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    The elevation contours (m MSL) for (a) the 45-km grid, (b) the 5-km grid, and (c) the 190-m grid. The locations of surface stations defined in Table 3 are shown in (c).

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    Surface data time series comparisons at site BB for (a) near-surface temperature and (b) surface soil temperature: observations (filled circles), ΔT = 0 K (open circles), ΔT = 10 K (open squares), and ΔT = 15 K (open triangles).

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    Contour of ground concentration for (a) case I and (b) case III, with (left) field observations and (right) ARPS results. Sensor and source locations are shown with black dots and black triangles, respectively.

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    Arc maximum concentration for cases I–VII: observa-tions (filled circles) and ARPS results (solid line).

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    Scalar dispersion direction for case I–VII: observations (filled circles) and ARPS results (solid line).

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    Vertical distributions of horizontal velocity, wind direction, and the horizontal and vertical turbulent fluctuations at the tracer release point (site AA or site BB): observations (filled circles) and ARPS (solid line). No observation data are available for Case V.

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    Vertical distributions of the horizontal velocity and wind direction at (a) site AA and (b) site BB for case III: observations (filled circles), Cmix = 1.0 × 10−4 (solid line), Cmix = 5.0 × 10−4 (dashed line), and Cmix = 1.0 × 10−3 (dotted line).

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    Vertical distributions of the horizontal and vertical turbulent fluctuations at (a) site AA and (b) site BB for case III: observations (filled circles), Cmix = 1.0 × 10−4 (solid line), Cmix = 5.0 × 10−4 (dashed line), and Cmix = 1.0 × 10−3 (dotted line).

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    Arc maximum ground concentration for case III: Cmix = 1.0 × 10−4 (solid line), Cmix = 5.0 × 10−4 (dashed line), and Cmix = 1.0 × 10−3 (dotted line).

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    Vertical distributions of the horizontal velocity and wind direction at (a) site AA and (b) site BB for case III: observations (filled circles), ΔTb = 10 s (solid line), ΔTb = 60 s (dashed line), ΔTb = 5 min (dotted line), and ΔTb = 30 min (dash–dotted line).

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    Vertical distributions of the horizontal and vertical turbulent fluctuations at (a) site AA and (b) site BB for Case III: observations (filled circles), ΔTb = 10 s (solid line), ΔTb = 60 s (dashed line), ΔTb = 5 min (dotted line), and ΔTb = 30 min (dash–dotted line).

  • View in gallery

    Arc maximum ground concentration for case III: observations (filled circles), ΔTb = 10 s (solid line), ΔTb = 60 s (dashed line), ΔTb = 5 min (dotted line), ΔTb = 30 min (dash–dotted line).

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    Energy spectra at (a) boundary, (b) site AA, and (c) site BB for case III: ΔTb = 10 s (solid line), ΔTb = 60 s (dashed line), ΔTb = 5 min (dotted line), and ΔTb = 30 min (dash–dotted line).

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    Vertical distributions of the horizontal and vertical turbulent fluctuations at (a) site AA and (b) site BB for case III: observations (filled circles), 190-m grid resolution (solid line), 65-m grid resolution (dashed line), and 25-m grid resolution (dotted line).

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    Arc maximum concentration for case III: observations (filled circles), 190-m grid resolution (solid line), 65-m grid resolution (dashed line), and 25-m grid resolution (dotted line).

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High-Resolution Large-Eddy Simulations of Scalar Transport in Atmospheric Boundary Layer Flow over Complex Terrain

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  • 1 Environmental Science Research Laboratory, Central Research Institute of Electric Power Industry, Chiba, Japan
  • | 2 Department of Civil and Environmental Engineering, University of California, Berkeley, Berkeley, California
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Abstract

This paper presents high-resolution numerical simulations of the atmospheric flow and concentration fields accompanying scalar transport and diffusion from a point source in complex terrain. Scalar dispersion is affected not only by mean flow, but also by turbulent fluxes that affect scalar mixing, meaning that predictions of scalar transport require greater attention to the choice of numerical simulation parameters than is typically needed for mean wind field predictions. Large-eddy simulation is used in a mesoscale setting, providing modeling advantages through the use of robust turbulence models combined with the influence of synoptic flow forcing and heterogeneous land surface forcing. An Eulerian model for scalar transport and diffusion is implemented in the Advanced Regional Prediction System mesoscale code to compare scalar concentrations with data collected during field experiments conducted at Mount Tsukuba, Japan, in 1989. The simulations use horizontal grid resolution as fine as 25 m with up to eight grid nesting levels to incorporate time-dependent meteorological forcing. The results show that simulated ground concentration values contain significant errors relative to measured values because the mesoscale wind typically contains a wind direction bias of a few dozen degrees. Comparisons of simulation results with observations of arc maximum concentrations, however, lie within acceptable error bounds. In addition, this paper investigates the effects on scalar dispersion of computational mixing and lateral boundary conditions, which have received little attention in the literature—in particular, for high-resolution applications. The choice of lateral boundary condition update interval is found not to affect time-averaged quantities but to affect the scalar transport strongly. More frequent updates improve the simulated ground concentration values. In addition, results show that the computational mixing coefficient must be set to as small a value as possible to improve scalar dispersion predictions. The predicted concentration fields are compared as the horizontal grid resolution is increased from 190 m to as fine as 25 m. The difference observed in the results at these levels of grid refinement is found to be small relative to the effects of computational mixing and lateral boundary updates.

