the wind speed error. This suggests that ABL depth uncertainty may be of similar importance to wind speed uncertainty in determining plume concentrations. We recognize that these estimates rely on wind speed and ABL depth values drawn from studies with differing methodologies, and stress that this estimate is intended only to demonstrate the potential importance of accounting for ABL depth uncertainty in ATD calculations.
To represent the uncertainty in the ABL depth for use in ATD/air-quality models, Lewellen and Sykes (1989) and Hanna et al. (2007) both used 20% of the ABL depth in constructing distributions of ABL depth. Within a Gaussian plume model, Lewellen and Sykes (1989) use 20% of the ABL depth diagnosed from an observed temperature profile as the standard deviation for their Gaussian distribution of ABL depth (but require the standard deviation to be at least 100 m). They use this distribution to account for three sources of uncertainty: 1) differences in ABL depth diagnosis technique, 2) temporal variations in ABL depth, and 3) spatial variations in ABL depth. For Monte Carlo air-quality simulations used to estimate uncertainties in pollutant concentrations, Hanna et al. (2007) assume 20% of the ABL depth as the range in which 95% of ABL depths occur for their lognormal distribution of ABL depth. This distribution is used to account for 1) the spatial distribution within a 15 km × 15 km box and 2) the temporal variation in 1 h. The 20% values are roughly consistent with the model–observation ABL depth comparison studies reviewed above.
b. Meteorological model: WRF
To quantify the uncertainty due to model physics, we use 12 members of the ensemble described by Lee et al. (2012) (Table 1), all employing WRF-ARW, version 3.2. WRF-ARW is a widely used open-source mesoscale numerical weather prediction model. The differences among the WRF-ARW ensemble members are that each uses a different combination of land surface model and ABL parameterization; all of the ensemble members from Lee et al. (2012) that use the Grell–Devenyi cumulus parameterization (Grell and Devenyi 2002) are included here. Varying the physics used to represent both the ABL and the land surface that forces the ABL provides variability in ABL depth, as is desired in this study focusing on ABL depth variability.
Each ensemble member is run with nested domains of 36- and 12-km horizontal grid spacing with the finer domain centered over the northeastern United States (Fig. 1). The 12-km domain includes portions of three time zones, with the LST of the western portion of the domain being UTC − 6, the LST of the eastern portion of the domain being UTC − 5, and the LST of parts of the extreme northeastern part of the domain being UTC − 4. Each member has 45 vertical levels with 16 model levels in the lowest 1 km and 24 model levels in the lowest 2 km. The integrations begin at 1200 UTC and are integrated for 48 h. Each member uses the WRF single-moment five-class microphysics scheme (Hong et al. 2004; Hong and Lim 2006), the general circulation model version of the Rapid Radiative Transfer Model (RRTMG) for shortwave and longwave radiation (Iacono et al. 2008), and the Grell–Devenyi cumulus parameterization (Grell and Devenyi 2002). The land surface and ABL schemes are varied among ensemble members (Table 1), and each member uses the surface layer scheme appropriate for its ABL parameterization. Four land surface parameterizations are used: thermal diffusion (Skamarock et al. 2008), Pleim–Xiu (Pleim and Xiu, 1995; Xiu and Pleim 2001), Noah (Chen and Dudhia 2001), and Rapid Update Cycle (RUC; Smirnova et al. 1997, 2000). These land surface schemes provide heat and moisture fluxes at the surface for use in the ABL parameterizations.
To represent the ABL, three different parameterizations are used: Yonsei University (YSU; Hong et al. 2006); Asymmetric Convective Model, version 2 (ACM2; Pleim 2007); and Mellor–Yamada–Janjić (MYJ; Janjić 2002). The YSU scheme prescribes the vertical profile of the vertical diffusion coefficient throughout the ABL and includes a countergradient term to represent nonlocal mixing. The ACM2 combines a nonlocal component that allows for mixing between nonadjacent vertical layers, with eddy diffusion for local mixing. The MYJ scheme is a Mellor–Yamada level-2.5 turbulence closure model and predicts turbulence kinetic energy (TKE). As in Lee et al. (2012), the background TKE in the MYJ scheme is decreased to better simulate low-TKE conditions, and the ABL depth diagnosis method is altered. The MYJ modifications and the ABL depth diagnosis methods used in this study are described in section 4e.
Initial conditions and lateral boundary conditions are based on Global Forecast System (GFS) output on a grid with 0.5° (~55 km) horizontal grid spacing. To enhance the initial conditions, we use the GFS data as the first-guess field for an objective analysis that incorporates observations. No data assimilation is used after the initialization time.
c. ATD model: SCIPUFF
Version 2.6I of the SCIPUFF model (Sykes et al. 2006) is used as the ATD model in this investigation. SCIPUFF is an atmospheric dispersion model that uses Gaussian puffs to represent the concentration of a released substance. SCIPUFF utilizes ABL depth in several ways including 1) limiting the vertical extent of puffs; 2) determining the surface layer height, which is a function of ABL depth and Monin–Obukhov length; and 3) calculating vertical profiles of turbulence-related parameters, which rely on ABL depth.
A SCIPUFF domain over the northeastern United States (Fig. 1) is used to simulate a hypothetical 48-h continuous release of a passive tracer at 38.5°N, −89.5°E (southern Illinois) at 10 m above ground level (AGL) (1000 kg h−1). Hourly output from the 12-km domains in the WRF-ARW ensemble described in section 2b provide the meteorological inputs for the SCIPUFF simulations, namely, the 3D fields of temperature, pressure, water vapor mixing ratio, and the three components of wind, as well as the 2D roughness length, terrain height, ABL depth, and sensible heat flux.
Data are extracted from SCIPUFF using a sampler grid that includes every other WRF-ARW horizontal grid point over the western half of the 12-km WRF-ARW domain (predicted concentrations are generally confined to the western half), excluding a 10-grid-point buffer along the edges of the domain. The 21 WRF-ARW vertical levels below 5000 m AGL are used to define the vertical levels of the samplers.
3. Case description
We choose to analyze the impact of ABL depth uncertainty on the concentration field uncertainty through a case study approach. We choose a case in which a high pressure ridge extended over large portions of the domain and for which there was limited convection in order to limit any confounding impact of wind uncertainty. The WRF-ARW and SCIPUFF simulations are integrated from 1200 UTC on 19 July 2009 until 1200 UTC on 21 July 2009, a period with generally light surface winds in this region. This case is chosen because widespread convection is generally not present in the immediate area of the release, which allows the relationship between ABL depth and concentration to be more clearly discerned. In general high pressure is in place over the midwestern United States during this period. However, some precipitation is present at 1200 UTC on 19 July over southwestern Michigan and northern Indiana, and more widespread convection forms at about 1600 UTC over Indiana and Michigan and moves eastward. The modeled plume does not appear to overlap with this area of convection. Additionally, precipitation ahead of a cold front reaches the western border of Illinois by the end of the period (1200 UTC 21 July).
4. Experimental design
We wish to construct numerical experiments to examine two potential sources of uncertainty in ABL depth: that due to uncertainty in the physics within the NWP model and that due to the method used to diagnose the ABL depth. To address the first, we directly leverage the 12-member NWP ensemble described in section 2b. To study the latter source of ABL uncertainty, we construct a special 4-member mini-ensemble around an ensemble member that allows for varying the method used to diagnose ABL depth.
a. 12-member physics ensemble
Each member of the WRF-ARW 12-member ensemble described in section 2b (Table 1) is used to drive an individual SCIPUFF simulation. This creates an explicit ensemble of SCIPUFF simulations differing only in the meteorology driving them, whose gridded output (section 2c) is used to explore the relationship between ABL depth and the depth of the plume among the members of the SCIPUFF ensemble. Note that for the 12-member WRF-ARW ensemble, the predictions of the ensemble members not only differ in ABL depth but can also differ in any other meteorological variable; this is in contrast to the mini-ensemble introduced in the following section.
b. Four-member ABL depth mini-ensemble
To better isolate the effect of ABL depth uncertainty on the vertical spread of contaminant in SCIPUFF, we apply four ABL depth diagnosis methods to a single WRF-ARW ensemble member from the 12-member physics ensemble. This provides a 4-member mini-ensemble of meteorological input for SCIPUFF that varies only in the ABL depth.
Member 5 (Table 1) from the 12-member physics ensemble was chosen as the basis of the 4-member ABL depth mini-ensemble because it uses the TKE-predicting MYJ ABL scheme and thus allows TKE-based ABL depth diagnosis techniques to be utilized.
Here, we evaluate ABL depth as defined by four methods, each an experiment.
- Experiment A—The bulk Richardson number (Rib) method (e.g., Seibert et al. 2000) diagnoses the ABL depth as the lowest height above the surface at which Rib for the layer from the surface to that height is greater than or equal to the critical Rib (Rib,critical): Table 1).