Corresponding author address: Takenobu Michioka, Environmental Science Research Laboratory, Central Research Institute of Electric Power Industry, 1646 Abiko, Abiko-shi, 270-1194 Chiba-ken, Japan. Email: michioka@criepi.denken.or.jp

Abstract

This paper presents high-resolution numerical simulations of the atmospheric flow and concentration fields accompanying scalar transport and diffusion from a point source in complex terrain. Scalar dispersion is affected not only by mean flow, but also by turbulent fluxes that affect scalar mixing, meaning that predictions of scalar transport require greater attention to the choice of numerical simulation parameters than is typically needed for mean wind field predictions. Large-eddy simulation is used in a mesoscale setting, providing modeling advantages through the use of robust turbulence models combined with the influence of synoptic flow forcing and heterogeneous land surface forcing. An Eulerian model for scalar transport and diffusion is implemented in the Advanced Regional Prediction System mesoscale code to compare scalar concentrations with data collected during field experiments conducted at Mount Tsukuba, Japan, in 1989. The simulations use horizontal grid resolution as fine as 25 m with up to eight grid nesting levels to incorporate time-dependent meteorological forcing. The results show that simulated ground concentration values contain significant errors relative to measured values because the mesoscale wind typically contains a wind direction bias of a few dozen degrees. Comparisons of simulation results with observations of arc maximum concentrations, however, lie within acceptable error bounds. In addition, this paper investigates the effects on scalar dispersion of computational mixing and lateral boundary conditions, which have received little attention in the literature—in particular, for high-resolution applications. The choice of lateral boundary condition update interval is found not to affect time-averaged quantities but to affect the scalar transport strongly. More frequent updates improve the simulated ground concentration values. In addition, results show that the computational mixing coefficient must be set to as small a value as possible to improve scalar dispersion predictions. The predicted concentration fields are compared as the horizontal grid resolution is increased from 190 m to as fine as 25 m. The difference observed in the results at these levels of grid refinement is found to be small relative to the effects of computational mixing and lateral boundary updates.

Corresponding author address: Takenobu Michioka, Environmental Science Research Laboratory, Central Research Institute of Electric Power Industry, 1646 Abiko, Abiko-shi, 270-1194 Chiba-ken, Japan. Email: michioka@criepi.denken.or.jp

1. Introduction

With the increasing availability of powerful supercomputers, numerical simulation has become a very attractive tool for simulating transport and dispersion of airborne materials in atmospheric flows. Many previous computational studies have focused on the prediction of concentration downwind of a scalar release point, a problem of great importance because of increasing environmental pollution and other hazardous material releases (Kemp and Thomson 1996; Sykes et al. 1992; Meeder and Nieuwstadt 2000). The models and approaches used vary greatly with the length and time scales of interest, though modeling choices are often limited by computational resources. Two broad classes of models can be described. The first includes what are commonly referred to as computational fluid dynamics (CFD) applications, using either large-eddy simulation (LES) or Reynolds-averaged Navier–Stokes (RANS) approaches for turbulence, and focusing on small-scale plume behavior. These models might be used, for example, to predict detailed plume dispersion in an urban area, but they have limited ability to incorporate effects of meteorological conditions. The second class of models includes mesoscale models (typically using a RANS turbulence closure), which are applied at regional scales to predict plume dispersion without giving much attention to small-scale fluctuations because of coarse space and time resolution and the inability to represent highly complex terrain (e.g., building geometries). Both small-scale CFD and mesoscale models use a range of either Lagrangian or Eulerian approaches to represent scalar transport.

An example of a typical small-scale CFD application comes from Sykes and Henn (1992), who performed LES with a Lagrangian-based puff method to predict concentration fluctuations emitted from elevated and ground-level sources. In a similar way, Sada and Sato (2002) conducted LES with a mixed method, combining an Eulerian method with a puff model to predict the instantaneous concentration fluctuations of a plume from stack gas dispersion around a cubical building. These LES simulations captured not only the mean concentration, but also the concentration fluctuations and instantaneous high-concentration values, which are needed to verify the behavior of detailed plume dispersion. In a more realistic application, Sada et al. (2006) performed RANS simulations with Lagrangian particle tracking to predict stack gas dispersion, considering the buildings located near the stack and the complex terrain located relatively far from the stack. The simulation reproduced the ground concentration observed in wind-tunnel experiments, but the horizontal spread of the plume far from the stack was underestimated relative to the expected plume spread in a real atmospheric boundary layer because the meandering effects of wind direction fluctuations were not represented by the simulation. These CFD studies were able to represent detailed plume behavior and complex geometries in urban areas and mountainous terrain, but they used homogeneous surface conditions and simplified boundary conditions (steady inflow) and did not allow for synoptic flow forcing such as the influence of meandering winds.

In contrast to these small-scale CFD studies, mesoscale models have been used to predict contaminant dispersion on larger scales. Mesoscale models incorporate heterogeneous land surface conditions and time-dependent synoptic boundary forcing but are typically limited by coarse resolution. Yamada (2000) performed 5-km-resolution mesoscale simulations using a three-dimensional atmospheric modeling system with a Lagrangian random puff dispersion model and compared results with observations from a tracer experiment in the complex terrain of the southwestern United States. Yamada found that the predicted surface concentrations in the simulations agreed with actual measurements within a factor of 2, with a small standard deviation. Koracin et al. (2007) used the fifth-generation Pennsylvania State University–National Center for Atmospheric Research Mesoscale Model (MM5) with Lagrangian particle tracking to investigate dispersion error; model results were within a factor of 3 of each other when using various turbulence schemes. Because these authors aimed to simulate relatively long distance transport and diffusion, they used relatively coarse resolution simulations, with a horizontal grid spacing of 3–5 km. Banta et al. (1996), however, showed that small-scale, topographically forced winds of less than 2 km in extent can have a strong influence on flow over complex terrain and thus can be important in the atmospheric transport of hazardous materials over a relatively short distance. Other examples of the need for higher grid resolution include Chen et al. (2004), who found that increasing the horizontal resolution (to 250-m spacing) improves wind and potential temperature in simulations over the mountains in the Salt Lake City, Utah, area. Chow et al. (2006) found that increased grid resolution (to 150-m spacing) also improved numerical simulation results in the Swiss Alps, though only when land surface conditions were properly initialized. Brulfert et al. (2005) modeled flow in two narrow valleys in the French Alps and also needed spacing as fine as 300 m to represent the complex topography; they used a photochemical model coupled with a mesoscale model to predict air quality in the valleys. High-resolution simulations with time-varying lateral boundary forcing are particularly important for accurately simulating the detailed concentration field resulting from atmospheric releases of toxic materials over complex terrain.

Most simulations of scalar dispersion from a small source have been calculated using Lagrangian particle dispersion models (LPDM) because the horizontal resolution is too coarse to resolve the region near the source with an Eulerian-type scalar diffusion model (ESDM) (Weil et al. 2004; Kim et al. 2005). Nguyen et al. (1997) investigated the performance difference between LPDM and ESDM by simulating releases from two elevated point sources in complex terrain with nonstationary flows. They showed that the LPDM approach is a more natural way of describing the dispersion process for coarse resolutions. There are difficulties in formulating an LPDM, however, because several empirical constants must be adequately chosen and the choices have large effects on the predicted scalar fields (Sada et al. 2006). In contrast, an ESDM does not require empirical constants except for those in the subfilter-scale turbulence closure model, and these are closely linked to the coefficients to model turbulent momentum transport.