Experiment B—The ABL depth is diagnosed as the height at which TKE falls below 10% of the column maximum (excluding TKE not connected to the surface). TKE threshold approaches are used in the standard WRF MYJ ABL scheme, the altered MYJ used in this paper, and in other TKE-based ABL schemes.
Experiment C—The parcel method (e.g., Seidel et al. 2010) is applied here such that if the virtual potential temperature at the 2 m AGL diagnostic level is greater than the virtual potential temperature at the lowest prognostic model level, then the ABL depth is diagnosed to be the height where the virtual potential temperature increases to the 2-m value. Otherwise, the ABL depth is diagnosed as the height where the surface-based inversion ends. A parcel method is also used in the original Blackadar ABL scheme (e.g., Zhang and Zheng 2004).
Experiment D—For the convective boundary layer (CBL) this experiment diagnoses the ABL depth as the first layer where TKE falls to a value that is half the maximum value in the column but is no larger than 0.1 J kg−1. This methodology is used for all of the WRF-ARW ensemble members of the 12-member ensemble that incorporate the MYJ ABL parameterization, including member 5, the basis of the 4-member mini-ensemble. This methodology is not the standard MYJ technique but rather is an ABL depth diagnosis methodology largely derived from that used in the Gayno–Seaman ABL parameterization (Stauffer et al. 1999; Shafran et al. 2000) in MM5. The Gayno–Seaman scheme, along with its ABL depth diagnosis methodology, has been successfully applied in air-quality studies, where ABL depth is an important parameter (e.g., Shafran et al. 2000, Stauffer et al. 2000). In the standard version of MYJ the background TKE is 0.100 J kg−1, but here it is decreased to 0.010 J kg−1 to better resolve low-TKE conditions. The default MYJ ABL depth diagnosis methodology of finding the level where TKE falls to 1% above the background TKE level now yields a TKE threshold of 0.0101 J kg−1. This use of a TKE threshold only 0.0001 J kg−1 above the background level would likely lead to an overestimation of ABL depth and, thus, the ABL depth diagnosis method used in the Gayno–Seaman scheme is applied here. Note that the ABL depth found using the altered ABL depth diagnosis methodology is not used internally within MYJ, but rather is used to calculate the ABL depth output by the model.
Note that experiments A–C alter only the ABL depth provided to SCIPUFF, and the other meteorological fields are the same as those in experiment D (ensemble member 5 from Table 1).
a. Analysis of 12-member physics ensemble
Figure 2 depicts surface concentrations 6 h after the release begins and Fig. 3 shows the same field after 30 h. These figures illustrate the horizontal evolution of the plume in order to provide context for the analysis of the vertical structure of the plume that follows. At the surface the plume generally spreads toward the south-southeast during the first 6 h (Fig. 2) but by the next day, the plume has generally spread northwestward (Fig. 3).
Several metrics are employed to analyze the relationship between ABL depth uncertainty and downwind concentration profiles. The first is a measure describing the relationship between concentration C and ABL depth relative height (z/zi) (e.g., Fig. 4a). Neglecting concentrations smaller than a background level (1 × 10−12 kg m−3; chosen as approximately five orders of magnitude less than the maximum surface concentration at the end of the simulation), at each time t, at each horizontal grid point (x, y), and for each ensemble member m, the concentration was scaled by the maximum concentration in that column such that in any column with at least one vertical level with nonzero concentrations, the maximum scaled concentration Cs is 1:
where za represents the 21 heights analyzed. This scaling is to allow the vertical structure of concentration for different ensemble members, at different locations, and at different times to be compared without the profiles with higher concentrations masking the signal of the other profiles. Next, the ensemble mean ABL depth, , is used to bin the scaled concentrations by ABL depth relative height . The bins used were in depth, leading to 10 bins within the ABL; this allows the general ABL structure to be fairly well resolved. The scaled concentrations are represented by Cs(x, y, b, t, m), where b is the index of the ensemble-mean ABL depth relative height bin [e.g., Cs(x, y, 2, t, m) is the scaled concentration of the second bin, ]. The ABL depth relative binning allows the vertical structure of profiles with differing ABL depths to be more directly compared.
These ABL depth relative binned scaled concentrations are then ensemble averaged, yielding , and the standard deviation among the ensemble members is σm(Cs)(x, y, b, t). These two quantities are then averaged over all horizontal grid points with at least one nonzero scaled concentration (denoted as set S) to provide a domain average:
Scaling the ABL depth standard deviation allows a measure of the variation of ABL depth among ensemble members to be included in an ABL depth relative plot:
The domain-average ABL depth standard deviation is
We plot the vertical profile of the domain-average ensemble-mean scaled concentration, (indicated by the curve with times signs), along with ±1 standard deviation among the ensemble members, (indicated by the horizontal bars). On the same graph the circle and vertical error bars indicate the mean and standard deviation of the scaled ABL depth among the ensemble members, . Standard deviation is analyzed because SCIPUFF represents wind variability among ensemble members using variance (standard deviation squared) and thus eventually SCIPUFF could potentially be modified so that ABL depth variance would be used to represent ABL depth variability among ensemble members. In Fig. 4a the domain average of the ensemble-mean ABL depth used for scaling is 1761 m and the domain average of the standard deviation ABL depth among the ensemble members is 188 m (about 11% of the depth of the ABL).
In Fig. 4a, at 1800 UTC (midday) the concentration drops off rapidly with height near the top of the ABL, indicating that the plume is generally trapped within the ABL. The largest variation among the ensemble members in the concentration occurs between 0.8 and , consistent with SCIPUFF-predicted concentrations dropping off most rapidly just below the top of the ABL. Given that one standard deviation below the ensemble-mean domain-average top of the ABL is , the concentration range represented by ±1 standard deviation from the mean is consistent with the bin ranging from being below the ABL-top concentration dropoff for some profiles to within the ABL-top concentration drop for other profiles. Similarly, the results for the bin are consistent with that bin ranging from being above the ABL top in some profiles to being near the bottom of the ABL-top concentration dropoff for other profiles. Thus, at 1800 UTC on 19 July 2009 variations in ABL depth predictions among the NWP ensemble members appear to be a primary factor in causing variations in SCIPUFF concentration predictions. These results suggest that variation in ABL depth among ensemble members may be useful in helping to diagnose concentration uncertainty.
Twenty-four hours later the dropoff in concentration with ABL relative height is spread further above the top of the ABL (Fig. 4b) [i.e., the and bins have larger scaled concentrations than at 6 h (Fig. 4a)]. The mean ABL depth is slightly lower (1649 vs 1761 m), but the standard deviation is larger (235 m or 14% of the ABL depth vs 188 m or 11% of the ABL depth for the earlier time). Perhaps most striking is the much larger variability among the ensemble members within the ABL in Fig. 4b than in Fig. 4a. Given the 30 h of continuous release, this is likely related to the variation in the NWP ensemble members’ predicted meteorological conditions during the 24 h separating these plots.
Figure 4a shows the result of a 6-h release as the ABL grows (1200–1800 UTC), but Fig. 4b (30 h) has higher uncertainty because between Fig. 4a and Fig. 4b the release has continued through a full diurnal cycle. Figure 4b includes the effects of the overnight collapse and subsequent regrowth of the ABL wherein part of the plume can remain above the ABL overnight and get reincorporated the next day. This suggests that using NWP ensemble ABL depth variability to diagnose a portion of the uncertainty in SCIPUFF concentrations is likely to be most effective during the well-developed CBL and prior to any nighttime spread of the release. While there can be various differences among the NWP ensemble members that result in uncertainty in the derived SCIPUFF concentrations, accounting for a potentially important contributor to the uncertainty in the SCIPUFF concentration, such as ABL depth uncertainty, would improve our quantification of the SCIPUFF concentration uncertainty.
The second metric compares the vertical extent of the plume zc with the depth of the ABL zi. The plume depth zc is defined here as the level where the plume concentration is 10% of the maximum concentration in the column. The rapid decrease of concentration with height near this level minimizes the sensitivity to the threshold percentage of the column maximum concentration chosen to determine the plume depth. Because turbulence is generally confined to the ABL and because the plume is mixed by the turbulence, we expect that, in general, the top of the plume may coincide with the top of the ABL. However, advection to a location with a lower ABL top can spread the plume above the top of the ABL.