In this study, we use high-resolution numerical modeling to simulate the flow and concentration fields accompanying scalar transport and diffusion from a point source near Mount Tsukuba in Japan. Our study uses large-eddy simulation in a mesoscale setting, providing advantages due to the use of robust turbulence models combined with the influence of meandering winds (synoptic flow forcing) and other meteorological forcing such as surface heating and soil moisture. Our simulation tool is the Advanced Regional Prediction System (ARPS)—a nonhydrostatic, compressible LES code written for mesoscale and small-scale atmospheric flows (Xue et al. 2000, 2001, 2003). An Eulerian model of scalar transport and diffusion has been implemented in ARPS to compare scalar concentrations with data collected during field campaigns conducted at Mount Tsukuba in 1989 (Hayashi et al. 1999). Chow et al. (2006) and Weigel et al. (2006, 2007) recently showed that the complex thermal and dynamic structure of flow over complex terrain in the Swiss Alps could be accurately reproduced using ARPS. The current study focuses on scalar transport over complex terrain using horizontal grid resolution as fine as 25 m with up to eight grid nesting levels to incorporate time-dependent meteorological forcing.

The traditional concept of LES is typically associated with simulations in which most of the wavenumber range is resolved. The method of LES, however, does not prohibit its application to high-Reynolds-number flows, in which a large range of wavenumbers may remain unresolved because of grid-resolution limitations (Wyngaard 2004). The coarser grids in our nested domain setup are more typical of mesoscale simulations but can use the same LES equations. The differences between LES and RANS become small when similar space and time resolutions are used; often the only difference in implementation is the formulation of the turbulence model. The LES formulation is preferred for studies of turbulent flows because it is clear which physical features (length scales) are resolvable and which must be modeled. Several challenges associated with scalar transport predictions over complex terrain will be described herein, together with recommendations for numerical formulations that can improve simulation comparisons with observations.

Scalar dispersion is affected not only by mean flow, but also by turbulent scalar fluxes that affect scalar mixing. This means that a focus on scalar transport in addition to mean flow prediction requires greater attention to the choice of numerical simulation parameters. This paper investigates the effects on scalar dispersion of computational mixing and lateral boundary conditions, which have received little attention in the literature—in particular, for high-resolution applications. The importance of the computational mixing scheme was emphasized by Zängl et al. (2004), who found that the effect of the horizontal computational mixing was larger than the effect of increased grid resolution, and they implemented an improved computational mixing scheme in MM5. Their new scheme allowed the simulations to capture the essential features of the observed valley wind. The authors did not suggest appropriate values for the computational mixing coefficient. The choice of the lateral boundary update interval has also not been thoroughly investigated. The standard or usually acceptable update interval for lateral boundaries in mesoscale simulations is a few hours (see Nutter et al. 2004; Chow et al. 2006). Nutter et al. (2004) suggested that the error introduced by aliasing of fields passing through the lateral boundaries becomes larger with larger update intervals, but they found that the error is negligible if the lateral boundary conditions are updated at least once per hour in their 25-km-grid-resolution simulations. They did not examine the effects of the update interval at higher resolutions such as those used in this study.

This work examines the performance of highly resolved large-eddy simulations for scalar dispersion in a mesoscale setting over complex terrain. The experimental conditions and numerical setup are briefly described in the next section. This is followed by an evaluation of the simulated surface velocity and temperature fields in section 3 and the simulated concentration fields in section 4. We then perform sensitivity experiments to evaluate the influence of the computational mixing, the update interval for lateral boundary forcing on the flow, and grid resolution on turbulent statistics and surface concentration predictions in section 5.

2. Numerical simulation setup

ARPS was developed at the Center for Analysis and Prediction of Storms at the University of Oklahoma and is formulated as an LES code that solves the three-dimensional, compressible, nonhydrostatic, filtered equations. ARPS is described in detail by Xue et al. (1995, 2000, 2001, 2003). The major modification we made to the original ARPS code (version 5.2.4) was to add an ESDM. The advection–diffusion equation for a passive scalar is given by
i1558-8432-47-12-3150-e1
where C is the concentration of the scalar, ρ is air density, Dc is the turbulent mixing term, and Qc is the source term.

ARPS solves equations for each velocity component and for the perturbation pressure, potential temperature, and moisture fields. Density is diagnosed from an equation of state. Fourth-order spatial differencing is used for the advection terms in the momentum, potential temperature, and pressure equations, and a multidimensional positive-definite central difference (MPDCD) scheme is used for the advection terms in the scalar transport equations. The MPDCD is based on flux correction/limiting on leapfrog-centered advective fluxes (Lafore et al. 1998). Temporal discretization is performed using a mode-splitting technique to accommodate high-frequency acoustic waves. The large time steps use the leapfrog method. First-order forward–backward explicit time stepping is used for the small time steps, except for terms responsible for vertical acoustic propagation.

The 1.5-order turbulent kinetic energy closure (TKE-1.5) was used for the subfilter-scale turbulence model for all prognostic variables on all domains. The turbulent mixing coefficients for scalars are related to the one for momentum through the turbulent Prandtl number, which is set to 1/3 (Xue et al. 2000). The TKE-1.5 closure is consistent with an LES formulation because it uses a length scale proportional to the filter width (or grid spacing). LES separates resolved and subfilter-scale motions using a physical length scale, the width of the explicit spatial filter. RANS, on the other hand, applies a time average, usually with a very broad averaging period so that only very large scales are resolved. In addition to a turbulence model, computational mixing is applied to remove high-frequency oscillations. A computational mixing coefficient of Cmix = 1.0 × 10−4 was used for all grid levels, as discussed further in section 5.