Scatterplots illustrating the relationship between zi and zc at 6 and 30 h into the simulation are shown in Figs. 5a and 5b, respectively. Note that because of the large number of data points, in order to enhance clarity the data has been grouped into 50-m bins, with the size of the plotted symbol varying based on the number of points in that bin. The symbol used for each bin is that of the ensemble member with the most data points in that bin. The color of the symbol is determined by creating a weighted average of the colors assigned to each of the ensemble members, with the weighting based on how many data points each ensemble member has within the bin. The color assigned to each ensemble member is based on the ABL parameterization used by that ensemble member. Thus, the symbol as well as its color and size provide information about the data points present in that bin. The correlation coefficient r between the zi–zc relationship in SCIPUFF and the linear fit line is 0.46 at 6 h (fit line of 0.81zc+366; Fig. 5a) and 0.69 at 30 h (fit line of 0.98zc+21; Fig. 5b). This suggests that the relationship between zc and zi is closer to one to one on the second day. If one considers the 5% of points farthest from zi = zc as outliers and excludes them, assuming a fit line of zi = zc improves r from 0.42 to 0.67 at 6 h and from 0.69 to 0.86 at 30 h. Thus, excluding a relatively small set of outliers, there is a fairly strong relationship between zi and zc, particularly during the second day (i.e., 30 h). In Fig. 5b a number of points yield a value for zc that is considerably higher than zi, suggesting that a portion of the plume became trapped above the previous day’s boundary layer. The relationship breaks down overnight when the boundary layer has collapsed.
Next, we examine the temporal evolution of the ensemble mean and standard deviation of zi and zc (Fig. 6). During the first day, the ensemble mean zi grows at a similar rate to that of zc, but zi remains somewhat higher, consistent with the plume being generally trapped within the ABL. The standard deviations among the ensemble members of zi and zc are fairly similar during this day, except from 2300 to 0000 UTC when the standard deviation of zi increases, likely due to differences in 1) the prediction of the ABL structure as it collapses and 2) the ABL depth diagnosis method’s performance in a collapsing ABL. At the end of the day, zi rapidly decreases to <100 m, where it remains overnight, while zc gradually decreases throughout the night to about 850 m by morning; thus, much of the vertical extent of the plume is above the ABL overnight.
On the second day shown in Fig. 6, the ensemble mean zc decreases and its variability among ensemble members increases relative to the first day, while for zi the changes between the first and second day are much less than for zc. This results in zc less closely corresponding to zi in terms of both the ensemble mean and variability among ensemble members on the second day as compared to the first day. This suggests that the relationship between ABL depth variability and plume depth variability is weaker on the second day; this is likely due to the nighttime transport of residual concentration above the ABL.
b. Analysis of the four-member ABL depth mini-ensemble
Varying the ABL depth diagnosis method in the four-member explicit SCIPUFF mini-ensemble does not appear to result in substantial differences in which areas are forecast to have the highest surface concentrations of the passive tracer. As with the 12-member ensemble, surface concentrations are shown to provide context for the analysis of the vertical structure of the plume. Generally, the plume appears to be moving east-southeastward after the first 6 h (Fig. 7) and northwest after 30 h (Fig. 8). The metrics utilized for the 12-member ensemble are also applied to the 4-member mini-ensemble.
Figure 9a plots the relationship between the ABL depth relative height and the scaled concentration 6 h after the release; the average ABL depth across the four members is 1793 ± 241 m. This figure is very similar to that for the 12-member ensemble presented in Fig. 4. Note that while Fig. 9 shows the variation in concentration among SCIPUFF simulations using meteorology input that varies only in the ABL depth field, Fig. 4 shows the variation among SCIPUFF simulations using meteorology input that also varies in many other fields. Because Fig. 4a showed the largest concentration variability near the ABL top, likely due to variations in ABL depth among ensemble members, it is not surprising that Fig. 9a, based on an ensemble where only ABL depth varies, demonstrates the same thing.
Figure 9b shows that 24 h later the largest concentration variability is still near the top of the ABL, unlike the 12-member physics ensemble where concentration variability was largest near the ABL top 6 h into the simulation, but 24 h later the concentration variability varied little with height from the surface through the ABL top (Fig. 4b). During midday on the second day, the 4-member mini-ensemble has much less variability in concentration among the ensemble members below than does the 12-member ensemble. This suggests that differences within the predicted ABL structure among the ensemble members in the 12-member ensemble (in contrast to differences only in the predicted ABL depth) are responsible for the large concentration variability within the ABL. The domain-average standard deviation of the ensemble mean ABL depth decreases from 241 m 6 h into the simulation to 88 m 24 h later (Fig. 9), suggesting that the ABL structure is less sensitive to the diagnosis method on 20 July than 19 July.