ARPS is used for simulations of seven tracer gas releases near Mount Tsukuba, where a field campaign was conducted from 13 to 19 November 1989 (Hayashi et al. 1999). Mount Tsukuba is at 877 m MSL elevation and is located in southeastern Japan, about 30 km inland from the Pacific Ocean. Trini Castelli et al. (2006) studied the Mount Tsukuba experiments using the Regional Atmospheric Modeling System mesoscale model with grid nesting down to 250-m horizontal spacing, but focused only on comparisons with surface wind and temperature observations and the effect of different turbulence closure models and did not simulate scalar dispersion. All of our simulations begin at 2100 Japan standard time (JST; =UTC + 9 h) of the day prior to the passive scalar release. The simulation period details are given in Table 1. In each case, the tracer gas was released at a steady rate for 90 min, and ground surface concentration statistics were obtained by averaging over the last 30 min of the release period. The predominant wind direction was from the east in cases I–V and from the west in cases VI and VII. During each case, the atmospheric stability near Mount Tsukuba was neutral or slightly unstable because of mostly cloudy conditions. Tracer gas [sulfur hexafluoride (SF6)] was released at 100-m elevation at site A for cases I–V or at site B for cases VI and VII (see Table 1; Fig. 1c). Sixty-two concentration sensors at about 1.5 m above the ground surface were distributed downwind of the release point. The sensors were moved to different optimal downwind locations for each case.

Details of the ARPS simulation domains are given in Table 2. Six one-way nested grids were used to simulate flow and scalar dispersion around Mount Tsukuba at horizontal resolutions of 45, 15, 5, and 1.7 km and 570 and 190 m (see Fig. 1). Two further grid nesting levels at 65- and 25-m resolution are described later. The vertical resolution was also refined; Table 2 lists the number of grid points below 1000 m for each grid level. The ratio of the coarser horizontal grid spacing to the finer grid was roughly a factor of 3 at each nesting level. The lateral boundaries are placed as far as possible from our region of interest to minimize contamination by errors generated at the lateral boundaries that are magnified when the boundaries cross through complex terrain (Warner et al. 1997). Topography for the 45-km through 570-m grids was obtained using U.S. Geological Survey (USGS) 30-arc-s topography datasets. The 190-m-resolution (and finer) terrain data were extracted from a Japanese Geographical Survey Institute 50-m dataset. The terrain is smoothed near the boundaries of each nested subdomain to match the elevations from the surrounding coarser grid.

To obtain realistic initial and boundary conditions, data from the Japanese 25-yr reanalysis (JRA-25) dataset were used to force ARPS simulations on the coarsest-resolution (45 km) grid. JRA-25 analyses are given at 6-h intervals with 1.125° (approximately 135 km) horizontal spacing and 40 vertical levels (Onogi et al. 2007). The spinup time was 13–17.5 h for each case; using a spinup time of more than 18 h did not significantly affect the results. Update intervals on subsequent nesting levels are between 1 h and 10 s. The effect of these choices is discussed in section 5.

Heterogeneous land surface forcing is provided through the ARPS land surface soil–vegetation model, which solves equations for soil temperature and moisture, as described in detail in Xue et al. (1995, 2001). Two soil layers of depths 0.01 and 0.99 m for the surface and deep soil, respectively, are used by the soil model. ARPS uses 13 soil types (including water and ice) and 14 vegetation classes (following the U.S. Department of Agriculture classifications). Land use, vegetation, and soil-type data are obtained from USGS 30-s global data. Initial soil moisture and sea surface temperature data are provided by the JRA-25 analyses. Initial soil temperature was chosen as an offset from surface air temperature, as described further in section 3.

3. Evaluation of the simulated surface velocity and temperature fields

To evaluate the performance of the numerical simulations in reproducing scalar transport and dispersion, we present a detailed comparison of results from ARPS with observation data in this and the following sections. All results are from the 190-m-resolution grid unless otherwise noted. The simulation nesting procedure, grid resolution, time steps, and land surface forcing were chosen to minimize errors in the flow field. As a first step, therefore, the velocity and temperature fields were examined to determine the accuracy of the underlying flow field that drives the passive scalar transport.

Table 3 shows the root-mean-square errors (RMSE) and mean errors (bias) between the ARPS simulations and surface observations at six sites. They are defined as
i1558-8432-47-12-3150-e2
i1558-8432-47-12-3150-e3
where L is the total number of cases, M is the number of time steps, Ao is the observed variable, and Ap is the model-predicted variable. The data for the error calculation were collected every 30 min in the last 90 min of the simulation (thus giving four time snapshots during the tracer gas release time) as listed in Table 1. For example, the overall bias and RMSE of the wind direction at the release point A are 6.06° and 42.24°, respectively. It is difficult to determine the exact reason for these errors because they are affected by complicated factors (e.g., the presence of complex topography, errors in the reanalysis or land surface data, and the choice of microphysics and turbulence parameterizations). These errors are not large, however, especially when compared with the results of other typical simulations over complex terrain (Zängl et al. 2004; Zhong and Fast 2003; Chow et al. 2006). As discussed further below, the effects of mean wind direction errors on scalar transport, however, are significantly more pronounced, because the mean wind determines the main direction of the scalar plume. Scalar concentration comparisons therefore show great sensitivity to driving flow conditions.

To improve the accuracy of the wind direction, we attempted to apply data assimilation with incremental analysis updating (IAU) to harmonize the wind direction with the observations (Bloom et al. 1996; Brewster 2003a, b). The horizontal velocity and potential temperature from radiosonde observations were assimilated at every hour for the last 3 h at sites AA and BB, but the dispersion results did not improve. The most likely reason for this is errors in the lateral boundary conditions at times between application of the analysis updates. Even if the IAU improved the flow field at a given time, the flow fields are so strongly influenced by boundary conditions from the coarser-resolution domain that the flow soon returns to the nonassimilated values.

We also investigated the sensitivity of temperature errors to land surface initialization, specifically soil temperature. The effects of soil moisture initialization were not considered here (see Chow et al. 2006). The surface soil temperature for all grids was initialized with a positive constant offset from the near-surface air temperature of 0.24 K, which is based on the observed temperature difference at site BB. The choice of the deep soil temperature was more difficult because no detailed dataset exists for deep soil temperature in Japan. We therefore explored the effect of the deep soil temperature on the flow field by using three different values as a positive constant offset from the near-surface temperature of 0, 10, and 15 K. (The deep soil temperature is generally higher than surface soil temperature in winter.) Figure 2 shows the evolution of the near-surface temperature and surface soil temperature at site BB. The near-surface temperature was measured at 5.5 m above ground level in the field campaigns. The ARPS data at the surface are from the lowest model level, which for the horizontal winds and temperature is at Δzmin/2 (10 m for the 190-m grid). During the night, the soil surface cools and heat is transferred from the deep soil to the surface. In the zero offset case (ΔT = 0 K), the surface soil temperature dramatically decreases with time because the deep soil temperature cannot adequately compensate for the heat loss at the surface. The decrease causes the surface temperature to decrease at night, resulting in a delay of the temperature rise in the morning. The near-surface temperature differences in the cases with ΔT = 10 or 15 K are small, but the soil temperature in ΔT = 15 K is too high during the night. Based on these comparisons, a temperature offset of ΔT = 10 K was chosen as an appropriate value for case III. For the other cases, a constant offset from the near-surface temperature ranging from 5 to 10 K was selected according to a similar comparison procedure. The soil temperature setting did not strongly affect wind velocity and direction as compared with the differences seen in near-surface temperature.

4. Evaluation of the simulated concentration fields

Figure 3 shows contours of ground concentrations from the observations and from ARPS for cases I and III. Concentrations are normalized by the source strength Q. In case III, the ground concentration distribution in the ARPS is in good agreement with that in the observations, but in case I the simulated concentration plume fails to overlap with the observed plume. This is caused by wind direction errors at site A of RMSE 42.24° and a bias of 6.06°, as shown in Table 3. As noted above, these RMSE and bias errors are not large relative to other typical simulation results, but the effect on the simulated concentration fields is very large. Direct comparisons of concentration values at the concentration sensor sites with ARPS results would in some cases lead to 100% error. Instead of a direct point-by-point comparison of concentration values, the arc maximum concentration is used to evaluate the ARPS model performance in this section. The arc maximum concentration is the maximum concentration observed along an arc of sensors selected at various distances from the source (Olesen 2000). The use of arc maximum concentration for model evaluation is fairly standard for evaluation of dispersion models and field experiments.

Figures 4 and 5 show the arc maximum ground concentrations and the scalar plume orientation defined as the position of the maximum ground concentration averaged for 30 min from release points AA for cases I–V or BB for cases VI and VII. During the field campaign, the sensors were not actually located along arc lines, so sensors were selected along prescribed arcs (centered on the release point). Sensors were selected at 400-m intervals, with a margin of error of 200 m. The scalar statistics in Figs. 4, 5 were averaged for 30 min. In case I, ARPS simulates the arc maximum concentration relatively well even though the simulated plume spreads south of Mount Tsukuba while the observed plume spreads north of the mountain (see Fig. 3a). In cases II and III, the ARPS concentrations agree well with the observations because the scalar plume orientation is accurate. The main reason for good agreement in cases I–III is that the horizontal velocity and turbulent fluctuations are in good agreement with observations. Figure 6 shows the vertical distributions of horizontal velocity, wind direction, and the horizontal and vertical turbulent fluctuations at site AA for cases I–V and site BB for cases VI and VII. The turbulent fluctuations are defined as the root-mean-square values of the velocity fluctuations, which are the deviations from the time-averaged velocity. The velocity and turbulent statistics in Fig. 6 were averaged for 10 min as shown in Table 1. In cases IV, VI, and VII, ARPS overpredicts the concentration in the vicinity of the release points. This is because the computational mixing adds artificial diffusion, resulting in a wider spread of the scalar, especially with the low wind speeds present in these cases. With low wind speeds, advection effects are negligible and the plume diffuses quickly in the vertical direction, leading to high concentrations (relative to observations) at the ground near the elevated release point. In case V, the ARPS concentrations agree well with the observations, though the simulated plume spreads in a different direction (see Fig. 5e). The reason for this disagreement can unfortunately not be evaluated because of the lack of observation data. The RMSE and bias of the mean scalar plume orientation (calculated using all seven cases) are 63.22° and −37.5°, which is almost the same deviation observed in the simulated and observed wind directions, as shown in Table 3. Thus, if the difference in simulated and observed wind directions is large, the scalar cannot be transported in the proper direction.

To evaluate the output of a model with observations quantitatively, Hanna et al. (1991, 1993) recommend the use of the following statistical performance measures: the fractional bias (FB), the geometric mean bias (MG), the normalized mean-square error (NMSE), the geometric variance (VG), and the fraction of predictions within a factor of 2 of observations (FAC2). They are defined as
i1558-8432-47-12-3150-e4
i1558-8432-47-12-3150-e5
i1558-8432-47-12-3150-e6
i1558-8432-47-12-3150-e7
i1558-8432-47-12-3150-e8
where L is the total number of cases, Nj is the number of selected sensors for each case, Co is the observed concentration, and Cp is the model-predicted concentration. The selected sensor locations are those from the arc maximum concentration from each case. A perfect model would have MG, VG, and FAC2 equal to 1.0 and FB and NMSE equal to 0.0. The FB and NMSE may be overly influenced by infrequently occurring high observed or model-predicted concentrations, whereas MG and VG may provide a more balanced treatment of extreme high and low values.

Chang and Hanna (2004) suggest that a good model would be expected to have about 50% of the predictions within a factor of 2 of the observations (i.e., FAC2 > 0.5), a relative mean bias within ±30% of the mean (i.e., −0.3 < FB < 0.3 or 0.7 < MG < 1.3), and a relative scatter of about a factor of 2 or 3 of the mean (i.e., NMSE < 4 or VG < 1.6). Note that these guidelines are based on ensemble concentrations that are collected from several realizations in a dataset, thus smoothing out the observed and simulated concentration values. In contrast, we compare time-averaged concentrations at selected sensor locations for each of the seven cases, making our statistics more sensitive to model errors. In our simulations, we find FAC2 = 0.51, FB = −0.2, MG = 0.98, NMSE = 1.184, and VG = 13.51. The main factors in the errors are wind velocity and direction bias, gaps in sensor spacing, and the difference in receptor position and height between the model and observations. The VG has a large value because of the overestimate of the concentrations near the release point for cases IV and VI. However, the values for all quantitative measures except the VG are within acceptable error bounds. Thus, based on comparing the results of the ARPS with observations of arc maximum concentration, the simulations presented here reproduce the observed ground concentration within acceptable error bounds.