Next, we consider the scatterplots relating zi and zc at 6 and 30 h into the simulation in Figs. 10a and 10b, respectively. As with the 12-member ensemble (Fig. 5), in general, zi and zc are fairly similar. While the best-fit line yields r of 0.57 at 6 h and 0.56 at 30 h, comparing the data with zi = zc yields r of 0.51 and 0.52, respectively. As in the 12-member ensemble, removing the top 5% of outliers improves r for zi = zc, here, for the 4-member ensemble to 0.79 at 6 h and 0.76 at 30 h.
Both times (Figs. 10a,b) indicate the dependency of the depth of the plume to the method used to diagnose the ABL. In Fig. 10a, the median of the “distance” (in zc, zi space) between each parcel method point (experiment A; like an Rib method that ignores shear) and the closest Rib method point (experiment C) is on the order of 10 m; the two TKE-based methods (experiments B and D) show similar results. In contrast to this, any other experiment pairing yields median distances between closest points >300 m. Note that this clustering can be seen in the colors represented in Fig. 10 because the color plotted for the point at a specific bin is a weighted average of the number of blue points (experiments A and C) and the number of red points (experiments B and D). The clustering is much less evident at the later time (30 h; Fig. 10b) likely because a portion of the plume ended up above the ABL when the ABL became much shallower overnight.
The temporal evolution of zi and zc for the 4-member ABL depth diagnosis ensemble (Fig. 11) is similar to that of the 12-member ensemble (Fig. 6). However, on the second day, the ensemble mean and the standard deviation among the ensemble members for zi agrees more closely to zc than in the full 12-member physics ensemble. This suggests that the large differences between zi and zc seen in the 12-member physics ensemble on the second day may have been due to changes in the structure of the lower atmosphere that were caused by differences in how each of the 12 ensemble members simulated the overnight period between the two days.
6. Summary and conclusions
The objective of this paper is to demonstrate the relationship between ABL depth uncertainty and the uncertainty in contaminant concentration in the ABL. To this end, we considered two different types of modeling uncertainty: that due to model physics and that due to the differences in the methods used to diagnose the ABL depth. We have analyzed a case generally dominated by high pressure in order to minimize the confounding issues of convection and we used two different types of ensembles to discern the uncertainty: a 12-member physics ensemble and a 4-member ABL depth diagnosis ensemble. For our case, at midday (1800 UTC) 6 h after the start of a continuous hypothetical tracer release, ensemble variability in the predicted concentration was highest just below the ABL top, consistent with the expected capping of the surface-based plume by the ABL top. This suggests the possible use of ABL depth variability within an NWP ensemble to infer SCIPUFF concentration variability in a growing CBL. In general ABL depth zi and the depth of the plume zc are similar for both the ensemble mean and the standard deviation during the daytime period on the day of the release, with zi larger for the mean and zc larger for the standard deviation. However, these results are only applicable in the daytime period, when the well-mixed boundary layer and capping inversion are the primary drivers of the vertical spread of concentration. On the second day of the continuous release, the relationships seen on the first day were made less clear by the presence of residual concentration above the day-2 CBL and the variability among NWP predictions of the intervening nighttime period. This hypothesis is supported by the generally more similar day-1 and day-2 results for the experiments varying only in their ABL depths. Effectively analyzing ABL structures among ensemble members used for ATD simulations requires new analysis methods such as those presented here and an understanding of the uncertainty represented by the ensemble, and this study illustrates one aspect of that uncertainty, namely the relationship between ABL depth uncertainty and plume depth uncertainty. Because this study examined a single case study, care should be taken not to assume that the relationships found for this case study apply for all cases. It is, however, indicative of the type of variability in contaminant concentration that could be expected to be caused by ABL depth uncertainty. The methodology developed here will enable future analyses of other cases.
Future work should include applying these methods to additional cases, and defining additional metrics to better quantify the uncertainty for specific applications. Also, possible theoretical implications of using ensemble ABL depth variability should be explored. We believe this work could be important for developing a methodology to directly represent the effects of ABL depth uncertainty in SCIPUFF.
We acknowledge Doug Henn of Sage Management for assistance with SCIPUFF and Walter Kolczynski for helpful discussions. We thank two anonymous reviewers whose comments led to the improvement of this manuscript. This research was supported by the Defense Threat Reduction Agency under Contracts W911NF-06-C-0162 and DTRA01-03-D-0010-0012 under the supervision of John Hannan.