5. Concentration sensitivity tests

The preceding error analysis confirms the sensitivity of simulated concentration fields to errors in simulated mean wind direction. These errors are largely due to errors in lateral boundary forcing. Attempts to improve the representation of the velocity field included data assimilation and land surface initialization options, as described in section 3. The mean velocity field error statistics are well within standard acceptable ranges for mesoscale simulations, but the consequences of these wind errors on the simulated scalar concentration fields can be very large, as discussed in section 4. This section evaluates the effects of chosen numerical schemes on the concentration predictions by investigating parameters that affect turbulence and hence scalar mixing. We specifically examine the effects of computational mixing, the update intervals used for lateral boundary forcing, and grid resolution, using case III as our test case.

a. Computational mixing

Computational mixing is used to damp high-frequency motions that can build up because of nonlinear interactions at small scales. This artificial mixing supplements the turbulence model at the highest frequencies to limit unphysical oscillations in the numerical solution. Because large values of computational mixing tend to relax the instantaneous velocity toward the base-state field, the computational mixing coefficients should be chosen to be as small as possible. In general, second- or fourth-order computational mixing is used, with fourth-order mixing preferred because it damps out short-wavelength noise more selectively than does second-order mixing. In mesoscale simulations, large computational mixing coefficients may not dramatically change the simulated flow fields because the computational mixing removes only the very small scale noise. In high-resolution simulations, however, the small-scale motions, which the computational mixing might remove, may be very important because they are part of the resolved turbulent flow field. The choice of computational mixing may therefore strongly affect the velocity and scalar fields.

In ARPS, the computational mixing term is added to the right-hand side of the governing equations as
i1558-8432-47-12-3150-e9
where ϕ′ = ϕ is the perturbation of ϕ from its base- state value , and the coordinates here are in computational space. Here, Cmix is the computational mixing coefficient and is chosen to be the same for the horizontal and vertical mixing terms. The base-state value is assumed to be horizontally homogeneous, time invariant, and hydrostatically balanced. Computational mixing is applied to all computed variables.

To investigate the sensitivity of the results to the computational coefficient, three different computational mixing coefficients of 1.0 × 10−4, 5.0 × 10−4, and 1.0 × 10−3 are used on the 190-m grid for case III. Note that coefficient values of less than 1.0 × 10−4 result in oscillations in the flow field.

Figures 7 and 8 show the vertical distributions of horizontal wind direction and horizontal and vertical turbulent fluctuations at sites AA and BB. Sites AA and BB are located on the windward and leeward sides of the mountain ridge, respectively. Observation values and ARPS results are averaged for 10 min (1550–1600 15 November). The computational mixing does not affect the time-averaged velocity and wind direction strongly, but it affects the horizontal and vertical turbulent fluctuations. With smaller values of the computational mixing coefficient, the turbulent fluctuations become closer to the observations.

Figure 9 shows the arc maximum ground concentration averaged for 30 min (1530–1600 15 November). As the computational mixing coefficient decreases, the peak of the concentration profile shifts upwind, giving better agreement of the results with the observations. This change of the ground concentration is attributed to the change in turbulent fluctuations. As the computational mixing increases, the vertical turbulent fluctuations became smaller (as shown in Fig. 8) and the tracer gas does not reach the ground early enough from its elevated release point. Note that the computational mixing causes the opposite effect under low wind speeds as discussed in section 4. The computational mixing acts to decrease vertical turbulent fluctuations but also acts to spread scalars by artificial diffusion. Under low wind speeds, the artificial scalar diffusion dominates because of the smaller advection, leading to high ground concentrations near the source. In any case, we conclude that, although it does not greatly affect mean velocity field quantities, the computational mixing coefficient is a very important factor for predicting scalar dispersion.

b. Update intervals for the lateral boundary forcing

In one-way grid nesting procedures such as the one used by ARPS, the update interval for the lateral boundary conditions must be specified. In two-way nesting, the nested finer domain and the outer coarser domain interact at every time step of the outer coarse-grid integration. Existing two-way nesting schemes (such as those in the Weather Research and Forecasting Model and MM5), however, do not allow the vertical resolution to change between grid nesting levels. This means that high-resolution grids cannot be used in the vertical direction when two-way nesting is applied, because the vertical levels must be suitable for all the nesting levels. The one-way nesting technique in ARPS allows adjustments in vertical resolution between grids, a very important feature for large-eddy simulations where the grid aspect ratio should be kept close to unity. In ARPS, the lateral boundary conditions for the nested finer domain are given by the stored coarser-domain output. Because larger data storage capacity is required when the update interval is smaller, a larger update interval is usually preferred to conserve computational resources (storage and input/output overhead costs). The optimal update interval has not been thoroughly investigated, because in the past the interval choice was highly constrained by practical computing choices. The standard or usually acceptable update interval for lateral boundaries in mesoscale simulations is a few hours (e.g., Nutter et al. 2004), but we choose to pass finer-scale perturbations from the coarser- resolution simulation into the finer-resolution simulation through the lateral boundaries. Thus, we use hourly update intervals for the 45-km grid; 10-min intervals for the 15-, 5-, and 1.7-km grids; and 5-min intervals for the 570- and 190-m grids. Note that applying updates at hourly intervals for all grids did not change any time-averaged quantities except scalar diffusion and led to worse results for turbulent fluctuations and ground concentration as discussed later. Output data from the coarser grids were interpolated to generate initial and boundary condition files for subsequent nested-grid simulations. The lateral boundary forcing is linearly interpolated at intermediate times between update intervals.

To investigate the effect of the lateral boundary forcing update interval ΔTb, four different update intervals of 10 s, 60 s, 5 min, and 30 min are implemented on the sixth grid level for case III. The update intervals were changed only during the last 3 h (1300–1600 15 November) of the simulation; other time periods (2100 14 November–1300 15 November) remain at 5-min intervals to conserve data storage space in the computer. The minimum update interval was set to be 10 s because it corresponds to a spatial wave scale of about 100 m (with a wind velocity of about 10 m s−1), which cannot be generated on the coarser domain (fifth region). The velocity and length scales that are fed into the finer domain at the boundaries will be affected by nonlinear interactions to produce finer scales as allowed by the finer resolution and triggered by the finer topography. Thus, we expect a change in the represented length scales at various distances from the lateral boundary.

Figures 10 and 11 show the vertical distributions of horizontal wind direction and horizontal and vertical turbulent fluctuations at sites AA and BB. The time-averaged horizontal wind speeds show some small differences below 200 m, but the wind directions are unchanged. The horizontal and vertical turbulent fluctuations, however, generally became larger with smaller update interval. The effect on the arc maximum ground concentrations is shown in Fig. 12, where it is clear that the results agree best with the observations when ΔTb = 10 s.

To investigate the effect of the turbulence on the simulated ground concentration, the energy spectra at site AA, at site BB, and on the boundary of the sixth region (190-m grid) are shown in Fig. 13. The spectra are calculated using data at 10-s intervals at the chosen observation sites AA and BB or at a single point on the eastern boundary. All data were extracted at 100 m above ground, which matches the tracer-gas release height. The larger update intervals do not allow high-frequency motions except high-frequency noise ( f > about 1.5 × 10−2 Hz) to be passed at the domain boundary (see Fig. 13a). The high-frequency noise appears as a result of aliasing generated by linear interpolation between update intervals. The larger update intervals also damp the low-frequency motions at the boundary because the larger scales are smoothed as they pass through the boundary. The reduction of the low frequencies at the boundary of the nested coarser domain generally results in a decrease of the turbulent fluctuations in the interior of the domain, as shown near the release point of the tracer gas (site AA; see Fig. 13b). The effect of the larger update interval does not always reduce larger turbulent motions, because the energy spectrum at ΔTb = 30 min is larger than those at ΔTb = 5 min at site AA; this is due to the change in the mean flow below 200-m elevation as shown in Fig. 10a. Thus, high-frequency motions can be generated locally, but they are also generally affected by the boundary update interval. Far from the upwind (eastern) lateral boundary at site BB, however, the difference between the energy spectra is very small (see Fig. 13c) because the turbulent motions on the lee side of the mountain ridge at site BB are strongly affected by the mountain ridge and thus are not as sensitive to upwind conditions. As seen in Fig. 12, the increase of the turbulent fluctuations shifts the peak of the concentration curves upwind, and the effect is almost the same as the computational mixing effect discussed in section 4a. Thus, the update interval does not strongly affect the time-averaged velocity quantities but is very important for estimating the scalar dispersion emitted from point sources.

c. Grid resolution

Fine grid resolution can be particularly important for simulating the scalar dispersion emitted from point sources. To demonstrate the effect of the grid resolution on the scalar dispersion, eight one-way nested grids were used as listed in Table 2 to simulate case III. These include two additional grid refinement levels from the six described previously. The sixth grid level in this nesting sequence covers a much larger domain. The sixth (6-H), seventh (7-H), and eighth regions (8-H) use horizontal resolutions of 190, 65, and 25 m, respectively.

Figure 14 shows comparisons of the horizontal and vertical turbulent fluctuations from the 190-, 65-, and 25-m grid resolutions. The higher-resolution simulations slightly increase the vertical turbulent fluctuations as expected, but the differences are not large. The variation in horizontal turbulent fluctuations is small. This is most likely due to the fact that turbulent fluctuations are dominated by motions that are already well resolved in the 190-m grid resolution simulation. The arc maximum ground concentration, however, becomes slightly larger with finer grid resolution as shown in Fig. 15 because there is better resolution and hence less smoothing of the concentration field—in particular, near the source. The present comparison of the concentration becomes somewhat worse, but the difference is very small and the error is within acceptable error bounds as discussed in section 4. Higher grid resolution has the advantage of capturing smaller eddies and concentration fluctuations, but the effect of grids finer than 190-m spacing is found to be small as compared with the improvements found by changing the computational mixing and the update interval for the boundaries. It is possible that the use of two-way nesting, increased vertical resolution, improved lateral and surface boundary conditions (e.g., land use), or data assimilation is needed to appreciate fully the effects of very high horizontal spacing.

6. Summary and conclusions

The ARPS large-eddy simulation code has been applied to simulate scalar transport and dispersion from point source releases during a field campaign conducted near Mount Tsukuba in Japan. We have demonstrated the ability to apply LES in a mesoscale setting using up to eight grid nesting levels from horizontal resolutions of 45 km down to as fine as 25 m. Several challenges associated with scalar transport predictions over complex terrain were described, together with recommendations for numerical formulations that can improve simulation comparisons with observations. The effects of computational mixing, the update interval for lateral boundary forcing on the flow, and higher grid resolution on scalar field predictions were investigated. The four major findings can be summarized as follows:

  1. It is difficult for the high-resolution LES (ARPS) to predict exactly the ground concentration from a small source by direct point by point comparison because the mesoscale wind typically contains a wind direction bias of a few dozen degrees. Comparisons of simulation results with observations of arc maximum concentrations, however, indicate that the simulations can nevertheless predict the ground concentration within acceptable error bounds.
  2. Changing the update intervals for the lateral boundaries does not affect time-averaged quantities (wind, wind direction, etc.) but strongly affects the scalar transport. As the update interval is set to be smaller, the model accuracy is improved.
  3. The computational mixing coefficient must be set to as small a value as possible because it significantly affects scalar dispersion. Some computational mixing, however, is required to prevent the occurrence of artificial high-frequency motions in the simulations.
  4. The representation of the concentration field improves at high grid resolutions of as fine as 190-m spacing in the horizontal plane. With finer resolutions (up to 25 m) the results do not improve, but the differences are small and still within acceptable error bounds. When compared with the effects of computational mixing and lateral boundary updates, however, the increased computational costs of these extrafine simulations do not seem warranted at this time.

LES applied in a mesoscale setting has the ability to predict scalar transport at high resolution while considering unsteady flow boundary conditions (such as meandering winds) and heterogeneous surface conditions. The simulations do not require prespecified wind directions, as used in small-scale CFD applications, but do take advantage of the improved representation of turbulent fluxes provided by LES at high grid resolutions. Our approach, therefore, brings together elements of both the standard CFD and mesoscale approaches to create a general modeling tool for predicting contaminant dispersion. The results, however, are very sensitive to errors in mean wind direction (provided by the lateral boundary conditions), which determines the main direction of the scalar plume. The simulations presented here perform very well in estimations of arc maximum concentrations and are able to take advantage of high resolution to provide accurate estimates of concentration fluctuations. Errors in the exact location of high-concentration regions may be acceptable in certain pollution regulation applications. On the other hand, if contamination areas from a toxic gas release need to be identified for emergency-response purposes, these simulations would not provide satisfactory predictions. Thus, although the simulations described here are a first step toward combining the fidelity of high-resolution CFD approaches with a mesoscale setting, much further work is needed to improve predictions of scalar dispersion over complex terrain under general atmospheric conditions.

Acknowledgments

The authors thank Megan Daniels and Ryo Onishi for many useful discussions. The datasets used for this study are provided from the cooperative research project of the JRA-25 long-term reanalysis by the Japan Meteorological Agency (JMA) and Central Research Institute of Electric Power Industry (CRIEPI). The first author was supported by a fellowship from CRIEPI while in residence at the University of California, Berkeley. The second author acknowledges support from NSF Grant ATM-0645784 (Physical Meteorology Program: S. Nelson, Program Director).

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Fig. 1.
Fig. 1.

The elevation contours (m MSL) for (a) the 45-km grid, (b) the 5-km grid, and (c) the 190-m grid. The locations of surface stations defined in Table 3 are shown in (c).

Citation: Journal of Applied Meteorology and Climatology 47, 12; 10.1175/2008JAMC1941.1

Fig. 2.
Fig. 2.

Surface data time series comparisons at site BB for (a) near-surface temperature and (b) surface soil temperature: observations (filled circles), ΔT = 0 K (open circles), ΔT = 10 K (open squares), and ΔT = 15 K (open triangles).

Citation: Journal of Applied Meteorology and Climatology 47, 12; 10.1175/2008JAMC1941.1

Fig. 3.
Fig. 3.

Contour of ground concentration for (a) case I and (b) case III, with (left) field observations and (right) ARPS results. Sensor and source locations are shown with black dots and black triangles, respectively.

Citation: Journal of Applied Meteorology and Climatology 47, 12; 10.1175/2008JAMC1941.1

Fig. 4.
Fig. 4.

Arc maximum concentration for cases I–VII: observa-tions (filled circles) and ARPS results (solid line).

Citation: Journal of Applied Meteorology and Climatology 47, 12; 10.1175/2008JAMC1941.1

Fig. 5.
Fig. 5.

Scalar dispersion direction for case I–VII: observations (filled circles) and ARPS results (solid line).

Citation: Journal of Applied Meteorology and Climatology 47, 12; 10.1175/2008JAMC1941.1

Fig. 6.
Fig. 6.

Vertical distributions of horizontal velocity, wind direction, and the horizontal and vertical turbulent fluctuations at the tracer release point (site AA or site BB): observations (filled circles) and ARPS (solid line). No observation data are available for Case V.

Citation: Journal of Applied Meteorology and Climatology 47, 12; 10.1175/2008JAMC1941.1

Fig. 7.
Fig. 7.

Vertical distributions of the horizontal velocity and wind direction at (a) site AA and (b) site BB for case III: observations (filled circles), Cmix = 1.0 × 10−4 (solid line), Cmix = 5.0 × 10−4 (dashed line), and Cmix = 1.0 × 10−3 (dotted line).

Citation: Journal of Applied Meteorology and Climatology 47, 12; 10.1175/2008JAMC1941.1

Fig. 8.
Fig. 8.

Vertical distributions of the horizontal and vertical turbulent fluctuations at (a) site AA and (b) site BB for case III: observations (filled circles), Cmix = 1.0 × 10−4 (solid line), Cmix = 5.0 × 10−4 (dashed line), and Cmix = 1.0 × 10−3 (dotted line).

Citation: Journal of Applied Meteorology and Climatology 47, 12; 10.1175/2008JAMC1941.1

Fig. 9.
Fig. 9.

Arc maximum ground concentration for case III: Cmix = 1.0 × 10−4 (solid line), Cmix = 5.0 × 10−4 (dashed line), and Cmix = 1.0 × 10−3 (dotted line).

Citation: Journal of Applied Meteorology and Climatology 47, 12; 10.1175/2008JAMC1941.1

Fig. 10.
Fig. 10.

Vertical distributions of the horizontal velocity and wind direction at (a) site AA and (b) site BB for case III: observations (filled circles), ΔTb = 10 s (solid line), ΔTb = 60 s (dashed line), ΔTb = 5 min (dotted line), and ΔTb = 30 min (dash–dotted line).

Citation: Journal of Applied Meteorology and Climatology 47, 12; 10.1175/2008JAMC1941.1

Fig. 11.
Fig. 11.

Vertical distributions of the horizontal and vertical turbulent fluctuations at (a) site AA and (b) site BB for Case III: observations (filled circles), ΔTb = 10 s (solid line), ΔTb = 60 s (dashed line), ΔTb = 5 min (dotted line), and ΔTb = 30 min (dash–dotted line).

Citation: Journal of Applied Meteorology and Climatology 47, 12; 10.1175/2008JAMC1941.1

Fig. 12.
Fig. 12.

Arc maximum ground concentration for case III: observations (filled circles), ΔTb = 10 s (solid line), ΔTb = 60 s (dashed line), ΔTb = 5 min (dotted line), ΔTb = 30 min (dash–dotted line).

Citation: Journal of Applied Meteorology and Climatology 47, 12; 10.1175/2008JAMC1941.1

Fig. 13.
Fig. 13.

Energy spectra at (a) boundary, (b) site AA, and (c) site BB for case III: ΔTb = 10 s (solid line), ΔTb = 60 s (dashed line), ΔTb = 5 min (dotted line), and ΔTb = 30 min (dash–dotted line).

Citation: Journal of Applied Meteorology and Climatology 47, 12; 10.1175/2008JAMC1941.1

Fig. 14.
Fig. 14.

Vertical distributions of the horizontal and vertical turbulent fluctuations at (a) site AA and (b) site BB for case III: observations (filled circles), 190-m grid resolution (solid line), 65-m grid resolution (dashed line), and 25-m grid resolution (dotted line).

Citation: Journal of Applied Meteorology and Climatology 47, 12; 10.1175/2008JAMC1941.1

Fig. 15.
Fig. 15.

Arc maximum concentration for case III: observations (filled circles), 190-m grid resolution (solid line), 65-m grid resolution (dashed line), and 25-m grid resolution (dotted line).

Citation: Journal of Applied Meteorology and Climatology 47, 12; 10.1175/2008JAMC1941.1

Table 1.

Model simulation period.

Table 1.
Table 2.

Nested grid configurations with dimensions.

Table 2.
Table 3.

Root-mean-square errors and mean errors (bias) for wind speed, wind direction, and temperature.

Table 3.
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